Handbook of Heterogeneous Catalysis

Edited by,G. Ertl, H. Knozinger, J. Weitkamc

Copyright 0VCH Verlagsgesellschaft mbH.1997

5 Elementary Steps and Mechanisms

was generally believed that more or less unspecified

5.1 Chemisorption long-range forces - we would today call this phys-
isorption - draw gases towards a solid. Langmuir,
5.2 Microkinetics shortly after the introduction of the concept of an or-
dered lattice for the arrangement of the atomic con-
5.3 Factors Influencing Catalytic Action stituents of a bulk solid by von Laue [4], considered an
arrangement of atoms at the surface, a surface lattice,
5.4 Organic Reaction Mechanisms that defines a specific density of adsorption sites. Atoms
from a gas phase, for example, striking the surface may
5.5 Computer Simulation either bounce back into the gas phase or establish a
bond to one of these sites. This process is equivalent to
the formation of a surface chemical bond and was
termed chemisorption [5-71. Chemisorption lowers the
free energy of the closed system containing the un-
covered, “clean” surface and atoms or molecules from
5.1 Chemisorption the gas phase. This lowering in energy can be measured
via calorimetry or - less well defined - by a Clausius-
Clapeyron analysis of isostere data. It was therefore
5.1.1 Principles of Chemisorption tempting to differentiate chemisorption with respect to
physisorption via the energy that is deliberated in bond
H.-J. FREUND formation [l]. Such a definition involves a limiting en-
ergy which separates chemisorption and physisorption
regimes. It was put in the neighborhood of 40 kJ mol-’
5.1.1.1 Introduction El]. Obviously, such a definition is rather artificial, and
today one generally disregards this kind of differen-
The term chemisorption was coined in order to classify tiation solely on the basis of the enthalpy of formation.
the interaction between a particle in the gas phase and The accepted definition of chemisorption today is in-
a solid surface, i.e. the result of the adsorption process dependent of thermochemical data and rests on the
[l]. If the interaction leads to the formation of a concept of a short-range chemical bond, which only
chemical bond the adsorbate formed is called a chem- forms when there is direct intermingling of the sub-
isorbate. Where chemical bond formation is not im- strate and the adsorbate charge densities. In order
portant the process is classified as physisorption. There then to differentiate between chemisorption and phys-
are several conceptual problems with such a differ- isorption one has to understand the electronic structure
entiation which we briefly address in the following, and of the system [6, 81. Experimentally, this means that we
which indicate that a more detailed look at the entire cannot rest the definition on a single measurement of
process of adsorbate formation is needed before a reli- the heat of adsorption but rather on an as complete as
able classification may be carried out. In fact, as it possible spectroscopical characterization of the surface
turns out, for a conclusive classification one would need interacting with the adsorbate in comparison with the
the full theoretical and experimental understanding of same measurements of the separated systems.
the system under investigation. Such an approach must The interaction between say a gas phase, containing
include the static aspects, i.e. the energies involved, as molecules AB, and a surface is discussed by consider-
well as the dynamic aspects, i.e. the processes involved ing various aspects of the process of AB-surface bond
in the formation of the adsorptive interactions. formation. We cover the dynamic aspects connected
Irving Langmuir in 1916 introduced and investigated with the sticking of AB such as its dependence on the
the idea that there can exist strong, short-range forces
between adsorbates and a substrate [2, 31. Previously, it References see page 938
912 5 Elementary Steps and Mechanisms

population of internal and external degrees of freedom which has the dimension of a two-dimensional pres-
of AB in the collision, mobility on the surface, i.e. sur- sure. This leads to the final equation
face diffusion etc., and the energetics, which will be the
starting point, all as a function of the surface coverage.
dGS= -S, d T + Vsd P + VdA + 11, dn,. (6)
We shall discuss associative versus dissociative chem- This equation refers to a system where the adsorbate
isorption and its dependences on surface structure. resides on a truly inert substrate. In other words, eq 6
Consideration of coadsorption and cooperativity in can only rigorously be applied to weakly interacting
the adsorption process is as important as invoking the physisorbate systems. For chemisorbates this equation
structure of the adsorbate, as well as the restructuring is not strictly applicable because the thermodynamic
of the surface as it interacts with an adsorbate. parameters of adsorbate and adsorbent cannot be
separated.
Bearing this restriction in mind, and assuming that
5.1.1.2 Thermodynamics and Energetics the adsorbate phase is in equilibrium with the gas
phase, a Clausius-Clapeyron analysis yields
As this point it is important to differentiate between
macroscopic and microscopic surface phenomena. Sur-
face phenomena can be treated macroscopically by
chemical thermodynamics, in which atomic concepts where we have changed to molar quantities s, u, and
are not neccessary. Accordingly, the thermodynamic the enthalpy h. The slope of a semilogarithmic plot of
relationships can be derived on the basis of pressure, the equilibrium pressure versus the inverse temperature
volume, surface area, composition, and temperature, at constant v, yields the adsorption enthalpy, Ahads, re-
which can be measured in a straightforward manner. leased upon adsorption of one mole of gas. The prob-
Historically, therefore, the thermodynamic approach lem, of course, arises because the surface tension is
was pursued first. Before discussing the atomic aspects hard to determine in general. However, the problem
of the energy content of an adsorbate phase we shall may be circumvented by considering the so-called sur-
briefly summarize the important thermodynamic as- face coverage 0 instead:
pects noting, however, that this cannot be a com-
prehensive treatment. For the latter we refer to the
literature [l, 7, 9-12].
Consider an adsorbate phase consisting of n, moles and resorting to partial molar quantities, e.g.

(")
of a nonvolatile adsorbent (surface) and n, moles of an
adsorbate (gas phase). They are assigned internal en- 6, = (9)
ergy U, entropy S and volume V. The surface A of the T,P,n,
adsorbent is assumed to be proportional to the ad-
Then, a similar Clausius-Clapeyron analysis leads to
sorbent volume. The Gibbs fundamental equation for
the full system is then
dG=-SdT+ VdP+padna+p,dns (1)
For the pure adsorbent, where qst is the isosteric heat of adsorption. This
quantity can be measured quite easily because constant
dG" = -Sa d T + Vad P + dna (2) coverage is not too difficult to establish experimentally.
Consequently, for the interacting adsorbate-adsorbent However, qst represents the difference between molar
system, the difference dGS= dG - dG" gives enthaply in the gas phase and partial molar enthalpy in
the adsorbed phase, a quantity not easily connected to
dGS= -Ss d T + Vs d P + @ dna + pSdns (3) microscopic considerations.
In order to directly see how the isosteric heat of ad-
where S, = S - Sa, V, = V - Va, and @ = pa - pz. sorption is measured, eq 10 is written in the form
Using the above mentioned proportionality between
adsorbent volume and adsorbent surface, -
dP = ( 2 ) d T
P
@dna=f@dA (4)
and integrated for a reasonably small pressure and
where f is a proportionality factor, the surface tension temperature interval so that we can assume the isos-
v, is given by teric heat to be constant. This yields
 5.1 Chemisorption 9 13

161
105 1’10
-
lo2
[K-’]
iis ‘b ’ 0:2 ’ O’L
Xe coverage 0
’ 0’6 18

Figure 1. Determination of the isosteric heat of adsorpton from

the measurement of adsorption isotherms for the system Xe/
Ni(100) [13].

Figure 2. Schematic drawing of the spherical calorimeter [ 191.

for two pairs of temperatures and pressures that pro-
duce the same surface coverage. For true equilibrium
conditions, a straight line with negative slope should be assumption of truly separable subsystems. Therefore,
obtained for the semilogarithmic plot, which in turn for such systems it is more appropriate to resort to a
yields the isosteric heat of adsorption. Repeating this direct calorimetric measurement of the adsorption en-
procedure for various coverages allows the coverage thalpy. Until very recently, it has not been possible to
dependence of the heat of adsorption to be determined. undertake such measurements for thin-film systems [l,
It is obvious that the isosteric heat is a differential 14-19]. The reason was that the increase in temper-
quantity, in contrast to the equilibrium heat of ad- ature of the calorimeter depends on the heat capacity
sorption. Both are, of course, isothermal quantities. of the system and the absolute number of adsorbed
From the differential heats of adsorption the integral particles. The most complete set of data for such thin-
heat of adsorption can be obtained as film systems has been reported by Wedler and co-

e1ntegr = 1
ns
qst dns (13)
workers [l, 201. They used the so-called “spherical cal-
orimeter” shown in Fig. 2 [17]. Briefly, the calorimeter
sphere is located inside an ultrahigh-vacuum glass re-
In the following we present an example of isosteric cipient and temperatures change of less than lop5K are
heat determination [13]. Figure 1 shows, in the upper registered with a thermometer connected to the calo-
panel, a set of four isotherms for the physisorption rimeter sphere. The metal film is evaporated onto the
system Xe/Ni( 100). The second panel contains the data sphere and gas is admitted. The change in temperature
set in the upper panel as a plot of lnppc, versus recip- measured by the thermometer surrounding the calo-
rocal temperature for various values of Ox,. From the rimeter sphere upon gas exposure is plotted versus time
shape of the individual straight lines the isosteric heat in Fig. 3. The heat of adsorption is determined from
has been determined and plotted in the third panel as a the integral of the T versus r curve. The example here is
function of Oxe.From the plot we see that the isosteric the adsorption of H2 onto a Pd film [21]. Converting
heat slowly varies with temperature, the decrease in- the temperature-time curve into a heat of adsorption
dicating repulsive interactions. yields 88 kJmol-I [21].
As mentioned above, the application of an isosteric
heat analysis to a chemisorption system is rather prob-
lematic, because inherently the analysis starts from the References see page 938
9 14 5 Elementary Steps and Mechanisms

entropy of adsorption, which is the quotient of the

reversibly exchanged heat and the temperature, may be
calculated from the equilibrium heat of adsorption, if
3- H,/Pd lT.273 K) the surface tension is known, or from the isosteric heat
of adsorption. Prerequisite is the knowledge of the
c
Y corresponding equilibrium gas pressure. Table 2 col-
-a
1 2-
52
l-
lects typical values for the entropy of adsorption of
several adsorbate systems.
Y
The number of values available is much smaller than
1-
for the enthalpies of adsorption. The interpretation of
entropies is considerably more involved than the inter-
O M pretation of enthalpies. Often the observed values and,
in particular, the coverage dependences, cannot be rec-
0 1 2 3 i 5 6 7 0 onciled on the basis of theoretical predictions. It ap-
I t / minl pears that the predictions as to how the various degrees
Figure 3. Temperature-time curve of a calorimetric measure- of freedom of the adsorbate contribute are not accurate
ment for the system HZ/Pd [21]. enough to date. However, in most cases large entropy
values are found when the mobility of the adsorbate
was expected or known (from other methods) to be
In Table 1 are assembled the heats of adsorption for large.
various absorbate systems on different substrates de- However, the most popular method by which to de-
termined via isosteric heat measurement as well as cal- duce the heat of adsorption of an adsorbate system is
orimetric measurements. In some cases the heat of ad- thermal desorption spectrometry (TDS) [53-571. A
sorption for one system has been measured using schematic setup for a TDS measurement is shown in
different techniques. This allows an estimation of the Fig. 5 [58]. The sample is heated resistively and the
error involved in using those values based on different temperature is monitored by a thermocouple. If the
measurements. It is clear that the value for CO ad- sample is a single crystal it responds rather rapidly to
sorption on Fe, for example, is considerably higher heating so that relatively high heating rates may be
than values for other CO-adsorbate systems. In order used. The concentration of desorbing species is mea-
to judge this, it must be understood that at room tem- sured with a quadrupole mass spectrometer (QMS).
perature CO partly dissociates on polycrystalline Fe Pumping capacity is important in thermal desorption,
which contributes to the observed calorimetric value. because only if it is high enough, readsorption of the
This is a useful reminder that consecutive processes desorbing species back onto the surface is excluded. If
have to be considered in calorimetric measurements. the pumping speed is infinitely high we can ignore
King and co-workers have recently extended calori- readsorption and the change in adsorbate coverage per
metric measurements to single-crystal surfaces by ap- unit time; a measure for the desorption rate ( r d e s ) , is
plying molecular beam techniques in combination with given by the Wigner-Polanyi equation [7, 591:
IR radiation emission measurements (Fig. 4) [23, 38,
46-48]. There are three important parts of the experi-
ment. First, there is a molecular beam source to pro-
vide accurate determination of coverage. Secondly, the
sample consists of a unsupported single-crystal thin
film to reduce the thermal mass to a minimum. Finally,
= v(0)O”exp{ - w} (14)

an infrared detector is used to sense the heat radiated +

where T = To Pt. This is the basis for the analysis of
as the gas adsorbs. In order to reduce white noise thermal desorption spectra.
experiments are performed using a pulsed molecular Figure 6 schematically shows a set of T D spectra for
beam, which must be capable of producing a significant various initial coverages 0, and a given heating rate p
enthalpy change per pulse upon adsorption. A set of [7, 581. The first step is the integration of the spectra
results is included in Table 1 where it is compared with starting from highest temperature, i.e. coverage 0 = 0,
results from other thermodynamic measurements. It is to a given coverage O’, say 0.15. This yields a pair
interesting to note that the results for the single crystal of (r, T ) values for each initial coverage larger than
surfaces are situated in the region of those determined 0’ = 0.15. A plot of l n r versus 1 / T yields Edes(@’)
for the polycrystalline films, indicating that the latter from the slope and v(0’) from the intercept, which
consist of many crystallites exposing low-index planes. is given by n l n 0 ’ + Inv(@’), if the order n of the de-
The free enthalpy of adsorption is determined by sorption reaction is known. However, for coverages
the enthalpy as well as the entropy of adsorption. The above 0.1, the second term is much larger than the first,
 5.1 Chemisorption 9 15
~~ ~

Table 1. Enthalpies of adsorption.

~~

Adsorbate Substrate q (kJ mol-') Remarks References

co Ni(ll1) 111 (i5) WF '1 22

130 Microcalorimetry 23
Ni( 100) 125 (0 5) WF 24
115 TDS~) 25
119 TDS 26
138 TDS 27
109 isosteric &d 28
123 isosteric &d 24
130 isosteric Ead 29
134 isosteric Ead 30
123 Microcalorimetry 23
Ni(ll0) 133 Microcalorimetry 23
Pd( 100) 150 (+5) WF 31
161 (+8) WF, TDS, LEED 32
Pd(ll1) 142 ( i 3 ) WF 33
Ru(0001) 160 (&lo) WF 34
Ru( 1OLO) 157 (*lo) Contact-pot., TDS 35
Cu( 100) 58 (*lo) WF 36
Fe(ll1) 325 273 K (dissociative) 37
Fe( 11 1) 200 195 K (partially diss.) 37
Fe(ll1) 100 (not dissociative) 20
CO/K Ni(100) 190 Microcalorimetry 38
co2 Fe 300 195 K (dissociative) 37
H2 Ni( 100) 96.3 (k5) WF 39
Ni(ll0) 90.0 (i5) WF 39
Ni(ll1) 96.3 ( i 5 ) WF 39
85 ( i 5 ) 40
Ni 7 5 , ..I76 1
Pd(ll1) 88 (i5) WF 41
Pd( 110) 103 (k5) WF 42
Pd( 100) 102 ( k 5 ) WF 41
Rh( 110) 92 (k5) WF. TDS 43
Ru( 1010) 80 ( i 5 ) 44
Co(1010) 80 ( i 5 ) 45
Ta 188.1 1
W 188.1 1
Cr 188.1 1
Fe 133.8 1
Fe 100 dissociative (273 K) 20
Fe 97 ( 2 3 ) 37
Pd 80/96 21
Na W 133.8 1
cs 267.5 1
0 Ni( 100) 532 ( I S ) IR (300 K)
x432 IR (100 K)
532 (is) 23
Ni(ll1) 470 ( 5 1 5 ) 23
Ni( 1 10) 498 ( 5 5 ) 23
02/CO Fe(ll1) 490 273 K 20

'1 WF, work function; 2, TDS, thermal desorption spectroscopy

so the latter may be neglected without large errors. It simplest picture and set v ( 0 ) equal to the frequency
should be noted that there are methods to determine of vibration of the adsorbed particle, values near
the order rigorously. This analysis, called the "com- 1013s-l are expected. The problems become even more
plete analysis" was first proposed by King in 1975 [55]. involved if we consider the number of successful at-
The preexponential factor v ( 0 ) can be regarded as tempts, i.e. after multiplication of v ( 0 ) by the ex-
representing the frequency of attempts of the adsorbed ponential in eq 14. Here, the activation energy for
particle to escape the chemisorptive potential. The desorption Edes(@)comes into play; both v ( 0 ) and
values determined vary by at least four orders of
magnitude, from lo'* to 10'6s-1 [7]. If we adopt the References see page 938
916 5 Elementary Steps and Mechanisms

a/c pre -
amp ld ier P e lens .-.. a / c amplifier

I
i
I‘ . G e generator
quadrupole mass
spectrometer
.
t
I
stagnation detector I

beamstopper II
1

Figure 4. Schematic drawing of the setup for microcalorimetric measurements on single crystals [46].

Table 2. Entropies of adsorption. It results in reliable values only for first-order desorp-
tion and provided that a reliable value for v is avail-
Adsorbate Substrate AS:! (J K-’ mol-’ ) References able. The Redhead equation can be directly derived
Xe Ni(100) 056 13, 49 from the Wigner-Polanyi equation by determining the
Pd(100) 258 50 temperature derivative of the rate, and realizing that it
H Pd(100) 0263 49 must vanish at the peak maximum temperature [7].
N2 Ni(100) 150 51 Additional procedures are given in the literature [58,
Ni(l10) 112 (i.5) 52
60-631. In connection with the initial question con-
cerning the heat of adsorption, it must be realized that
the desorption energy may be directly related to the
heat of adsorption if adsorption is a nonactivated pro-
cess. In other words the adsorption process is, ener-
getically, continuously “downhill”. A detailed under-
standing, however, necessitates an understanding of the
dynamics of adsorption.
A connection exists between the phenomenological
view of the energetics from the standpoint of thermo-
dynamics, and the microscopic view of adsorbate en-
ergetics. In this context the question as to whether a
process is activated or nonactivated may already have
been answered.
Figure 5. Schematic drawing of the experimental setup for a This approach goes back to Lennard-Jones who dis-
thermal desorption expriment. cussed adsorption energetics in a landmark paper in
1932 applying a quasi-one-dimensional approach [64].
Edes(@)depend on coverage. These coverage depend- Neglect for the moment all problems connected with
ences partly compensate each other for certain systems the question as to how a gas-phase particle is actually
in the sense that high values of v ( 0 ) are associated with trapped in a bound state at the surface of a solid, and
large values of Edes [7]. This has to be considered when simply consider the interaction potential between the
dealing with predictions and interpretations of de- gas-phase particle and a surface. Figure 7(a) shows the
sorption rates. It is therefore important to resort to a well known Lennard-Jones potential energy diagram.
complete or close to complete analysis of desorption It represents the superposition of attractive (longer
data. Simplified analyses were published much earlier. range) and repulsive (short range) forces according to
The most popular one is the so-called Redhead analy- E ( z )= -AzP6 + Bz-12
(16)
sis, based on the peak maximum temperature observed
in a thermal desorption spectrum [54]: where A and B are empirical constants and I’ is the
distance between the adsorbed particle and the surface.
To describe this interaction on the basis of ab initio
 5.1 Chemisorption 917

Figure 6. Determination of the desorption energy Edes from a model-independent analysis of thermal desorption data. The analysis is
carried out for an artificially chosen coverage of 0 = 0.15: (a) TDS data; (b) integration of the TDS data to give 0 versus T plots; (c) plot
of In dO/dt versus 1/T to determine Edes according to eq 14. The basis for the diagram are data for Ag/Ru(0001) [58].

t-
quantum mechanical calculations it would be necessary
to consider a semiinfinite solid interacting with an atom
or a molecule. This can be done in favorable, simple
cases using various approaches [65-681. The most
a prominent one, at least for metal surfaces, is the den-
sity functional approach with which one can come
~~~~ , ads close to the exact solution [65, 671. Another approach is
the so-called embedded cluster ab initio approach
where the solid surface is represented by a cluster of
atoms, augmented by an embedding scheme to repre-

k-
sent more accurately the infinite extension of the two-
dimensional system [68]. Assume for the moment that

b \ , this problem has been solved. Then, the potential en-

ergy curve in Fig. 7(a) represents the case where the
particle incident from the gas phase “sees” a con-
m z&@ tinuously “downhill” energy change until it reaches the
Eods
2Eads equilibrium position at 2,. (Note that, for the present,
the dynamics of the trapping process is being re-

I f
.0--.-.- -.-.- gg glected.) In such a case the desorption energy, as de-
termined from thermal desorption data, is equivalent
to the heat of adsorption. It is this situation that is
l i dissociation often considered for associative molecular adsorption.
C energy However, the situation becomes more difficult if either
a molecule which is associatively adsorbed may assume

dEods mEads . =@ different adsorption geometries on the surface, or the

molecule may dissociate upon adsorption and - to in-
crease complexity - may do so via a molecularly ad-
sorbed precursor state. Figures 7(b) and 7(c) schemati-
Figure 7. Schematic potential energy diagrams for a molecule AB cally show the corresponding quasi-one-dimensional
approaching a surface: (a) associative chemisorption (&&); (b)
associative chemisorption (’&&) with precursor (’ &&); (c) dis-
sociative chemisorption (dEads) with molecular precursor (mEads). References see page 938
9 18 5 Elementary Steps and Mechanisms

unsuccessful

I Y
C X 4

Figure 8. Two-dimensional potential energy surfaces (schematic) for (a) early and (b) late barrier (B) of dissociation of H2 on a transition
metal surface.

potential energy diagrams. In Fig. 7(b) there is a sec- be situated well above the reference level corresponding
ond minimum in the potential energy diagram repre- to the infinitely separated molecule and surface, which
senting the two possible adsorption geometries. It in turn has strong consequences for the ability to pop-
is already obvious that, in this case, the use of such ulate the dissociative adsorbate. As will become clearer
a quasi-one-dimensional diagram becomes very prob- considering multidimensional potential energy surfaces
lematic because only a single spatial coordinate is used in such a situation, the molecule has to have a certain
to represent the molecule-surface interaction. There- impact energy to be able to surmount the activation
fore, such a situation calls for a multidimensional po- barrier. Whether this impact energy should be repre-
tential energy diagram, and we shall come back to this sented by translational degrees of freedom or internal
more general requirement later on. For the moment, (rotational or vibrational) degrees of freedom cannot
however, Fig. 7(b) already allows us to visualize the be concluded on the basis of the quasi-one-dimensional
transformation between the two inequivalent molecular potential energy surface. However, it is already fully
adsorption geometries as an activated process. It is transparent that the shape of the potential energy sur-
immediately clear that a desorption experiment will faces will determine the kinetics as well as the dynamics
probe this more complicated potential energy curve, of the system, and thus the probability to chemisorb.
and thus a simple interpretation of the measured de- Experimentally, we measure (for example) the sticking
sorption energy as the heat of adsorption will not be probability of a particle from the gas phase into a par-
possible in general. ticular adsorbate channel by probing the number of
The situation becomes even more complicated if, adsorbed species as a function of gas pressure and sur-
upon interaction with the surface, the molecule dis- face temperature. In other words, a relatively complex
sociates. This is depicted in Fig. 7(c). In this case it is scenario is condensed into basically a single number.
necessary to consider two intersecting potential energy As the next section shows, it is far from easy to resolve
curves which refer to two different zero-energy levels, the details.
namely the diatomic molecule being infinitely sepa- Before tackling the problem of sticking consider, as
rated from the surface for the associative interaction, alluded to above, potential energy diagrams that allow
as well as the two constituent atoms being infinitely the incorporation of some essential additional features
separated from the surface. The difference between the such as simultaneous motion along several coordinates
reference levels, of course, represents the heat of for- (often normal coordinates). Clearly, the situation be-
mation of the diatomic molecule in the gas phase. In comes very complicated as soon as many such coor-
this case, the above-mentioned difficulty with the quasi- dinates come into play. Consider therefore, for sim-
one-dimensional representation becomes particularly plicity the most simple case of a hydrogen molecule
clear, in the sense that here the coordinate representing interacting with a transition metal surface. In recent
the separation between the two constituent atoms has years, this problem has been treated experimentally as
not been considered at all. Nevertheless, it can be seen well as theoretically in great detail so that a clear pic-
that there may be a rather large activation energy be- ture of the factors influencing the activation process
tween the molecularly adsorbed precursor and the dis- has emerged. A good review for the case of H2/Cu can
sociatively adsorbed atoms, which is very crudely rep- be found in Ref. 69.
resented by the energy near the crossing point with Figures 8(a) and 8(b) show potential energy dia-
respect to the potential energy minimum of the mo- grams for such a system [70]. The potential energy is
lecular precursor. Clearly, the point of intersection may plotted as equipotential lines in a coordinate system
 5.1 Chemisorption 9 19

where the ordinate represents the surface-molecule sensitive, and therefore these aspects have to be con-
(center of mass) distance, and the abscissa the inter- sidered. It should be pointed out that hydrogen
atomic distance of the diatomic molecule, i.e. the adsorption on Cu surfaces may not be typical for
hydrogen molecule in this case. Denoting the inter- interaction with transition metals in general [78]; in
molecular distance in the molecule by x and the dis- particular, remember that H2 dissociates with almost
tance of the center of gravity of the bond to the surface no barrier on metals such as Ni, Pd, etc. [73]. It is clear
by y , small x values are found for large y values, in- that in order to understand the barrier heights elec-
dicating the intact bond between the hydrogen atoms. tronic structure calculations must be resorted to [79,
As the molecule gets closer to the surface, i.e. y de- SO]. However, the difference between Cu and Ni may
creases, x finally increases to large values that are be argued on a qualitative basis [79, SO]. Cu has the
characteristic of the bond-breaking process. It is the electronic configuration 3dI04s’, with the rather diffuse
exact position of the barrier, indicated by the letter B at 4s orbitals occupied. If a closed-shell H2 molecule ap-
the top of the saddle point in the potential energy dia- proaches the Cu surface it will be repelled by the diffuse
gram, that now governs the dynamics of the process. 4s electrons so that it is hard for the H2 to come in
Two different situations are depicted. In Fig. S(a) the close to dissociate. Ni has the electronic configuration
activation barrier is located in the entrance channel. A 3d94s’ in which the 4s orbital is occupied, which again
molecule entering the entrance channel with sufficiently leads to Pauli repulsion with the H2 molecule. How-
high translational energy can surmount the barrier, as ever, in Ni the 4s electron may be promoted into the
indicated by the trajectory. However, it may well move hole within the d shell, forming a 3dl04s0 config-
up the wall before it can follow the bend (as if on a uration - this reduces the repulsion dramatically and
“bobsleigh” course) and the system will consequently allows the H2 molecule to come in close and dissociate.
come out the exit channel vibrationally excited (i.e. the Therefore, the barrier for Ni is much lower than for Cu
hydrogen surface modes are excited) as indicated by where it is in the range of 1 eV [69].
the curved trajectory. In Fig. 8(b) the activation barrier Another aspect that is important in connection with
is located more towards the exit channel. Here a the discussion of adsorbate thermodynamics and en-
vibrationally excited molecule has a better chance to ergentics, so far neglected, is the aspect of interaction
surmount the activation barrier as indicated by the full between adsorbed species. In Langmuir’s picture of
trajectory. An unsuccessful attempt with a translation- adsorption [2, 31, mentioned in the introduction, the
ally excited molecule is shown for comparison. Once adsorbed particles occupy the lattice points of a two-
the vibrationally excited molecule has crossed the bar- dimensional substrate with equal probability and with
rier, the hydrogen atoms formed will move across the hard wall potentials between them, preventing double
surface with relatively high translational energy. The or multiple occupancy of any particular site, and with
whole problem outlined so far can be mapped almost well defined adsorption energies typical of the site.
perfectly onto the so-called Polanyi rules [711, where- (Note that at this point structure sensitivity comes into
after an exergonic reaction of type A + BC + AB + C the picture; however, this aspect is deferred until later.)
with an early barrier request translational energy, As a result of this view of adsorption, saturation would
whereas, if the reaction has a late barrier, it requires be characterized by complete coverage and the forma-
vibrational excitation of the reactants. tion of a true l x l adsorbate layer. Obviously, the
Molecular beam studies [72] have been undertaken formation of ordered layers with coverages far below
in recent years to prepare selectively translationally or complete coverage are more the rule than the ex-
vibrationally excited molecules before they were scat- ception, and are a direct consequence of the existence
tered off the surface, and a great deal has been learned of interaction potentials. Such an interaction potential
about how the molecules stick to a metal surface, spe- is shown in Fig. 9 for the system CO/Pd(l00) reported
cifically for hydrogen-transition metal systems [65-731. by Tracy and Palmberg in 1969, compared with a CO-
In the case of hydrogen absorption on Cu, the barrier CO interaction potential in the gas phase [31]. Inter-
[74-771 is in an intermediate position, so that both action potentials may be either attractive or repulsive
translational as well as vibrational excitation helps to and may be classified into direct and indirect inter-
surmount the barrier. There are still a lot of open actions [81-83]. Direct interactions involve dipole-
questions as to which role rotational excitation plays dipole (multipole-multipole) and orbital-overlap inter-
[69]. However, even with a full understanding of the actions, and are often repulsive. On the other hand,
processes occurring on the potential energy surfaces indirect interactions mediated through the metal sur-
shown in Figs. S(a) and 8(b), there are still some im- face may be either attractive or repulsive depending on
portant ingredients missing. This has particularly to do distance and surface sites, i.e. the kind of charge mod-
with the fact that in the discussion so far the geometric ification of the electronic structure of the substrate by
and electronic structure of the surface has not been
considered. It is known that chemisorption is structure References see page 938
920 5 Elementary Steps and Mechanisms

adsorption sites are separated by a small activation

energy if compared with the activation energy for
desorption, which gives rize to a sinusoidal energy
dependence across the surface. At low enough tem-
perature the adsorbed particles will reside within the
potential wells because their thermal energy is too
small to overcome the activation barrier for diffusion.
Correspondingly, for higher thermal energies, particles
will site exchange resulting in a mobile adsorbed layer
with short residence times in the individual wells. We
shall discuss this situation in more detail further below.
The potential energy diagram parallel to the surface
gas phas changes significantly if the interaction between ad-
sorbed particles is taken into account. This is sche-
matically depicted in Fig. 10(b) where we have added
an attractive as well as a repulsive potential to the one-
dimensional diagram of Fig. 1O(a). The consequences
are energetic heterogeneities, weakening the adsorbate
surface bond in the case of the repulsive interaction,
and strengthening the adsorbate surface interaction in
the case of attractive interaction potentials. As men-
1.0 2.0 3.0 L.0 5.0 tioned above, phenomenologically this leads to the
CO-co separation [ A 1 formation of ordered phases on surfaces. In fact, there
Figure 9. Intermolecular potential for CO in the gas phase and
may be several different ordered structures depending
CO adsorbed on a transition metal surface. on both temperature and coverage, because surface
diffusion may act against the formation of ordered
structures, i.e. favoring disordered layers while, for ,
the adsorbate. The interplay of the interaction poten- example, coverage increase locks in certain structures.
tial and the adsorption energy of the isolated particle A way to represent the various structures is to plot a
with the clean surface finally determines the observed so-called phase diagram [MI. An example is shown
properties of the adsorbed layer. In other words, the in Fig. 11. For the system CO/Cu(lOO), two ordered
structure of the adsorbed layer depends on the heat of phases are found in the given temperature range [86].
adsorption as well as on the coverage [ 5 ] . These are denoted by I and II+, and they occur at
The situation again may be depicted in the form of a coverages 1/2 and 4/7. Phase I is a c(2 x 2 ) structure,
potential energy diagram; however we have to include while phase 11, consists of stripes of the c(2 x 2)
the existence of different surface sites [84]. Figure 10(a) structure of width n = 3 separated by domain walls.
[7] shows a one-dimensional potential energy diagram The main part of the phase diagram is filled by a dis-
where the spatial coordinate extends parallel to the ordered phase. A very interesting and frequently stud-
surface. It has been assumed that every surface site ied aspect of such phase diagrams are the two-dimen-
provides identical binding conditions. All identical sional phase transitions. In two dimensions, similar to

a b
t' tE
attractive interaction

ground state

Figure 10. One-dimensional potential energy parallel to the surface: (a) empty surface with a single particle bound with adsorption energy
&&; (b) superposition of the potential energy in (a) with a painvise interaction potential of particles on the surface (E,,,,), which may be
either attractive or repulsive.
 5.1 Chemisorption 921

1
7 CO/Pd( 1001

\
fl
A

0
\
E 120-
7
Y
Y
m
U
0
w 100-
coverage

80-

I I I

I 0 02 04 06
0
-_
Figure 12. Adsorution energy (E2,+ as a function of surface
coverage 0 [7]: (A\ CO/Pd(100) [32]; (v) CO/Ni(lll) [22]; ( 0 )
~ --I

II+ H/Ni(llO) [39].

Figure 11. Phase diagram for the system CO/Cu(lOO), also

showing the ordered structures [86].
sorption close to saturation for CO/Pd(lOO) [32] is due
I to the population of additional weakly bound species
three dimensions, phase transitions may be classified as on the surface [91, 921. These weakly bound species
discontinuous first-order, and continuous higher order. may be rather reactive. Owing to their small heat
In general, phase transitions may be evaluated accord- of adsorption they may react rather easily with co-
ing to the temperature dependence of the thermody- adsorbed, neighboring functional groups. At high re-
namic functions. This subject is considered in greater actant pressures and not too elevated substrate tem-
detail elsewhere [87-901. peratures this kind of scenario may play a significant
More important with regard to the heat of adsorp- role.
tion are the particle-particle interactions. As stated
above, according to the Langmuir picture of adsorp-
tion [2, 31 we would expect constant adsorption energy 5.1.1.3 Sticking
until saturation of the surface is reached. In reality, this
is never the case [85]. Rather, the adsorption energy This section considers the traditional description of the
generally decreases at medium and high coverages due process where a molecule approaches a solid surface
to interactions between the adsorbed particles. It is and eventually is trapped by the potential. A con-
possible to estimate the interactions from the coverage venient way to gain access to this problem is through
dependence of the isosteric heat of adsorption. In Fig. the consideration of the rate of adsorption. In the most
12 [7] are several examples [22, 32, 391 where the work simple case, the rate of adsorption is proportional to the
function has been used as a measure for the coverage number of molecules impinging per unit time on the
(which may be sometimes dangerous). It is obvious surface, the so-called particle flux, and to the (dimen-
from Fig. 12 that in all cases the adsorption energy sionless) efficiency with which an impinging particle
sharply decreases as saturation is approached. At low actually sticks to the surface, i.e. the so called sticking
coverge, however, the isosteric heat turns out to be ei- probability. The initial sticking coefficient so is the ratio
ther constant, decreasing, or increasing with coveage. of the number of adsorbed particles oS and the num-
The observed changes are a consequence of the par- ber of impinging particles for the uncovered surface.
ticle-particle interactions on the surface, in the sense Therefore,
that increase means attractive interactions, as for ex-
ample in the case of hydrogen for low coverage [39], O<S,<l (17)
decrease repulsive interaction, as in the case of CO on
Ni( 11 1) [22]. The step-like decrease of the heat of ad- References see page 938
922 5 Elementary Steps and Mechanisms

In principle, determination of this quantity is straight- lation energy shows a typical "normal energy scaling",
forward. In an adsorption experiment a clean surface in other words an exclusive dependence of the sticking
held at temperature T is exposed to a well defined probability on the normal component of the energy of
pressure P for a given time t (exposure is measured in the incident particle, which has been found rather fre-
Langmuir: 1 L = lop6 torr for 1 s), and the amount of quently [95-1001, and in particular for hydrogen ad-
gas taken up by the surface (by a suitable surface sci- sorption on transition metals.
ence technique) is compared with the total amount of With this in mind we can go back to equation (18)
gas that has struck the surface. A method frequently and analyse the rate of adsorption further. First, write
used is the one proposed by King and Wells [93, 941. In the rate in terms of coverage and not in terms of the
this case a molecular beam strikes the surface and the absolute number of particles:
change in the background pressure of a given gas is
measured by a mass spectrometer. The procedure is
calibrated with respect to a gold sample that is known
not to adsorb any molecules in the considered temper-
In the case of the most simple treatment according
ature range.
to Langmuir [2, 31, where it is assumed that each
Knowing how s is measured experimentally, we can
adsorbed particle occupies only one surface site, the
turn to further conceptual considerations. The rate of
adsorbed species does not interact with other adsorbed
adsorption, i.e. the change of the number of adsorbed
particles present on the surface. It is further assumed
particles with time is given by [7]
that the adsorption energy is completely exhausted as
soon as one monolayer has been formed; the function
f (0) reduces to (1 - 0).If the particle dissociates
upon adsorption - it occupies two sites - the function
where the flux of impinging particles has been treated f (0) becomes (1 - Remembering that under
according to the kinetic theory of ideal gases, and a equilibrium conditions the rate of adsorption must
function f (g,) accounts for the loss of empty sites as equal the rate of desorption
the adsorption process proceeds. The term so may be
written in terms of a preexponential O s and an activa- Tad = rdes (22)
tion energy adsEact as we arrive at the following condition for the coverage:
so = Osexp( - +)
ads
( 0 )= b(T)P
+
1 b(T)P
There is a different adsorption probability depending which is the famous Langmuir adsorption isotherm [2].
on whether the adsorption site is occupied or not. In its derivation we have employed eq 14 for the de-
From what has been said before, the sticking coefficient sorption rate assuming a first-order process, and con-
must also depend on the population of internal and secutively just solved for @. In addition, we have used
external degrees of freedom of the impinging molecule. an abbreviation for a constant b ( T ) which only de-
This can be done in a closed form by assuming the pends explicitely on temperature once the adsorbate
sticking probability s to be composed of terms for the parameters are known. b( T ) is given by
vibrational states involved, each weighted by a Boltz-
mann factor (FB) representing the population of the
corresponding vibrational state [69]:
s(ujEej T )= CFB(~,
V
T)sa(u,Ee) (19) In this case the preexponential factor O s should not de-
pend on coverage because it has been assumed for the
where v represents the vibrational quantum state under derivation that there is no intermolecular interaction.
consideration, which is populated according to the Many different adsorption isotherms may be derived
Boltzmann factor depending on the temperature T of where all or some of the basic assumptions going into
the gas (effectively the nozzle temperature in a mo- the derivation have been released or relaxed [101- 1051.
lecular beam experiment). The effective translation It should be stated, however, that the general form of
energy Ee is given by [74] the Langmuir isotherm, which is shown for two tem-
peratures in Fig. 13, may be used for a phenomeno-
E, = E i COS"($~) (20) logical description of many processes. It is clear, from
in whch E i is the translation energy of the incident the adsorption isotherm, the sticking probability so
particle, and $i is the angle of incidence with respect to may also be determined given that all other parameters
the surface normal. If n = 2 then the effective trans- are known [l, 71.
 5.1 Chemisorption 923

metal surfaces regardless of their crystallographic ori-

entation. On open surfaces they even tend to dissociate.
The tendency to dissociate increases when going from
the right to the left in the periodic table. Co is approx-
imately on the border line.
We note at this point that in addition to the surface
crystallography, surface defects (point defects as well
as steps) are important to accommodate chemically
I/ active species [112, 127, 1281. Initial sticking proba-
II I bilities are interesting, but for real systems it is impor-
" tant to consider the coverage dependence of the stick-
pressure p
ing coefficient. Of course, a model-free discussion of
Figure 13. Plot of the Langmuir isotherm for two temperatures this aspect is very difficult. It is therefore common
( T I and T2). practice to assume a set of possible kinetic processes
which are important in connection with sticking to a
surface. A possible scenario is shown in Fig. 14 sepa-
Table 3 collects a set of sticking probabilities deter- rately for adsorption and desorption [7]. We introduce
mined for various absorbate systems. The values vary precursor states which may be classified as either in-
between unity and lo-*, although the range is usually trinsic or extrinsic precursor states [129, 1321. The for-
between 0.15 and 1. Obviously, there is a clear trend mer exist at empty surface sites and the latter at sites
that sticking is higher for atomically rough surfaces as already occupied. While trapped into such a precursor
compared with atomically smooth surfaces depending state the particle is only weakly held to the surface.
on the nature of the gas. It seems that energy accom- Thus it can diffuse across the surface and be eventually
modation is particularly easy on the rough surfaces as trapped into an empty surface site. Given a precursor
compared to the smooth ones. Carbon monoxide and lifetime of lop6s, the molecule probes the surface for a
nitric oxide stick quite effectively on many transition sufficiently long time to find an empty site, if the pre-

Table 3. Initial sticking coefficients

Adsorbate Substrate Sticking coefficient Remarks References

~~~

H Ni( 100) 0.06 106, 107

Ni(l11) 20.01 108
Ni(ll0) Z1 109
0.96 1 I0
Pt(ll1) 0.1 111
~0.0001 112, 113
Rh(ll0) ZI 43
Ru( 1010) Z l 44
Co( 1OLO) 0.75 (i20%) 45
W(100) 1 114
0 C U ( 100) 0.03 300 K 115
Ni( 100) 1 1 I6
Pt(l11) 0.2 1 I7
co Ni(lll) 1 22, 118
Ni( 1 10) 0.89 119
Pd( 100) 0.6 32
Pd(l11) 0.96 120
Ru( 1010) 1 35
Pt(l11) 1 121
N W( 100) 0.2-0.6 see Figure 94
W(110) 1-5 x P-N2 122, 123
0.22 Y-N~ 124
W(111) 0.08 93
N2 Fe( 100) 10-~-10-~ 125
Fe( 111) 10-~-10-~ 126
Fe( 11 1) > (100) > (1 10) 10-6- 10-8 126

References see page 938

924 5 Elementary Steps and Mechanisms

direct processes
0- Pch 0
0 pd

precursor
mediated
processes

-0 0.5 1.0

I , I
8
Figure 15. Relative sticking probabilities as a function of surface
coverage according to the Kisliuk model [131, 1321. For an ex-
planation of K see text.
~ prec:sor
chemisorbed I gas phase
state
K = - Pi (26)
Pih +PA
I
1
The Kisliuk model for a coverage-dependent sticking
coefficient contains the linear Langmuir behavior as
' - r - ; s to the surface
perpendicuiar
well as the coverage-independent sticking probability
as limiting cases. Clearly, as K = 0, s ( 0 ) = so. Also, as
1 1
1
I
J K = 1, s(O) = s o ( l - 0),i.e. the linear Langmuir be-
zch zp havior is retained. As K is always larger than zero, we
have to consider two cases, namely for K > 1, and for
Figure 14. Schematic representation of direct and precursor-
mediated processes on a surface [ 129, 1301. Processes occurring
0 < K < I . The result is a convex curve for the former,
along the surface normal are plotted along the abszissa. The pro- and a concave curve for the latter case (Fig. 15) [131,
cesses are correlated with the potential energy diagram of Fig. 1321. Which behavior is actually encountered is largely
7(b) (ex = extrinsic precursor, in = intrinsic precursor, n , = num- determined by the probability p i , i.e. the probability
ber of impinging particles from the gas phase, d and 2'' are frac- for desorption out of the extrinsic precursor. It has to
tions of trapped molecules, p = probabilities, p k = migration
probability along the surface). become smaller than the sum of probabilities to desorb
out of the intrinsic precursor and the probability to
chemisorb out of the intrinsic precursor, in order to
coverage is not too large. In order to set up a scheme achieve K < 1. Under ultrahigh-vacuum conditions,
we have to define probabilities (p,) with which the var- the population of extrinsic precursors is only easy
ious states at the surface are populated. On the basis to realize at low substrate temperatures. Therefore,
of this (Fig. 14), it is possible to arrive at equations concave sticking probabilities are generally found, as
for the rate of adsorption and desorption. However, in demonstrated for some examples in Fig. 16 [39, 120,
the present case, different from the situation discussed 133, 1341. However, at higher pressures, the population
above for direct sticking, the sticking probability s ( 0 ) of weakly bound precursor states may be of im-
will be dependent on the surface coverage. Kisliuk, as portance, so that the population of the chemisorbed
one of the first, has proposed a coverage dependent state through the precursor becomes rate limiting. In
sticking coefficient based upon such considerations such cases we may find a convex curve of the sticking
[131, 1321: probabilities. Of course, additional complications may
arise if the structure of the surface changes upon
changes of coverage [ 1351. Then the dependences may
become very different altogether. Oscillatory surface
chemical reactions are connected with such behavior in
The constant K is connected with the probabilities to some cases [136].
populate a chemisorptive state via the various pre- To end the section on sticking we would like to de-
cursor states or desorb from them, respectively (Fig. scribe a very interesting development that has recently
14): become more visible, namely the experimental in-
 5.1 Chemisorption 925

1
I
before colliding with the substrate. Depending on the
polarity of the electric field in front of the surface, two
different orientations can be achieved: preferential N-
m end and preferential O-end collisions. The rotational
temperature of the colliding molecules determines
0 0.25 0.5 '0 0.5 1.0 the degree of orientation of the molecules. Therefore
I e seeded pulsed nozzle beams are used to cool the par-
ticles before collision. The integral number of mole-
cules leaving the surface after scattering is detected
from the NO partial pressure with a quadrupole mass
spectrometer located behind the target and thus
CO/Pd(lll) shielded from the direct beam [93]. Figure 18 shows a
0' 0.25 0.5 0.25 0.5 typical result in terms of partial pressures (right panel)
for the scattering of NO from Pt(100) as a function of
field strength and orientation of the NO molecule [142].
Figure 16. Relative and absolute sticking probabilities for car-
bon monoxide as a function of surface coverage [39, 120, 133,
The observed asymmetry, which is plotted in the left
1341. panel, is very high. Note that the degree of orientation,
given as the averaged cosine (cos3) of the angle be-
tween molecular axis and external electric field 3, is
vestigation of the dependence of sticking on the ori- 30%. The result documents the strong preference for
entation of the particle, in particular a molecule, upon trapping in the chemisorptive potential if the molecules
surface impact. Kleyn and co-workers [137, 1381, as approach the surface with the N-end. At higher surface
well as Heinzmann and co-workers [139-1411 have temperatures the asymmetry decreases as expected,
shown that a molecule such as NO can be state selected because the number of molecules that do not stick
and focused by taking advantage of a hexapolar elec- increases for both orientations. It seems that for a
tric field, and subsequently oriented in a homogeneous detailed understanding of the temperature dependence
electric field, as schematically indicated in Fig. 17 [140], a kinetic model involving precursor states has to be

guiding and
orientation field
OMS
for determination
kV
+ 1_0 ot stickinq coefficient
hexapole - field
(with central beam stop1
velocity

Figure 17. Experimental setup to study sticking probabilities of oriented NO molecules [139].

7 3-

n N-end collisions
5 1-
._
.ad

n
b
0
- 0
6 8 10 12 1L
= 076 z

8
,
10
I I

12
3 I I

I
field strength [kVlcml field strength [kV/crnl

Figure 18. (Right) NO partial pressure after scattering from a Pt(100) surface as a function of field strength and NO orientation [141].
(Left) Corresponding orientation asymmetry of the partial pressure of NO [142].

References see page 938

926 5 Elementary Steps and Mechanisms

invoked. A fit to a Kisliuk model [131, 1321 (see ments, for example, via low energy electron diffraction
above) indicates that not only chemisorption is favored (LEED). Furthermore, surface diffusion helps to over-
for N-end oriented molecules but also trapping into a come lateral concentration gradients due to non-
presursor state. If we change the adsorbate system from equilibrium clustering phenomena often found at low
a chemisorptive system such as NO on Pt(100) to a temperatures. There is a large amount of information
more weakly interacting system such as NO/Ag(l 1 1) available on surface diffusion [129, 148, 1491, both on
[137] we realize that the observed symmetries are ac- the experimental methods to measure diffusion co-
tually much smaller even at low temperature, and in- efficients as well as on the theoretical aspects of the
deed, slightly favor trapping of NO molecules with the problem. We shall only give a brief, nonexhaustive
0-end approaching the surface even at lower coverage. overview of the situation [7].
Conceptually, the process is thought to occur as a
random walk where adparticles hop between adjacent
5.1.1.4 Surface Diffusion sites, i.e. from an occupied to an adjacent empty site.
The hopping frequency depends then exponentially on
The motion of adsorbed particles obviously plays an the temperature of the system which leads to the fol-
important role for adsorbates and for surfaces in gen- lowing form of the diffusion coefficient:
eral, because this process enables the system to achieve
its equilibrium structure. Particularly, at elevated tem- D = DOexp(--) AEdiff
(27)
peratures the atoms of the substrate material can move,
lowering the free energy content of the surface. The with the preexponential factor DO and the activation
process of diffusion of substrate atoms has been in- energy for diffusion A E d i f f . It is correlated with the
vestigated frequently in the past. Applying various height of the energy barrier in Fig. 10 parallel to the
methods such as scattering methods, field emission and surface. An expression for DO may be derived from
contact potential measurements Bonze1 and co-workers transition state theory and depends on the activation
[143-1451, Butz and Wagner [146, 1471, Ehrlich [148], entropy of the process. The important quantity for
and Holzl and co-workers [149, 1501 have contributed surface diffusion is the activation energy. Its magnitude
to this area. Due to the rather high activation energies is about a tenth of the adsorption energy for a typical
required for the substrate atom displacements, tem- chemisorbate such as CO/Pd, i.e. it amounts to ap-
peratures up to 1OOOK have to be employed in order proximately 15-20 kJ mol-' . For physisorbates it is
to obtain reasonable rates of diffusion of substrates probably considerably lower.
atoms. In connection with the discussion of chem- The diffusion coefficient may be measured via several
isorption, however, we are more concerned with a dif- experimental techniques. The most prominent ones
ferent type of surface diffusion, namely when diffusion at present are the direct observation of a diffusion
occurs within the adsorbate phase. Such processes may boundary in either a field electron microscope [159,
be separated from the motion of substrate atoms be- 1601 or a photoelectron emission microscope [158] or
cause much lower temperatures are needed to induce via laser desorption experiments [ 161, 1621. In the latter
diffusion. Typical diffusion coefficients are given in case a short laser pulse is used to heat the surface to
Table 4. momentarily desorb the adsorbate from a well defined
Diffusion within the adsorbed layer is instrumental region of the crystal. Subsequent laser pulses with well
to establish long-range order and to obtain optimal defined time delays with respect to the first one, and
experimental conditions to perform diffraction experi- measurement of the number of particles leaving the
surface, allow one to determine the rate of diffusion
into the depleted zone. Other methods to determine
Table 4. Diffusivities of adsorbates. surface diffusion are spectroscopicmeasurements which
cover the proper time window, for example magnetic
Adsorbate Substrate Do (cm2s-l) References
resonance-based methods [163, 1641. In favorable cases
cs W(110) 0.23 151 these methods may even be applied to single crystal
K ViP) 1o -~ 152 surfaces [165].
N W(110) 0.014 153 As mentioned above, the diffusion process is thought
0 W(110) 0.04-0.25 154
to be a random walk across the surface. Then the
H Ni( 100) 2.5 x 10-3 155
D Ni( 100) 8.5 x 10-3 155 mean-square displacement of the adparticles is related
H WiP) 1.8 x 10-5 156 to the diffusion coefficient via the relation
D Pt(ll1) 8 x lo-' 157
co Pt(ll1) 10-~-10-~ 157 (A?) = 4 Dt (28)
co Pt(iio) [iio] 2.1 x 10-9 158 where is it understood that the surface itself only con-
co Pt(ll0) [OOl] 0.8 x 10-9 I58
tains a very low concentration of adparticles which do
 5.1 Chemisorption 927

not interfer with each other. In other words, the model titania, or highly dispersed metals such as platinum
so far is coverage independent. However, we know black. However, even these materials possess a regular
from previous considerations that coverage dependence geometric structure on the microscopic scale. Often,
has to be considered. For example, if a particle wants microscopically analyzed, these materials expose regu-
to move to an empty site the probability to hop clearly lar crystallographic planes, which may be characterized
depends on the number of empty sites in the neigbor- via scattering methods or real-space imaging. In catal-
hood, or even on the concerted motion of adparticles. ysis, the correlation between surface geometric and
Coverage dependences may be introduced by using the electronic structure, the geometric shape and electronic
general transport equations, or specifically Fick's law structure of a molecule, and the observed macroscopic
[166]. The solution of Fick's law again yields an ex- reactivity represents a very important and long dis-
ponential dependence of the diffusion coefficient as in cussed, but not yet solved problem. One distinguishes
equation (27): between structure-sensitive and structure-insensitive
reactions. Special site requirements have been discussed
(29) in terms of the so-called ensemble effect [167-1691
whereafter a molecule can only adsorb if a certain
where the coverage dependence of the process enters group of adjacent surface atoms is available. Studies
through a coverage dependence of the activation energy: on bimetallic alloy surfaces have often been used as
examples for such ensemble effects [167, 1681.
The present section enters into the discussion of the
electronic and geometric structure by considering first
an example where we can vary the strength of inter-
( 30) action between a given adsorbate and various metal
where B is the short-range order parameter, B = and metal-oxide surfaces. We have chosen carbon
1 - exp(Epair/RT),2 is the number of nearest neigh- monoxide as the adsorbate because it offers the largest
bor sites, and Epair is the nearest neighbor interaction available data set, including structure determination.
energy. Using this approach Fick's equation may be Photoelectron spectroscopy (PES) is a very sensitive
solved numerically. tool with which to monitor the change in the electronic
Table 4 contains a collection of diffusion coefficients structure, which is why it is the method of choice to
determined experimentally for a variety of adsorbate shed light on this question [170]. Figure 19 shows a set
systems. It shows that the values may vary consid- of photoelectron spectra of CO adsorbates on four
erably, which is of course due to the specific bonding of different hexagonally close packed metal surfaces [1711
the adsorbate to the surface under consideration. Sur- as well as on two transition metal-oxide surfaces [172-
face diffusion plays a vital role in surface chemical re- 1731. For comparison we show the spectrum of gaseous
actions because it is one factor that determines the [174] and condensed CO [175]. The binding energy
rates of the reactions. Those reactions with diffusion as (& = &in - hv) refers to the vacuum level, which al-
the rate-determining step are called diffusion-limited lows us to put adsorbates on metals, on insulators, and
reactions. The above-mentioned photoelectron emis- molecular solids on the same energy scale. (Often the
sion microscope is an interesting tool to effectively binding energy is referenced to the Fermi level (EF)of
study diffusion processes under reaction conditions the system. The binding energy with respect to the
[158]. In the world of real catalysts, diffusion may be vacuum level and the binding energy with respect to
vital because the porous structure of the catalyst par- the Fermi level are connected via the work function CD
ticle may impose stringent conditions on molecular of the system.) The region where we expect photo-
diffusivities, which in turn leads to massive conse- electron emission from the three outer valence levels of
quences for reaction yields. CO, i.e. 50, ln, and 40 levels, is shown, and most of the
following discussion will concentrate on these levels.
From the bottom to the top the heat of adsorption in-
5.1.1.5 Structure Sensitivity creases from 19 kJmol-' to 142 kJmol-' for the metal
surfaces. This is accompanied by clearly recognizable
So far we have neglected the fact that the substrate has changes in the photoelectron spectra. There are several
a particular geometric structure which influences, as we interesting differences in binding energies, line inten-
shall see further below, the adsorption behavior in a sities and line shapes between gas phase [174], con-
very pronounced way. Furthermore, in practical cases densed phase [175] and adsorbate phases [172, 173,
the macroscopic geometric structure is rather complex. 176-1791, which we shall comment on in the following.
Consider, for example, a real catalyst used in hetero- We shall start with the adsorbates on the metal surfaces
geneous reactions. It may consist of bimetallic precip-
itates, or of thin films supported on alumina, silica, or References see page 938
928 5 Elementary Steps and Mechanisms

Figure 20. Schematic diagram for the bonding of an isolated CO

molecule to a metal atom (right hand side) and a free two-
dimensional array of CO molecules (left panel) to a metal surface
(middle).

displayed, and compared in the middle with the full

band structure of the CO adsorbate interacting with the
compact metal substrate with (1 11) orientation. Both
aspects, the molecule substrate as well as the inter-
molecular interactions, have consequences for the ob-
served spectra, but the main effect we shall dwell on
first is the molecule-metal interaction. What happens
electronically can easily be explained in the so-called
25 20 1'5 10 Blyholder model [IXO]. The carbon lone pair of CO is
binding energy donated into empty d or s levels of the metal atom, es-
tablishing a a-metal-molecule interaction; synergeti-
Figure 19. Photoelectron spectra of CO adsorbed on metal and
metal oxide surfaces in comparison with gaseous and condensed
cally, metal d electrons are donated into empty mo-
CO. The spectra are taken in normal electron emission. lecular orbitals (2.n) of CO forming a n-metal-molecule
interaction. From the view point of the molecule we
can look at this charge exchange process as a .n-dona-
[176-1791, and later turn to the oxide surfaces [172, tion-n-backdonation process. This means that the dis-
1731 because bonding considerations are rather differ- tribution of electrons among the subsystems, i.e. CO
ent for these systems. molecule and metal atom, in the CO-metal cluster
In order to systematically approach an under- is considerably different to the noninteracting sub-
standing of molecule-metal bonding and to relate the systems. For example, the electron configuration of the
conceptual considerations to experiment we briefly re- metal atom in the cluster may be different from the
fer to Fig. 20 [171]. In this figure the molecule-metal as isolated metal atom, or the electron distribution within
well as the molecule-molecule interaction effects are the CO molecule bonded towards the metal atom may
illustrated on the basis of a one-electron level diagram look like the electron distribution of an "excited" CO
for the valence electrons It shows on the right-hand molecule rather than the ground state CO molecule
side a diagram for an isolated CO molecule correlated [181]. This scheme has been used to explain the well
with a one-electron level diagram for a CO molecule known changes in the vibrational properties of ad-
interacting with a single metal atom. On the left-hand- sorbed CO as compared with the gas phase. In addition
side the band structure of an isolated CO overlayer is to the loss of the rotational fine structure upon ad-
 5.1 Chemisorption 929

sorption, the CO stretching frequency often shifts by to the gas phase. Via angle resolved photoelectron
more than l00cm-' to lower values [182-1851. It is the spectroscopy [170] it has been shown that the two
filling of the CO antibonding 271 orbital via the back- bands really contain three components as indicated in
donation contribution which weakens the CO bond in the figure as well as expected from the simple bonding
the adsorbate and concommitantly shifts the stretching considerations made above [197]. The carbon lone pair
frequency to lower values [186]. Also, as a consequence is shifted close to the 171 ionization due to the strong
of this interaction certain electronic levels of the sub- charge exchange and is actually located at higher
systems are strongly influenced. Naturally, the dis- binding energy. The overall shift of the bands to lower
tortions of the molecular as well as the metal levels are binding energy is a consequence again of the relaxation
reflected by changes in the ionization energies, their in the ionized state of the adsorbate due to the presence
ionization probabilities, and the line shapes of the ion- of the highly mobile metal electrons. Therefore, the
ization bands. In CO/Ag(lll) [176] at T = 20 K CO is experimental observation are in line with our simple
physisorbed as documented by the small adsorption charge-exchange model for CO-metal bonding but one
energy of 19 kJ mol-' . This explains why a spectrum so has to be careful in the interpretation not to forget the
similar to condensed CO is observed for this adsorbate. effects of the probe, in the case of PES the creation of a
The splittings in the 40 and 50 ionizations are con- hole in the system [170].
nected with the formation of a two-dimensional layer We now come to the comparison of the electronic
and will not be discussed at t h s point [187]. If com- structure of the adsorbates on the metal surfaces with
pared with the gas phase, however, rather dramatic those on the oxide surfaces [215, 2161. Very detailed
changes are found. The bands are shifted by about 1 eV electronic structure calculations [217-2241 have re-
to lower binding energy and the line widths increase, cently shown that the interaction of molecules with
which destroys to a large extent the vibrational fine oxide surfaces differs considerably from the interaction
structure observed in the gas phase, too. Theories have with metal surfaces in the sense that in the latter case
been developed that allow one to understand these interaction, at least on the regular surfaces, is much
processes on the basis of hole hopping and relaxation, weaker. However, it is not necessarily a physisorptive
i.e. effects in the ionized state, within the quasi-two- interaction. Briefly, on the (100) surface of the strongly
dimensional solid but for the present review we refer ionic NiO the interaction of a CO molecule is not gov-
to the literature for details [188-1931. If the heat of erned by short-range charge-exchanges processes as in
adsorption increases to about 47 kJ mol-' [194], as for the case of the metal surface but rather by electrostatic
example in the case of CO on Cu(l11) [177], the interaction between the multipolar moment of the mo-
features in the spectrum shift and the intensities are lecular electron density and the multipolar moment of
altered. Three lines are still found but their assignment the ionic surface. The reason for this behavior is that
is very different as compared with the physisorbate due to the presence of the closed shell oxygen ions in
[177]. the (100) surface the molecule cannot approach the Ni
We only briefly state here that many-particle effects site close enough to exchange charge. Pauli repulsion
in the ionized state of the adsorbate due to the presence sets in at rather large distances from the surface and
of the highly polarizable metal electrons dominate the repels the molecule. The balance between the electro-
spectrum, and this alters the assignment considerably static attractive forces and the Pauli repulsion results in
[177]. If we later turn to the oxide surfaces where such a rather weak chemisorptive bond of CO on a typical
effects do not occur as strongly but the bond strength is oxide surface. In addition, due to the rather weak in-
comparable, we shall see that the interaction may be teraction there is no longer a strong preference for one
directly deduced from the spectrum. We note in passing given orientation of the molecule with respect to the
that the assignment of the bands to states of different surface. For example, the molecular axis may be either
symmetry has been made on the basis of experimental perpendicular or tilted, or there may be interaction
investigations using angle resolved photoelectron spec- either with the carbon end or the oxygen end of the
troscopy (ARUPS) [170]. Reviews on this subject exist molecule with the surface. In other words, from an
in the literature [170, 195, 1961. The next step is the experimental point of view, we have to check in each
study of the strongly chemisorbed systems with ad- case individually which situation is adopted by the
sorption energies larger than lOOkJmol-'. Out of a system [172].
wealth of experimental data [197-2141 we have shown To a certain extent, the vibrational spectra [225, 2261
here only two systems, i.e. CO/Ni(l11) and CO/ again provide a clue towards a verification of the gen-
Pd(l11). In these cases the spectra show two bands, eral statement made above. On oxide surfaces, in gen-
whose binding energies are almost independent of the eral, the observed shifts of the stretching frequencies
particular system under consideration as long as inter-
molecular interaction does not play an important role.
The bands are shifted by more than 2eV with respect References see page 938
930 5 Elementary Steps and Mechanisms

2060
term;”‘-p f
205C

r
- 1900
Y

Figure 21. Schematic proposed arrangement of CO on a CrzOl >

surface [173]. 5 1880
5
a,

’
0
are considerably smaller as compared to adsorbates on 1860
metals [183-1851. The vibrations may be either red or
blue shifted depending on the interaction. The small
red shift observed in some cases may be interpreted by a
limited charge transfer from the oxide to the adsorbed 18LO
molecule in the same sense as for adsorbates on metal
surfaces. The often observed blue shift, however, has a
different origin. It can be explained by the so called 1820
“wall effect” [219, 2201 in which the weakly held C O
molecule vibrates against the hard wall of the substrate 0.2 OIL
I
0.6
which shifts the stretching frequency to higher values, CO coverage Gco
thus leading to a blue shift. The statement made above
concerning the interaction of CO with the oxide surface Figure 22. Stretching frequency of CO adsorbed on Ni(l11) as a
function of CO coverage. The surface was dosed at 9 0 K and
can now also be verified via the photoelectron spectra subsequently annealed to 240 K [ 1841.
in Fig. 19 [172]. We find the binding energy of the
oxygen lone pair located very close to the energy in the
condensed C O film indicating that there is no strong
intermingling between the oxgen long-pair density and details of the electronic structure of a system, in par-
the surface electrons. The same is true for the CO 71- ticular on an oxide surface.
bond electrons. However, we see a pronounced shift The next step in the discussion of structure sensitivity
of the carbon lone pair electrons originating from of chemisorption is to consider the site of adsorption
the strong Pauli repulsion with the surface electronic on a given surface and to answer the question as to
charge. The relaxation shift found for the metal oxide whether and how the site changes as the coverage of
systems is rather small also because the response of the adsorbate is increased. Figure 22 shows the famous
the oxide surface towards the creation of holes on the dependence of the C O stretching frequency on cover-
molecule in the ionization process is less pronounced age for the system CO/Ni( 111) [184]. This dependence
than with the metal surface. Comparing the spectrum has been interpreted as being due to two effects, namely
for the CO/Ni0(100) system with the last example, i.e. a change of adsorbate site upon increase of coverage
CO/Cr203(111) [ 1731 indicates a similar situation as far and additionally a shift caused by the coupling of the
as the overall position of the adsorbate induced fea- dynamic dipoles which depends on intermolecular dis-
tures are concerned. However, a detailed analysis of tance [183-1851. Figure 22 indicates the adsorbate
this fi x fi)-ordered adsorbate system shows that the geometry deduced for the various coverage ranges
individual ionizations are considerably shifted with re- based on the stretching frequency data. In recent years
spect to the CO/Ni0(100) system. The reason is simple, it has become more and more clear, however, that a
and it can be proved by angle resolved photoelectron structural assignment based on vibrational data has to
measurements or X-ray absorption measurements, that be taken with caution. At low coverage a CO stretching
the orientation of the molecule with respect to the sur- vibration at 1816cm-’ shows up. This is replaced by a
face has changed. CO is no longer vertically oriented band at 1831 cm-’ if the coverage increases and even-
on the surface but rather strongly inclined. A schematic tually shifts to 1905cm-’ at @ = 0.5 corresponding to
model of the local bonding situation is shown in Fig. a c(4 x 2) structure. On the basis of the suggestions by
21. The analysis of the chromium oxide system under- Eischens and Pliskin [182] the band at 1816cm-’ has
lines the necessity of determining individually the ori- been interpreted to be due to adsorption in a threefold
entation of the molecular axis before we discuss the hollow site at low coverage and the band shifting in the
 5.1 Chemisorption 93 1

Figure 24. Geometric arrangement of CO molecules on a

Ni(l10) surface at low coverage (right) and high coverage (left).

u w w the intermolecular distance would be 2.5 A if the

molecular axis remained perpendicular. Therefore the
Figure 23. Schematic drawing of the geometric arrangement CO molecular axis tilts from the normal orientation in
on Ni(ll1) in the c(4 x 2) superstructure. Values are distances as
determined by XPD [228].
order to enlarge the average distance between mole-
cules [234-2361. The equilibrium structure assumed is
shown in Fig. 24, on the left. This system has been
range 1831-1905cm-* to a CO bridge site. In a very studied in some detail in order to understand the elec-
convincing study based on the analysis of X-ray pho- tronic structure of the system [237-2401. In line with
toelectron diffraction data Bradshaw and coworkers Fig. 20 where the schematic band structure of an ad-
[227-2291 have shown that the adsorbate site over the sorbate system is shown, the present system has been
whole coverage regime remains the same and is a studied with angle resolved photoelectron spectroscopy
threefold hollow site as indicated in Fig. 23. The ob- and the band structure has been experimentally deter-
served shift in the stretching frequency is then purely mined [187]. Figure 25 shows the complete experi-
due to intermolecular dynamic dipole coupling. Note mental band structure in the occupied region, i.e. of the
that both the inequivalent threefold hollow sites (fcc 50, In, and 40 levels [237, 239, 2401. Included is the
and hcp) are occupied in this structure [228]. Another band structure in the unoccupied region as determined
important factor in chemisorption becomes obvious by by inverse photoemission. The 50, ln, and 40 levels
looking at the structures in Fig. 23, namely the coop- lead to twice the number of bands due to the non-
erativity of the process. There is a 3% expansion symmorphic space group symmetry of the system with
($0.07 A) of the outermost Ni-Ni lattice spacing. This two molecules per unit cell [234]. Following the bands
is meant here to stress the finding that although the through the Brillouin zone shows that the energetically
surface provides a particular site for adsorption, the close 50 and In bands hybridize. Also, one can clearly
final geometry is determined via the interaction with identify the C0(2n)-Ni(3d) backbonding states below
the adsorbate and therefore depends on its chemical the Fermi edge. The unoccupied 271 derived levels are
identity. This phenomenon is important in connection located above the Fermi edge. It is interesting to note
with the well known adsorbate induced reconstructions the different magnitudes of the band dispersions for the
of surfaces [135]. If the reactivity of the surface towards different levels. This is clearly due to the variations in
another adsorbate changes through the reconstruction interaction strength for the different molecular orbitals
then cooperative phenomena are essential for the over- depending on directionality and spatial extent. The
all chemical reactivity in the system. largest dispersions are exhibited by the n orbitals. In
Whereas in the above example the local structure fact, the 271 orbital shows the largest effects because
remains the same for increasing coverage, there are they are most diffuse and show large electron density
other cases where intermolecular interaction changes off the molecular axis. To summarize, the strong inter-
the geometry of the adsorbate. In the case of CO on molecular interaction is reflected in the adsorbate band
Ni(ll0) at low coverage CO molecules adsorb in two structure and mainly due to 71-n interaction.
different adsorption sites, namely on atop and on We now turn to the question of how the adsorption
bridge sites with vertically oriented axis, as shown in properties of a given molecule changes when we change
Fig. 24 [230-2331. The molecule-substrate bond in this the geometric structure of the surface keeping its
case is so strong that the system can tolerate even large
lateral intermolecular stress. At a coverage of 0 = 1 References see page 938
932 5 Elementarv Stem and Mechanisms

CO(2x11 p 2 mgI NI(1101

0
0
. .
0 1
LEE0
-6 X I

top l a y e r
-L- second Lay

-3. (100)
- 2-

(110)

Figure 26. Structure of the close packed surfaces of iron (bcc).

surfaces. The adsorption of nitrogen on iron is chosen

because of its importance in connection with ammonia
synthesis [244]. In particular, Ertl and co-workers [125,
1261 have investigated the structure sensitivity of dis-
sociative nitrogen adsorption on the low-index surfaces
of iron, i.e. the (loo), (110) and (111) surface ori-
entations. Figure 26 shows the arrangement of these
surface structures on top of the body-centered cubic
iron crystal. The (110) surface has a very low sticking
coefficient for dissociative adsorption while the most
open (1 11) surface has a much higher sticking coeffi-
cient [125, 1261. With a combination of photoelectron
spectroscopy [245] and vibrational spectroscopy [246-
2481 the important factors influencing this face specif-
124
A r
I
I:
+X icity have been uncovered. Briefly, on Fe(ll1) high
Y
[lo01 r 1701 resolution electron energy loss spectra (HREELS)
Kl, [248] are observed as a function of temperature (Fig.
27). At about liquid nitrogen temperature a dominant
Figure 25. Measured band structure in the range of occupied feature with a stretching frequency at 2100cm-' is
and unoccupied levels for CO(2 x l)p2mg/Ni(llO). The wave
vector K is determined along the two orthogonal directions in found. With angle resolved photoelectron spectroscopy
the surface Brillouin zone as shown at the top and its energy de- [245] it has been shown that this species is oriented
pendence according to Kll= ( 2 meh-2Ek,n)''2sin 8. perpendicular to the surface. It is most likely to be
bound to an atop site. The same species is found on all
low-index iron surfaces [244]. It is weakly held by the
chemical constitution constant. There are many exam- surface. Upon heating the system slightly above 100 K
ples in the literature. Again CO adsorption could be a second molecular nitrogen species shows up in the
chosen [241]. Also, hydrogen chemisorption [73] or vibrational spectra of Nz/Fe( 11 1) at a lower stretching
oxygen chemisorption [242, 2431, which has been stud- frequency (1415 cm-'). Again, photoelectron spectros-
ied and reviewed in detail by Christmann [73], Wandelt copy has been used to show that this species is bound
[242], Brundle [243] and others are prominent examples in a strongly tilted geometry, in line with the low
for the structure sensitivity of chemisorption on metal stretching frequency typical for side-on bonded dini-
 5.1 Chemisorption 933

15
N, IFe(ll1)
I
I 2100 I

z T=7L K
.-v,
c

C
01
c
U
N
0
E0

0
position on Fe(ll1) surface

Figure 29. Two-dimensional potential energy diagram for the

I\ I I
convesion of y-N2 (vertically adsorbed) to r-N2 (side-on bonded)
0 800 1600 2LOO [246-2481 on the Fe(l11) surface [249].
electron energy Loss [cm-']

Figure 27. Electron energy loss spectra of 15N2on Fe(ll1) as a back-donative bond via the unoccupied 7c orbital. The
function of surface temperature [248]. back donation will weaken the nitrogen-nitrogen bond
which finally leads to dissociation. Since both nitrogen
atoms are already in close contact with the metal sur-
face, this picture appears to provide a natural pathway
to dissociation. It is believed to explain the observed
strong face specificity of dissociative nitrogen chem-
top layer isorption on Fe surfaces. Figure 29 shows a semi-
empirical potential energy diagram for N2/Fe( 11 1)
second layer
where the pathway from the molecular precursor to the
third layer dissociative adsorption is shown [249]. The value for
W the activation barrier is based on experimental date
[250].
Figure 28. Proposed arrangement of N2 on Fe(ll1) [245]. Finally, we would like to have a look at the structure
sensitivity of transition metal oxide surfaces [215]. For
such systems [251, 2521 it is necessary to resort to some
trogen complexes. This species only exists on the sur- basic considerations about the electrostatics of ionic or
face within limited temperature range. Above 160 K partly ionic systems with respect to surface stabilities.
the stretching frequency typical for molecular nitrogen Figure 30 schematically shows the arrangements of
species disappears and only atomic nitrogen (460 cm-') planes in a crystal of rock salt (AB) structure for the
is present on the surface. This scenario is typical for the termination of (100) type on the left and of (1 11) type
(1 11) surface, while the existence of the intermediate on the right [254]. The (100) surface of an AB-type
species cannot be detected on the other low-index solid is the typical case for a nonpolar surface with
planes, i.e. (110) and (100) [244]. It is now generally vanishing dipole moments between the planes and full
accepted that the intermediate with the low stretching charge compensation within the planes. This arrange-
frequency is a precursor to nitrogen dissociation, and it ment leads to a converged, finite electrostatic surface
is thought that the (1 11) surface provides the sites, energy. Upon going to the (1 1 1) surface of an AB-type
necessary to assume the strongly tilted geometry [244]. lattice we create a polar surface. In this case there is no
Figure 28 shows the bonding geometry for the inter- charge compensation within each layer and there is
mediate species [245]. The nitrogen molecule can do- also a dipole moment within the repeat unit perpen-
nate both its lone pair as well as the 17c electrons into
empty metal orbitals, and at the same time establish a References see page 938
934 5 Elementary Steps and Mechanisms

stoblelnon-polar stablelpolar unstableipoiar

AB -type AB2-type AB-type
repeat repeat
vacuum VOCUUm units vacuum unlts

Figure 30. Stable and unstable surfaces of AB-type and ABz-type ionic crystals [253]

dicular to the surface. Consequently, the surface energy

LEED XPS 01s
does not converge but increases unbound as the num-
grazing excidence
ber of repeat units increases. In general, polar surfaces
are not unstable, as illustrated for the ABz-type solids.
Even though there is no charge compensation in the
plane, the dipole moment in the repeat unit perpendic-
NiO( 1 1I)/
ular to the surface vanishes, thus leading to a stable Ni( 1 1 1)
situation. Returning to polar surfaces of the AB-type to
consider the surface potential V in more detail [253],
2.n
V = -[Nb(20 - 1) + (1 - ~ ) b ]
NiO( loo)/
S Ni( 100)
where S is the area of the unit cell. Equation 31 gives
the surface potential as a function of the number of
layers N, their separation b, and the parameter CJ which NiO( 100)
describes the difference in charge of the surface layer cleaved
with respect to the bulk layer. It is quite obvious that
the reduction of the surface charge such that CJ = 1/2 515 550
leads to the disappearence of the first term in eq 31, Binding energy [ eV ]
and thus to a converging surface potential independent Figure 31. O(1s) XP spectra of a cleaved NiO(100) crystal: (a) a
of the number of layers. While this is only a qualitative grown NiO(100) film; (b) a grown NiO(l1l) film. The corre-
argument, it shows possible routes for the system to sponding LEED patterns are shown [254, 2551.
respond in order to stabilize polar AB-type surfaces.
Surface-charge reduction may be accomplished by re-
constructing [254], i.e. removing half of the ions, or by
the creation of steps. The latter leads to the coexistence ature [256]. At low temperature an ice layer forms
of A-terminated and B-terminated patches on the same which can be removed without residue by heating to
surface and thus to a microscopic charge compensa- room temperature. This indicates that a NiO(100) sur-
tion. Also, relaxations in the layer distance are ex- face does not dissociatively chemisorb water. The sit-
pected to occur in the near surface region which could uation is different for a NiO(100) surface containing
help to reduce the surface potential. In certain cases defects, as indicated by the much broader LEED spots
other causes of stabilization may be considered. Upon as compared with the cleaved surface [252, 2551. Here a
adsorption of H+, provided by exposure to water, for small feature is found at 2.2 eV higher binding energy.
example, OH- may form on an oxygen terminated It becomes particularly pronounced in the spectra if
surface thus effectively reducing the surface charge they are recorded at grazing electron excidence in order
[252]. Thus one would predict a strong structure sen- to amplify the surface sensitivity of the method. EELS
sitivity of water adsorption on oxide surfaces which, investigations have shown that the feature is due to
indeed, has been observed [254, 2551 and is exemplified hydroxyl groups on the surface. These hydroxyl groups
in Fig. 31. The O(1s) XP spectra are shown for three may be removed from a NiO(100) surface by thermal
different samples [255]. The lower trace shows the treatment. Exposure of the cleaned surface to water
spectrum of a cleaved NiO(100) surface with very low leads to the reappearence of hydroxyl, indicating that
defect concentration (sharp LEED pattern). The fea- water dissociatively chemisorbs on defect sites of a
ture is symmetric after cleavage and it remains sym- NiO( 100) surface. Dissociative chemisorption becomes
metric even after exposure to water at room temper- even more pronounced on the NiO(ll1) surface. The
 5.1 Chemisorption 935

Figure 32. Schematic drawing of OH-terminated (left), bulk-terminated (middle) and octopolar reconstructed (right) NiO( 1 1 1) surfaces.

upper trace in Fig. 31 indicates a rather high concen- dependence of adsorbate properties and especially en-
tration of hydroxyl groups at the surface. When (1 11) ergetics. Coadsorption of different chemical species is
polar surfaces are prepared they often become OH the general case in connection with the discussion of
stabilized, due to the electrostatic instability discussed intermolecular interaction. Intermolecular interaction,
above. In favorable cases such as NiO( 11l), the hy- however, is the basis for the understanding of chemical
droxyl groups can be removed from the NiO(ll1) sur- reactions between adsorbed species. There is such a
face as water by thermal treatment. As a consequence, vast literature on the subject [260] that a compre-
the OH-free unstable surface reconstructs. The most hensive and exhaustive review of the field cannot be
stable reconstruction of a polar surface of an ionic provided here. Nevertheless, we would like to briefly
crystal is, according to Lacman [257] and to Wolf address two coadsorbate systems where a broad
[258], the so-called octopolar arrangement, shown in knowledge has been accumulated over the years. To
Fig. 32 in comparison to the ideal (1 x 1) surface. The represent the limiting cases we resort again to carbon
octopolar reconstruction leads to p(2 x 2) unit cell on monoxide as one component and study its coadsorp-
the surface and is characterized by the removal of three tion with an electropositive additive, and also with
out of four oxygen ions in the first layer (in the case of electronegative additives. Needless to say, all aspects
an oxygen terminated surface) and one out of four discussed above for chemisorbate systems in general
nickel ions within the second layer [254, 2591. The third are important, even at a more complex level, for
layer contains then again a complete hexagonally close coadsorbate systems. In the latter case it is necessary
packed oxygen layer. A p(2 x 2) reconstruction has to consider the different chemical identities of the ad-
been observed for iron oxide and nickel oxide but only sorbed species, and more importantly their influence on
in the latter case are there clear indications that an the electronic structure of the substrate, and on each
octopolar reconstruction has actually taken place [255]. other. In other words, the aspect of cooperativity that
Readsorption of water leads to a lifting of the re- adsorbates and substrate interfere and determine each
construction and the reoccurrence of the (1 x 1) struc- others properties becomes particularly noteworthy.
ture [254]. Note for completeness that the reconstructed The most prominent and most frequently studied
surface exhibits a considerably higher chemical activ- electropositive additives are alkali metals. Several
ity, for example in the DeNO, reaction, than the comprehensive reviews have been published on the
hydroxyl-covered surface which is basically inactive subject which provide more detailed information [260-
towards further chemisorption [256]. In other words, 2621. Characteristically, adsorption of alkali leads to
water desorption and readsorption leads to a strong dramatic changes of the work function of the system
change in the chemical activity of certain crystallo- [260-2621. An example, K on Pt(l1 l), is shown in Fig.
graphic planes of oxide surfaces which may be relevant 33 [263]. In general, small alkali coverages already
with respect to the catalytic activity of powders of real lower the workfunction considerably before monolayer
samples. coverage is reached (in the present case more than
Previous sections have discussed the interaction be-
tween adsorbed species in connection with the coverage References see page 938
936 5 Elementary Steps and Mechanisms

1.5-
KIPt(ll1)

-2
T=300 K
aI

-
c 00-

Ib
0 I
I I
Q

0 1.5
-

0.0-
0.1 0.2 0.3 I I I
600
I I I
potassium coverage 8 300 LOO 500
Figure 33. Work function of Pt(ll1) as a functionof potassium
temperature [K]
coverage at 300 K [263]. Figure 34. Thermal desorption spectra of (a) clean and (b) po-
tassium covered (0 = 0.015 ) Pt(1 l l). Various CO coverages are
plotted indicating the population of sites close to the alkali at low
4eV). Before completion of the first monolayer cov- CO coverage. On the unmodified Pt(ll1) surface at higher cover-
erage the work function reaches a minimum, turns ages similar sites are observed [265].
around and then approaches, for increasing coverages,
the value of the work function of the bulk alkali [260-
2621. We are concerned only with the regime of alkali 1565
coverages below or close to monolayer coverage. It is
generally accepted that in the low coverage regime the
alkali atoms transfer charge towards the substrate, set-
ting up a strong adsorbate-surface dipole which lowers
the work function, hinders the alkali atoms to cluster
on the surface, and allows them to adsorb as isolated
atoms well separated from each other [264]. The energy
needed to remove the alkali from the surface has been
determined from TDS and calorimetric investigations
to vary between 130 and 250 kJ mol-'. Coadsorption
of CO onto such an alkali-precovered surface leads to
considerable effects on the energetics of the CO-sub-
strate interaction as compared with the pure CO ad-
I
sorbate. TD spectra of the pure and the coadsorbate I I I I 1 1 !
0 1000 2000 3000
system are shown in Fig. 34 [265]. The molecule still energy LOSS [cm-'1
adsorbs associatively on the surface but note that the
dissociative sticking coefficient increases considerably Figure 35. Electron energy loss spectra of CO on clean (lower
in the coadsorbate as has been observed for several trace) and K-modified (upper trace, OK = 0.02) Pt(l1l) [267].
CO-alkali coadsorbates [260]. The adsorption en-
thalpy increases for a typical CO-metal system from
130 kJ mol-' to 197 kJ mol-' for the alkali-adsorbed adsorbate. The explanation is straightforward: elec-
system [266]. There are coverage dependences as well, trons from the electropositive additive are transferred
but we shall concentrate here on a single coverage. To either directly or via the substrate surface into the un-
learn more about how the observed energetic changes occupied CO antibonding orbitals thus weakening the
come about, consider the vibrational spectra of the CO bond [261]. Simultaneously, this stabilizes the CO-
system shown in Fig. 35 [267]. As compared with the alkali interaction on the substrate surface and enhances
pure CO adsorbate the CO stretching frequency in the CO substrate interaction. It turns out, however, to
the coadsorbate is lowered by several hundred wave- be rather difficult to exactly partition the interaction
numbers, indicating a weaker C-0 bond in the co- strength between CO-alkali and CO-substrate. It was
 5.1 Chemisorption 937

Table 5. Desorption energies for some transition metal surfaces modified by electronegative additives.

Adsorbate Surface Modifier E: (kJmol-') References

co Ni( 100) - 140 270

P(2 x 2)s 90
110
C(2 x 2)s x 30
P(2 x 2)O 120
P(2 x 2)N x 90 27 1
(2 x 2)P4gc 93 272
Ni( 111) - 140 273
P(2 x 2)s 91 273
P(2 x 2)O 105 274
Pd( 100) - 160 275
P(2 x 2)s 86
60
Pt(l11) - 154 276
P(2 x 2)s 106 276
P(2 x 2)Se 110 271
Ru(0001) - 170 278

H Ni( 100)
P(2 x 2)s
-
P(2 x 2)s
105
102 5*
84 10
278
279

C(2 x 2)s 48 & 16

Fe( 100) - 87 50 280
P(l x 1)O 60 & 10 280
Pd( 100) - 85 28 1
0.15s 49 28 1

believed for some time that in the coadsorbate the CO- leads to a decrease in the desorption energy. This may
substrate interaction changes dramatically, leading to a have different reasons. It could be due to repulsive
change in the CO bonding geometry on the surface, i.e. modifier-CO interaction, or it could be due to the fact
from a vertically bound CO in the pure adsorbate to a that the modifier blocks those sites of the surface lead-
side-on-bonded CO in the coadsorbate [268]. Near ing to the strong CO-substrate interaction for the clean
edge X-ray absorption fine structure (NEXAFS) has surface [260]. As judged from the vibrational data the
again been instrumental in showing that this is not the influence of an electronegative additive onto the CO
case [269]. In fact, CO remains vertically bonded on stretching frequency is much less pronounced if com-
the surface and possibly interacts side-on with the pared to the electropositive additives [282]. Often, in-
coadsorbed alkali atom. The side-on geometry was stead of a strong red shift as observed for electro-
particularly attractive because, similar to the case of positive coadsorbates, a weak blue shift is observed
nitrogen adsorption, this geometry could easily explain which in certain cases may even lead to stretching fre-
the increased dissociative sticking coefficient [260]. quencies higher than in the gas phase [282]. In this case
However, as it stands today, either the molecules tran- it is even more difficult to disentangle the various con-
siently pass through such a side-on geometry before tributions, i.e. direct and substrate-mediated inter-
dissociation, and the concentration is so low that it actions. The wealth of data presently available suggest
cannot be identified, or dissociation can also start from than an electronegative additive mainly influences the
vertically oriented, but electronically strongly modified substrate locally, i.e. in its direct vicinity, in the sense
CO. The described interaction between alkali and CO that (a) the adsorption sites which involve substrate
in a coadsorbate may be considered as special case of atoms directly coordinated to the modifier are blocked,
alkali promotor action, which is well established in and (b) the adsorption sites sharing some substrate
catalysis [260]. atoms with the modifier are substantially perturbed.
A completely different situation is encountered when This means, as schematically shown in Fig. 36 [260],
we coadsorb carbon monoxide with an electronegative that for a fcc(lO0) plane and a modifier residing in a
species. Table 5 [260] collects desorption energies for fourfold site four atop sites and four bridge sites are
carbon monoxide absorbed on transition metals modi- blocked, and eight bridge sites, four close and four re-
fied by electronegative additives. In general, and op- mote fourfold sites are perturbed. With increasing
posite to the effect observed for the electropositive
modifier, coadsorption with electronegative modifiers References see page 938
938 5 Elementary Steps and Mechanisms

nitrides, and oxides are formed [260]. Then, of course,

the activity of the surface is determined by the proper-
ties of the new types of compounds formed. Often
island formation is encountered in these systems which
leads to a considerable reduction in the relative number
of modified surface sites because the effect is restricted
to the neighbors of the modifier island boundary.
Summarizing, in such systems the problem of coopera-
tivity, i.e. the phenomenon that the adsorbate and
coadsorbate create their own active sites which are not
present on the clean surface becomes particularly im-
portant. The future study of these effects in chem-
isorption is essential, even under ambient conditions, in
order to identify which are the key effects that operate
during catalysis at a microscopic level.

Figure 36. Schematic representation of the influence of an ad-

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253. P. W. Tasker, J. Phys. C 1978,12,4977;Phil. Mag. A 1979, gins to enrich experimental information by providing
39, 119. results of model systems that are not easily accessible
254. F. Rohr, K. Wirth, J. Libuda, D. Cappus, M. Baumer, H.-J. to experiment. In addition they allow us to probe the
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255. D. Cappus. M. HaDel, E. Neuhaus, M. Heber, F. Rohr, nature of transient surface species such as short-lived
H.-J. Freund, Surf Sci., 1995, 337, 268. intermediates and activated complexes. Nonetheless,
256. G. Illing, Thesis, Ruhr-Universitat Bochum, 1990. the qualitative theoretical framework that has been es-
257. R. Lacman, Colloq. Znt. CNRS 1965, 152, 195. tablished over the past 50 years remains highly rele-
258. D. Wolf, Phys. Rev. Lett. 1992, 68, 3315. vant. It provides a sound framework for conceptual
259. C. A. Ventrice Jr., H. Hannemann, Th. Bertrams, H. Ned-
dermeyer, Phys. Rev. B 1994, 49, 5773. analysis and interpretation. Computation and experi-
260. M. P. Kiskinova, Poisoning and Promotion in Catalysis ment then can be used to test ideas on the electronic
Based on Surface Science Concepts and Experiments, Studies and structural parameters which control the geometry,
in Surface Science and Catalysis Vol. 70, Elsevier, Am- energetics, and dynamics of the chemisorbed molecule.
sterdam, 1992.
261. H. P. Bonzel, Surf Sci. Rep. 1987, 8, 43. Two different schools of thought in chemisorption
262. H. P. Bonzel, A. M. Bradshaw, G. Ertl (Eds), Physics and theory can be distinguished. The first is born out of the
Chemistry of Alkali Metal Adsorption, Material Science solid-state physics community, while the second origi-
Monographs Vol. 51,Elsevier, Amsterdam, 1989. nates from the theoretical chemistry community. For-
263. M. P. Kiskinova, G. Pirug, H. P. Bonzel, SurJ Sci. 1983,
133, 321. mal chemisorption theory dates back to the 1950s and
264. M. Scheffler, Ch. Droste, A. Fleszar, F. Maca, G. Wa- 1960s where the relevant electronic factor for chem-
chutka, G. Barzel, Physica 1991, 1728, 143. isorption was considered to be the local electron den-
265. L. J. Whitman, W. Ho, J. Chem. Phys. 1989, 90, 6018. sity of states at the Fermi level. This is especially true
266. H. Pfniir, P. Feulner, D. Menzel, J. Chem. Phys. 1983, 79,
4613.
in catalysis. Magnetic and conductivity measurements
267. J. E . Crowell, E. L. Garfunkel, G. A. Somojai, Surf: Sci. were usually interpreted in these terms. With progress
1982,121, 303. in solid state physics, theory became more refined and
268. T. E. Madey, C. Benndorf, Surf Sci. 1985,164, 602. surface physicists developed a more physically realistic
269. F. Sette, J. Stohr, E. B. Kollin, D. J. Dwyer, J. L. Gland, J. view of the surface chemical bond. Koutecky [l],
L. Robbins, A. L. Johnson, Phys. Rev. Lett. 1985, 54, 935.
210. J. L. Gland, R. J. Madix, R. W. McCabe, C. DiMaggio, Newns [2], Grimley [3], and Schieffer [4]are considered
Surf: Sci. 1984, 143,46. to be the founders of formal chemisorption theory.
271. W. M. Daniel, J. M. White, Surf Sci. 1986, 171, 289. Many of their concepts remain today and are the basis
212. J. C. Bertolini, B. Tardi, Surf: Sci. 1981,102, 131. of our current views on chemisorption. Formal chem-
213. M. Trenary, K. J. Uram, J. T. Yates, Jr., Surf: Sci. 1985,
157, 512. isorption theory is therefore the subject of the fist sec-
274. Xu Zi, L. Surnev, J. T. Yates, Jr., unpublished results. tion. One of the most important results derived from
215. T. Yamada, Z. Runsheng, Ya. Iwisawa, K. Tamaku, Surf formal chemisorption theory was the rationalization of
Sci. 1988, 205, 82. strength of adsorbate-surface interaction in terms of
276. M. Kiskinova, A. Szabo, J. T. Yates, Jr., J. Chem. Phys. the ratio of adsorbate-surface-atom strength versus the
1988,89,1599.
211. M. Kiskinova, A. Szabo, J. T. Yates, Jr., Surf: Sci. 1990, interaction energy between the surface atoms. It raised
226, 231. the issue of the existence of the concept of a surface
278. J. L. Brand, M. V. Arena, A. A. Deckart, S . M. George, J. adsorption complex, hence identifying chemisorption
Chem. Phys. 1990,92, 4483. physics with surface complex chemistry.
279. S . Johnson, R. D. Madix, Surf Sci. 1981, 108, 77.
280. J. Benziger, R. J. Madix, Surf: Sci. 1980, 94, 119. The theoretical chemical application of surface
281. M. L. Burke, R. J. Madix, Surf: Sci. 1990, 237, 1. chemical bonding theory, highlighted next, is related to
282. J. G. Chen, W. Erley, H. Ibach, Surf: Sci. 1989,224, 215. formal chemisorption theory as developed in surface
physics, but concentrates on quantum chemical con-
cepts as the electron distribution over bonding and
antibonding orbital fragments [5, 61. It will be seen that
5.1.2 Chemisorption Theory both approaches complement each other. The notion
of a surface molecule relates to the surface physicists’
R. A. VAN SANTEN
AND M. NEUROCK concept of surface state.
The final section provides an overview of the current
understanding of the factors that govern the physical
5.1.2.1 Introduction chemistry of chemisorption. Our understanding of the
factors that determine the site preference of surface
Computational quantum chemistry and solid state dependence of chemisorption is summarized. We dem-
physics have reached the stage where quantitatively re- onstrate many of those concepts through a series of
liable predictions on the interaction of small and mod- first-principle quantum chemical results on different
erate sized molecules with transition metal clusters or example systems. The results allow us to specifically
surfaces are now possible. Computation therefore be- quantify different aspects of the interaction, such as
 5.1 Chemisorption 943

lateral interactions and adsorbate and surface structure

relaxation. The first-principle nature of the calculations
leads to very good overall comparisons with available
experimental data. This chapter focuses specifically on
chemisorption to transition metal surfaces.

5.1.2.2 Formal Chemisorption Theory

A Introduction
Quantum theoretical models of chemisorption were in-
itially developed within the framework of two idealized Figure 1. Parameters in the tight-binding model of chem-
theories of the electronic structure of the solid state: isorption.

(i) the tight-binding approximation;

(ii) the jellium model. In general @+ds and +j are nonorthogonal:

In the tight-binding approximation discussed first, the (4)

one-electron wave function Yk are considered to be a
linear combination of atomic orbitals yi: This nonorthogonality has to be explicitly included
into chemisorption theory to account for the Pauli re-
I
pulsive part of the interaction energy. The quantum-
mechanical solution of the chemisorption problem
This approximation applies best to the d electrons of has been found, when the coefficients af and eigenvalue
the transition metals and has been used effectively by energies Ei are known. A very useful expression is the
the theoretical chemistry community, to study chem-
local density of states p , ( E ) , that gives the probability
isorption. In the free electron or jellium model, dis-
of finding an electron with energy E in adsorbate orbi-
cussed in the second section, the one-electron wave
tal i. In the case where the adsorbate is described by
functions are, instead, considered as linear combina-
a single atomic orbital yo with energy ZO, the corre-
tions of plane waves: sponding expression is

The jellium model best applies to the s and p valence

electrons as in the alkali metals. The consequences of T ( E ) and A ( E ) are the line width and energy shift
electron-electron interactions are explored effectively. functions and are given by
The two approaches can be coupled to form a hybrid
model as in effective medium theory [7], where the i
tight-binding description is used for the d electrons and
the jellium approach is used to describe the s and p
valence electrons. We will limit the discussion in this (7)
chapter to a review of the main results and concepts. A
more extensive treatment of the theoretical basis of Figure 2 depicts the energy dependence of po(E)
these methods and derivations is available [6]. sketched as a function of the interaction energy be-
tween adsorbate and surface. In the weak adsorption
B The Tight-Binding Quantum Theoretical Model of limit, T ( E ) and A ( E ) can be considered energy inde-
Chemisorption pendent. The maximum electron density of states on
Within the tight-binding approximation (Fig. l), the the adsorbate appears to be shifted by A and is broad-
general form of the one-electron wave function that ened by a Lorentzian distribution over width 2r.
describes the electronic structure of the chemisorption The dependence on the interaction energy can be
system is deduced by substituting the expression for tight binding
wave function in the bulk
(3)
1 i
The wave functions $j correspond to the undisturbed
substrate, and qldSare the one electron wave functions ~

of the adsorbing molecule. References see page 957

944 5 Elementary Steps and Mechanisms

upper band edge

E 1 upper hand edge

I, lower band edge

----f ---c ----c
lower band edge p (El p (E) p (El
no interaction weak interaction intermediate
interaction

increasing adsorbate -
metal surface interaction
’ a b C
Figure 3. Adsorption-induced changes in the surface local den-
surface sities of states (schematic).
weak intermediate
free atom
adsorption adsorption mo’ecuie
limit

Figure 2. Adsorbate local density of states as a function of

adsorbate-metal surface interaction (schematic).

into eq 5-7 for T ( E ) and A ( E ) .In the situation where

I

‘s
A s ( E )= -( E - E,) (15)
the adsorbate orbital yo interacts only with one surface zb - 1
atomic orbital eqs 6 and 7 reduce to where z , is the number of nearest atom neighbors of
the surface atom, Zb is the number of nearest atom
neighbors in the bulk, and p the overlap energy integral
A ( E )=
1 dE’- T ( E ’ )
E-E’
between metal atomic orbitals (see Fig. 1). The result-
ing energy dependence of ps(E)is sketched in Fig. 3.
The bulk electrons are contained in an electron band
of width

4Jzb-Ii~i
The symbol $’ in eq 10 means that only the principal This width describes the degree of delocalization of the
part of the integration has to be computed. P’ is given by bulk electrons. It is proportional to the overlap energy
integral of the metal atomic orbitals and increases with
P’ = (ddSI/HlylL) (12) the number of metal atom neighbours.
The delocalization of the electrons in the surface is
This is the overlap energy integral between the adsorb- less and, hence, the surface bandwidth is smaller. Sub-
ate orbital and surface atomic orbital qsps(E) is the stituting expression (1 3) into (9) leads to the following
surface local density of states. Its general form, shown line width function:
here, is similar to eq 5: or2

In the weak interaction limit,

T s ( E )and As(,?) contain the information on the elec- R12
tronic structure of the solid itself, and x s is the energy
of the surface atomic orbital. Expression 13 can only
be evaluated analytically by making further simplify- provided that as z 10.The more general case is dis-
ing assumptions about the bulk electronic structure. cussed in subsection D. It is useful to study the inter-
Useful analytical approximate expressions for Ts( E ) action system in this limit.
and A s ( E ) ,correct up to the second moment of the The local electron density of states on the adsorbate
electron energy distribution (eqs 6 and 7) are: in the weak adsorption limit is sketched in Fig. 2. The
 5.1 Chemisorption 945

adsorbate orbital electron density is broadened into This is the same result that would be derived from the
a Lorentzian distribution around a slightly displaced recombination of a free surface atom and the adsorbate
adsorbate orbital energy ao. Electrons on the adatom orbital. Now, as also sketched in Fig. 2, two sharply
with energy less than a0 gain in energy compared to defined energy states appear outside the surface elec-
the nonchemisorbed situation. Electrons with energy tron energy band. The energies correspond to the
higher than NO are destabilized with respect to NO. The bonding and anti bonding molecular orbitals of the
chemisorption energy will therefore depend on the surface complex. The first order correction to eq 19 is
electron distribution of the electrons on the substrate, the localization energy of an electron on a surface
which effectively determines their distribution over atom. This relates to the sublimation energy of a sur-
bonding and antibonding fragment orbitals. face atom into the gas phase and can be easily deduced.
In the situation where the single electron of the ada- In the near surface molecule limit the interaction en-
tom and the Fermi level (the highest occupied surface ergy becomes
orbital) of the metal have the same energy a0 (prior to
chemisorption), the interaction energy equals E,"n;s'(a0 = E F )= 20' - (20)
FZ 28' -a,& x 0 (21)
where a is a numerical constant that depends on sur-
face electron occupation.
The localization energy is proportional to the square
This is the interaction energy corresponding to the root of the number of surface atom neighbors and the
weak adsorption limit. metal-metal overlap energy integral. Again, we find
The interaction energy decreases with increasing that the chemisorption energy decreases with increas-
delocalization of the surface electrons. The larger the ing delocalization of the surface electrons. In the sur-
width of the surface local density of states, the lower face molecule limit, chemisorption becomes corrosive.
the interaction energy. This result also implies that the The metal-metal bonds next to the surface complex
energy of interaction with a coordinatively unsaturated weaken.
surface (small z,) is larger than to a higher coordi- The results discussed so far are generally valid even
natively saturated surface. When the parameter when more sophisticated computational approaches
are used. Critical to the results discussed so far is the
p=- assumption that only bonding orbital fragments be-
zsP2 tween adsorbate and surface are occupied. We will now
which measures the relative value of adatom surface show that the results can qualitatively change when
atom interaction versus that between the metal atoms, antibonding orbital fragments become occupied. This
increases, the Lorenzian electron energy distribution on becomes especially relevant when one is interested in
the adatom broadens and changes shape (see Fig. 2). A differences in adsorption energy as a function of sur-
double peaked structure evolves, which can become face atom coordination number. This is the subject of
wider than the valence electron energy band of the the next topic which analyzes chemisorption to the
surface. The doubly peaked energy distribution in- (111) surface of a face centred cubic metal. The ad-
dicates the formation of a surface molecule. The low- sorbing molecule can choose between four different
energy peak corresponds to the binding part of the adsorption sites: atop, twofold, and two threefold sites.
electron density, the high-energy portion of the distri- For higher coordination sites, eqs 9 and 10 are no
bution corresponds to the antibonding part of the longer valid for evaluating I-(E). One now has to find
electron density. Similar features arise in the local den- the linear combination of surface atomic orbitals, that
sity of states of the surface atom due to its interaction correspond to the local symmetry of the adsorption
with the adatom (Fig. 3). The bonding and antibond- site. These are the group orbitals q~i[8, 91. The surface
ing electron density in the surface molecule is also atom local density of state in eqs 9 and 10 are now re-
controlled, to a significant extent, by the contribution placed by group orbital local density of states p t ( E ) .
of the surface electron density. In the surface molecule For instance, in twofold coordination, two s atomic
limit, orbitals from each surface atom are combined to form
the surface group orbital
>>I
ZSP2

with a0 be equal to EF the interaction energy becomes:

References see page 957

946 5 Elementary Steps and Mechanisms

-3.6

-3.2

-2.8

energy
-2.4
Figure 4. Group orbitals and their energies.

4
-2.0

and the group orbital density of states

(4;lw -w4;) -1.6

-
The overlap energy integral becomes

(VOIw;) = m’ 0 4 0.8 1.2 1.b

%I
2.0

The general expression for T ( E )is now Figure 5. Bethe lattice results. Interaction energies of onefold,
twofold, and threefold adsorbed hydrogen, as a function of Bethe
T ( E )= nnp’2p:(E) lattice atomic orbital electron occupation. For the points (a,b ) ; a
is the hydrogen atom coordination number; and b the number of
where n is the coordination number of the adsorbate. Bethe lattice neighbor atoms nearest neighbor of atom involved
For this more general case, the interaction parameter p in the adsorption bond.
becomes

The binding energy is proportional to the square root

of the adatom coordination number. The apparent
It might be expected that the linear dependence of p on preference for higher coordination sites strongly de-
n would lead to a linear dependence of the interaction pends on the distribution of electrons over bonding
energy between adsorbate and surface coordination and antibonding absorbate-surface atom fragment
number n. This is, however, only the case in the limit orbitals. When the electron occupation of antibonding
of weak adsorption ( p << 1) and when bonding adsor- orbitals dominates, low coordination sites may become
bate-surface orbital fragments are occupied. preferred.
It is found in the surface molecule limit that the This is illustrated by a set of model calculations
bonding orbital is the low-energy solution of the which use the Bethe lattice approximation to describe

I
equation the embedding of a surface cluster in a metal lattice.

I
n = 1; x(n) = 0 Each metal atom is represented by one s atomic orbital
npI2 and the interaction energy with a hydrogen atom is
=O n=2; x(n)=l
(No -E)-
as + x(n)p - E n = 3; x(n) = 2
computed for varying metal electron occupation. This
simulates the analogous change in d bond filling of
(24) transition metals. This implies that the metal Fermi
Equation (24) corresponds to the clusters depicted in level now varies as a function of surface orbital elec-
Fig. 4. The group orbital and its group orbital energy tron occupation. The electron-electron interaction be-
are also listed for the situation where an asymmetric p tween the electrons on the adsorbate therefore had to
orbital interacts with surface s atomic orbitals in a be explicitly included in the calculation. The calcu-
twofold coordination site. lation results are shown in Fig. 5.
In the surface molecule limit the bonding orbital According to the Newns-Anderson model [2] in the
fragment energy becomes weak adsorption limit ( p << l), the paramagnetic state
on hydrogen becomes most stable. In Fig. 5 the regime
E,” = a, + fib’ (a, = a, = a ) (25) where this occurs (high metal valence band electron
 5.1 Chemisorption 947

Embedding of the surface complex clusters into the

A Bethe lattice leads to a broadening of the group orbi-

/l
tals electron densities. This is due to electron delocali-
zation. The maximum surface group electron density

0.6 1 3 - 1
EF
I
1
/I
/ . I
moves to lower energy with increasing adsorbate coor-
dination number, similar to the corresponding group
orbital energy in the isolated metal clusters (Fig. 4). As
a consequence, when comparing bonding at the same
surface, i.e. constant value of E F , the antibonding ad-

o'2k
0 ''/ -14 -12 -10 -8 -6
I
-4
I I
-2 0
I I
2
I
4
4
I
6
sorbate-metal surface fragment orbitals for the atop
geometry are less occupied than those that correspond
to the high coordination geometries. Therefore when
the electron occupation increases, the bond energies for
the high-coordination sites will decrease more readily
E
than those for the low-coordination sites.
Figure 6. Group orbital local density of states on Bethe lattice The emphasis of the tight-binding approximation is
representing (1 11) surface of face centred cubic lattice [ 181: on covalent binding aspects. Effects due to electrostatic
I . Surface group orbital local density of states of single atomic
orbital. screening are more appropriately handled by in the
2 . Surface group orbital local density of states of group orbital jellium model descriptions, to be discussed next.
1
-(d + ulil C The Free-Electron Approach to Chemisorption:
Jz Jellium Model
3. Surface group orbital local density of states of group orbital
Within the free-electron approximation the discrete at-
1 traction potentials due to positive nuclei are replaced
-(ul3 + $4+ $4)
Jz by a continuous electrostatic background. The charge
4. Surface group orbital local density of states of group orbital density is chosen such that attraction by the electrons is
1 equal but opposite in sign to the electron-electron re-
pulsion energy. This is the so-called jellium model. It is
possible to combine a free-electron calculation for the s
and p valence electrons with a tight-binding description
occupation) is indicated with broken lines. Results pre- for the interaction with the d valence electron bond.
sented are for hydrogen adsorbed atop, twofold, and This is the essence of effective medium theory [9]. The
in threefold coordination. The metal surface atom co- advantage of free-electron theory is that explicit ex-
ordination number is also varied, in order to compare pressions for kinetic, exchange, and correlation energy
adsorption between open and more dense surfaces. are known as a function of electron density. In contrast
Within the surface electron density regime presented, to the tight-binding approaches, electrostatic interac-
it is found that the interaction energy for the atop de- tions can be described rigorously within free-electron
scribed configuration moves through a maximum value models. Density functional theory (DFT) approaches,
(actually a double maximum) and that the interaction which include accurate descriptions of the discrete
energies for the twofold and threefold coordination atomic potentials have been implemented in sophisti-
sites decrease with metal valence electron occupation. cated computational schemes and predict adsorption
At low valence-electron occupation where only bond- properties in close agreement with experiment. They
ing adsorbate-metal fragment orbitals are occupied, are regarded as computational extension of the free-
the expected preference for bonding is for high coordi- electron/tight-binding methods [ lo]. The exchange and
nation sites. correlation energy functionals used are based on jel-
This leads to higher interaction energies for the open lium-type expressions. Using the variational principle,
surface. However, as the valence electron occupation differential equations for the wave functions can be
increases, both these trends invert. This inversion arises formulated, and solved for limited and infinite systems.
from the now very different distribution of electrons The first success of the jellium model was the pre-
over bonding and antibonding surface fragment orbi- diction of the work function changes as a function of
tals for the same metal valence electron occupation. adsorbate concentration. The presence of a surface can
This is due to the very different group orbital local be simulated within this model by choosing a coor-
density of states of the surface electrons that interact dinate, such that the positive background potential
with the adatom when surface coordination is varied. Vt,(r) is positive when x < 0, but equal to zero when
The corresponding group orbital LDOS at different ~ ~~

coordination sites are shown in Fig. 6. References see page 957

948 5 Elementary Steps and Mechanisms

rn x=o
"t

x-
w
c 2

-2
ioc
-4
Figure 7. Potential energy at a surface with low electron density
atom adsorbed according to the free-electron model (schematic).
0 0.01 0.02 0.03
no(a.4

Figure 9. Embedding energies of He, H, Li, B, N, C, 0, and Ne

in a homogeneous electron gas as a function of electron gas den-
sity [I I].

where r is the adsorbate surface distance and 2 the free-

electron screening length. A similar result is found for a
positive charge, which will attract electrons. This image

I
charge screening effect will therefore alter the effective
energy levels of adsorbate molecules bound to con-
x=o _c
ductive surface. Charges become stabilized due to the
induced image potentials. The basic idea of effective
medium theory [9] is to replace the density of an ad-
Figure 8. Electron density profile near a surface, x is the surface sorbing atom by that of the jellium substrate. The em-
plane.
bedding energy,
AE = AEernb[no(?)]
x > 0. If the electron density remained unchanged up
to the surface defined by x = 0, vb(r) would be equal is equal to the difference in energy between the com-
to -n+. This is sketched in Fig. 7 . bined atom and host system minus that of the sepa-
However there is a spillover of electrons due to their rated atom and the host, where no(?) is the density of
finite kinetic energy and the real electron density gen- the host. Curves for A(E)emb are shown in Fig. 9. As
erates a surface dipole. This is depicted schematically expected the interaction with Ne is repulsive, due to
in Fig. 8 . Pauli repulsion even at very low densities. For oxygen,
Adsorption of an atom, as for instance an alkali the attractive interaction reaches a maximum for a
atom, can be simulated by adding additional potential particular density because it will readily accept elec-
density (see Fig. 7), corresponding to that of the ada- trons. Above the substrate density that corresponds to
tom. A lower potential will result in electron backflow the interaction energy maximum antibonding adsor-
from the adsorbate into the metal, resulting in a re- bate metal surface orbitals become occupied.
duced work function. A higher potential will attract In effective medium theory, the interaction energy
electron density with an opposite effect. The charge includes an induced image potential interaction term
that develops on the adsorbate is screened by electron- computed from the free-electron part. The contribu-
electron attractions. For instance a negative overall tions from d-electron interactions computed within the
charge in the regime 0 < x < d , will push away surface tight-binding model discussed in subsection B are ex-
electrons so that a positive charge 6 develops. The re- plicitly included. The effective medium theory, while
sulting image potential attraction is still approximate, is quite powerful because of the in-
clusion of electrostatic terms. It has especially been
6= very useful in the analysis of alkali coadsorption effects
Ei,
4r + 2
=-
WI.
 5.1 Chemisorption 949

D The Quantum Chemistry of Chemisorption a

- Energy diagram Bond Order Overlap Molecular Orbital
I l
Hoffmann has been instrumental in developing and
demonstrating the extension of the tight-binding ap-
proximation to relate the surface electronic structure to
the nature of the chemisorbed state [ 5 ] . This is im-
plemented in his extended Huckel (EHT) molecular
orbital approach, which has been extensively used to
analyze and understand chemisorption in many dif- a :
ferent catalytic systems. The simplicity of the EHT -\

approach makes it quite easy to explore how changes

in electronic structural parameters affect changes in
chemisorption. This is certainly an advantage for
this approach. The main limitation of the approach
is that it can only provide qualitative results and
trends. Quantitative results require more extensive, b
-
The bond energy equals: 2E + 2e - 4a = 4 ( P - as )S
first-principle theoretical treatments. Nonetheless many I.S*
important insights and concepts about chemisorption Definition of pk= ,kcks
Bond Order Overlap
can be explored in the framework of the EHT approach. - IJ I 1 lJ

Many of these concepts can then be further verified Figure 10. Extended Hiickel molecular orbitals and energies for
by more detailed quantitative ab initio or density func- hydrogen.
tional methods as will be discussed. We review here the
chemisorption of CO and CH3 to illustrate the quan-
tum chemical description of chemisorption. The EHT &-2 ~

method uses the same functional form of the one-elec- &.I - E

T-..
tron wave functions described for the tight-binding ap- donation- .
~.
proach in eqs 1 and 3. The extended Huckel method

+-
EF
explicitly includes nonorthogonality of the atomic backdonatiopc ~.
-.
orbitals (eq 4). The important interaction term that &+1
depends on orbital overlap, S,, is Pauli repulsion. This 11 Pauli repulsion Eb
E+2
is responsible for the repulsive part of the potential
energy curve for the interaction energy of a chemical adsorbate surface metal surface
orbitals electron distribution
bond. Pauli repulsion arises for the exclusion principle
that states that electrons of the same spin cannot Figure 11. Frontier molecular orbital scheme for adsorbate-
occupy the same orbital. surface interaction.
As illustrated in Fig. 10, inclusion of orbital overlap
leads to larger destabilization of antibonding orbitals
than bonding orbitals. Hence when bonding as well as given in eq 28. It is a relation that depends on the
antibonding orbitals are occupied, the overall inter- group orbital density of states around the Fermi level
action becomes repulsive. In the interaction between s multiplied by terms that depend on the electron occu-
atomic orbitals. Pauli repulsion is linear in the coordi- pation of the valence electron bond:
nation number of the adsorption site:
E,,,(Pauli) = 4n($ - xS)S
(27)
z 4ns2
Hence Pauli repulsion favors bonding to low coordi-
nation sites. where w* =weak interaction limit. Expression 28 pro-
The attractive part of the chemisorption energy can vides an approximate relationship between the electron
be found from the interaction between occupied frag- density near the Fermi level and the chemisorption en-
ment orbitals and unoccupied fragment orbitals (fron- ergy. ~ , ( E Fis) the group orbital local density of states
tier molecular orbital theory). This is illustrated in Fig. at the Fermi level averaged over an energy width of
11.
In the weak interaction limit, the attractive part of npI2
% 2-
the potential energy curve can be computed from sec- fiiai
ond-order perturbation theory. For the simple atomic
metal orbital system, the corresponding expression is References see page 957
950 5 Elementary Steps and Mechanisms

around the Fermi level. Relationship (28) agrees with As expected, the increase in coordination extends the
the computed electron occupation dependence of the width of the LDOS of the 2n* orbital. The change in
chemisorption energies for the different adsorption the 50 orbital is much less coordination dependant be-
modes in Fig. 5. It parallels approximately the group cause of the directed nature of this orbital. At the atop
orbital local density of states dependence shown in Fig. site it will overlap significantly with surface dZ2 and p
6 . Additional parameters that control the energy dif- orbitals, as can be seen from the corresponding bond
ference between adsorbate and metal surface orbitals, order overlap population densities (Fig. 12). In twofold
are the surface work function, adsorbate image poten- and threefold coordination, however, the 5 0 is directed
tial, electron affinity, as well as the unoccupied and to the surface normal instead of the surface orbital and
occupied surface electron density of states. Note that hence has a small overlap with the surface atomic
we explicitly introduced the image potential term, orbitals.
which arises from the screening of charge on the ad- q ( E ) orbital occupation provides a bonding contri-
sorbate that is generated by electron donation and bution to the surface chemical bond. When nii(E) is
backdonation. The first term of eq 28 is the contribu- negative, orbital occupation tends to antibonding and
tion to the bond energy due electron donation of elec- repulsive contributions. For the corresponding discrete
trons from bonding adsorbate orbitals into empty sur- bond order overlaps P:, this is illustrated for H2 in
face orbitals. The second term arises from electron Fig 10. The functions nij presented in Fig. 12 enable
backdonation of surface metal electrons into the un- analysis into the extent to which s, p, and d electrons
occupied adsorbate orbitals. contribute to the bond energy. Note that the 5 0 - d ~ ~
We will analyze the quantum chemistry of the sur- interaction has both bonding as well as antibonding
face-chemical bond further by the use of extended character. A further increase in the valence electron
Huckel calculations of the electron energy distribution occupation (higher E F )will increase the occupation of
of CO chemisorbed to a large Rh cluster [13], simulat- antibonding orbitals and hence weaken the interaction
ing a Rh (1 11) metal surface. In the next section we will energy. This is a very general result for the interaction
discuss in detail the consequences of the cluster size of adsorbate orbitals that are doubly occupied and
choices on the variation in the chemisorption bond have a nearly filled d valence electron bond. Similar to
strength. Clusters of 50 metal atoms or more reproduce the results depicted in Fig. 5 , the interaction is a max-
the electronic structural features found for calculations imum when only bonding orbital fragments occupied.
on extended surface. The electronic properties of inter- The interaction decreases when the d valence elec-
est are the local density of states of the adsorbate orbi- tron occupation is such that bonding orbital fragments
tals or metal atomic orbitals, given by become depleted. Analysis of the Tc5,,diz -orbital (Fig. 12
(E)) shows that the downwards-shifted 5 0 orbital be-
PdE) = (V,lfi(E - H ) l V i ) (29) comes part of the bonding surface orbitals. However,
the broadened and upwards shifted pdz2 surface atomic
local density of states becomes part of the antibonding
surface orbitals.
and the bond-order overlap population (eq 31). The Opposite behavior is found for the 2n* electron den-
bond-order overlap energy density of states ng(E) rep- sity. The 2n* local density of states has bonding surface
resent the atomic orbital interference terms as a func- electron density in the energy regime of the surface d
tion of energy and provides information on the bond- electron density. The antibonding nature of the surface
ing and antibonding character of the adsorbate-surface electron density near the gas phase 2n* electron energy
fragment orbitals. level is also reflected in the upwards shift of this den-
sity. The 2n*-surface interaction is mainly of bonding
character. For most metals only bonding surface orbi-
tal fragments are occupied. Whereas the 2n* orbitals
for the gas-phase CO molecule are not occupied, the
interaction of CO with the surface broadens the CO
2n* local density of states and leads to a partial occu-
In figure 12 the computed local density of states of pation of these orbitals. The CO 2n* orbitals are anti-
the highest occupied molecular orbital (HOMO), 5 0 bonding and hence their occupation will weaken the
and lowest unoccupied molecular orbital (LUMO) C-0 interaction energy, which is experimentally re-
2n' molecular orbitals of CO adsorbed atop, twofold, flected in a lowering of the C-0 stretching frequency.
or threefold coordinated to the (111) surface of Rh The 2n* LDOS broadens more when CO is in higher
are presented. Due to the interaction with surface coordination sites. This leads to a larger contribution
orbitals the local density of states (LDOS) distributions of low-energy bonding orbitals and a resulting in-
broaden with respect to their sharp gas-phase values. creased 2n" electron occupation.
 5.1 ChemisorDtion 951

t f
A tEF EF EF

ki A
twofold twofold

threefold threefold

;?:'
-30
I ,
-20
I /Ll
-10
;-I I I I
0
~
edge

-30
I I I I
-20
I I I
-1 0 0
CO-onefold

-30 -20 -10 0

Energy (eV) Energy (eV) Energy (eV)

A.
- 0
.A Energy (eV) Energy (eV)

Figure 12. The electronic interactions of CO with the Rh(l11) surface [13].
A. The CO, 5 0 local density of states p 5 , ( E ) on different adsorption sites.
B. The CO, 2n* local density of states p2n.( E ) on different adsorption sites.
C. The local density of states of the surface atomic orbital dZ2 for CO chemisorbed atop before and after chemisorption (b).
D. Bond order overlap density of states of the CO 5u orbital for CO chemisorbed atop: (a) ~5~ dz2; (b) nsa s; (c) ~ 5 , , ~. ,
E. Bonder order overlap density of states of the CO 2n' orbital for CO chemisorbed atop: (a) ~ 2 ~ d , (b)
, ; n2n,p,.

The 5a orbital has a strong bonding interaction with bonding 5a-surface orbital fragments is that CO will
the surface s and p valence electrons which is depen- prefer the low coordination atop site to relieve Pauli
dent on the relative values of Fermi level and 5 0 posi- repulsion. However, the 271*-p orbital interaction will
tion. The antibonding orbital fragments can also be- favor the higher coordination sites.
come occupied when interacting with the surface s A consequence of these opposing forces is that the
electrons. For CO adsorbed atop, the 2n* CO orbitals differences in bond energies of Co adsorption at differ-
have only a weak interaction with the surface s atomic ent coordination sites is small.
orbitals, because of zero overlap between 2n* and its In practice, bonding with atoms such as C, 0, or S ,
next-neighbor s atomic orbital. For this reason p-type is dominated by the interaction with the adatom p
orbitals drive the surface adsorbates to twofold and atomic orbitals and strongly favors high coordination.
threefold coordination sites where group orbitals of the Such atoms bind an order of magnitude stronger to the
required symmetry can favorably interact.
The resulting bonding scheme is summarized in Fig.
13. The consequence of the high occupation of anti- References see page 9.57
952 5 Elementary Steps and Mechanisms

Outstanding representatives of this approach in catal-

‘I--
ysis are Siegbahn [16], Bagus [17], Goddard [18] and
__c their co-workers. The other first principle approach
is based upon the application of density functional
theory. With the incorporation of nonlocal gradient
corrections to the exchange-correlation functional and
the application of energy minimization techniques, this
technique has the potential to become widely adapted
in chemisorption theory, due to the reliability of the
I
results and its significant savings in CPU. In addition,
I) 50 the development and application of DFT-slab pro-
~

grams allow one to treat very realistic catalytic sys-

tems. Baerends [lOa], Salahub [lob], and Ziegler [lOc]
metal ‘:obi co have made significant contributions to the development
d valence metal valence
electron d valence atomic electrons of these approaches.
distribution orbitals
Within the ab initio computational scheme frame-
Figure 13. Orbital scheme (schematic) of the interaction of the work, Whitten [19] has developed an interesting and
CO 5 g and 27r* orbitals with surface dX2 and dZ2orbitals. useful approach, whereby small clusters (e.g. the sur-
face complex) are embedded into a larger cluster model
of the bulk, which is described by lower quality wave
metal surface because of the relatively low energy of functions. An alternative embedding scheme has been
the unoccupied atomic orbitals. developed by Pisani [21]. Next to the embedding
A general bonding trend for the transition metals in schemes density functional theory applications have
a given row of the periodic system is that there is an appeared to use extended sates to simulate the tran-
increase in the interaction energy in moving from right sition surfaces. For example, te Velde and Baerends
to the left (e.g. from Cu, Fe, or Ag to Ru). Three fac- were recently able to deduce highly accurate adsorption
tors contribute: values for the adsorption of CO to Cu [21] and resolve
(i) the d valence electron occupation decreases; the long-standing theoretical question of the coordi-
(ii) the ionization potential (work function) of the nation of CO to Cu, with their DFT-slab approach.
metal decreases (only true for Group VIII and Feibelman [22] used a related approach to analyze the
early transition metals); vibrational motion of hydrogen.
(iii) the spatial extent of the d valence electron in- Finally we have to mention the important empirical
creases. approach developed by Shustorovich [23], the bond
order conservation-Morse potential (Boc-MP) method.
The lower adsorption energies for Group IB elements This is a parameterized scheme that enables the esti-
compared to Group VIII elements, is due to the com- mate of adsorption energies of complex molecules
plete filling of the d valence electron band for the IB based on parameters derived for those of the free mol-
metals. This leads to large repulsive interactions with ecules or adsorbed atoms.
occupied adsorbate orbitals (e.g. the CO 5a orbital) BOC-MP theory is approximately valid for many
and occupation of antibonding orbital fragments. systems. Its expressions work most satisfactory for sit-
uations where bonding is nondirectional. Each atom is
assigned a particular valency . When an atom becomes
5.1.2.3 Concepts in Chemisorption coordinated to neighbors this valence is distributed
over the different chemical bonds. Because the valency
A Introduction is constant, the larger the number of the neighbors, the
So far we have discussed the electronic nature of the smaller the energy per bond. This phenomenon is often
surface-chemical bond based on parametrized model observed in chemisorption. When a molecule adsorbs,
considerations. The current status of computational intramolecular bonds as well as metal atom bonds of
chemistry and physics has reached a state where quan- the surface atoms involved in the adsorption complex
titatively reliable studies on small clusters and even weaken. Ultimately this may lead to surface recon-
transition metal slabs are feasible. struction or surface corrosion.
Herein, we simply outline the available first-princi- In this section we will revisit many of the concepts
ple-based methods for analyzing chemisorption sys- presented earlier and review their validity within the con-
tems. A more detailed review is available elsewhere text of results based on first-principle density functional
[14]. The first is based on the ab initio Hartree-Fock theory calculations. Elsewhere [6] we provided an exten-
approach and its successive improvements by the ap- sive review of first-principle-based calculations adsorp-
plication of configuration interaction techniques [ 151. tion and reactivity on transition clusters and surfaces.
 +
5.1 Chemisorption 953

B Chemisorption to Clusters
It is now widely recognized that the interaction be-
tween an adsorbing molecule and metal particle may
be strongly cluster dependent. Interestingly, the cluster-
size dependence is most significant for adsorption on
I’c,co= 0 081
small unoptimized metal clusters. Such clusters have Pc,co= 0.276 Pc,co= 0.209
been studied extensively as models of surfaces. We E = 127 kJlmol E,,,, = 21 8 kJ/mol E ini = 2 10 kJ/i1101
illustrate this cluster-size effect here for the interaction
of CO with Co and Rh clusters, based on density I.

functional theory results [24]. The question we address

is what is the preferred coordination site of CO. On the
dense surfaces such as Rh and Co, CO prefers atop
coordination. However, as illustrated in Fig. 14(a), CO
prefers the higher coordination site on small clusters
that model the dense surface.
The result has been shown to be due to the response Pc,c0=0.282 0 240 P&,= 0 100

of the cluster electrons to the disturbance with CO. E i n r = 200 kJiiiioi E = 263 kJ/mol E lnt = 241 kJ/mol
A bond order overlap analysis of the CO nearest-
neighbor atom interaction indicates that the preference
for CO bonding is for onefold coordination. Coordi-
nation differences for the Co atoms in the respective
clusters result in different Co-Co interactions. This
ultimately controls the overall adsorption energetics.
The low Co atom coordination numbers in the clusters
biases CO bonding, to high coordination sites. This is
attributed to the Co electron higher electron local- E Int = I G O kJ/inol E ,nt = 140 l\J/iiioi E = I23 k.lhiol
ization energy. The choice of the spherical clusters Col3
(Fig. 14(b)), enables the study of the three CO coordi- Figure 14. Interaction energies and bond orders of CO adsorbed
to different Co clusters [24]. The bandorder overlap occupations
nation modes on the same clusters confirm this analy- are computed from
sis. Now, the atop coordination of CO is found to be occ

preferred [24]. P,=2CP,:

k
Bond order overlap population analysis confirms
the explanation proposed earlier on the basis of the
extended Huckel method. The repulsive interaction
between the doubly occupied CO 50 orbital and the Co the valence electrons of the Rh atom, with three Rh
3d valence orbitals with approximately eight electrons neighbors and the Rh atom in the middle of the tetra-
per atom leads to occupied antibonding admolecule- hedral edge with six Rh neighbors are also shown in
surface atom orbitals. This preferred atop interaction is Fig. 15. Also given are the interaction energies of CO
only partially counteracted by the backdonating inter- on the two Rh atoms. CO is found to interact most
action with the CO 2z* orbitals that prefer the high strongly with the coordinatively most unsaturated Rh
coordination site. atom. Its local density of states distribution has the
The spherical cluster is but one approach to reduce smallest degree of delocalization.
cluster-size anomalies, a second method would be to use It follows from the analyses in the previous section,
extended surface clusters, as discussed later, whereby that the cluster-size dependence will be stronger for the
a large enough top layer surface exists to remove more weakly bound adsorbates (as molecules) than the
edge localization at the central sites. The importance of strongly interacting atoms, when the surface complex
cluster atom coordination number is again found in energy is large compared to the electron localization
density functional theory calculations of CO interact- energy. The computed dependence of adsorbate inter-
ing with tetrahedral R h and Rhlo clusters [25]. On the action energy on cluster size is now well documented
R h cluster, CO coordination is preferred in twofold experimentally. For small particles fluctuations in
coordination, instead of the onefold surface coordina- cluster-size interacting energy are observed that appear
tion site, again the result is due to a low coordination to correlate with cluster ionization potential [26]. In-
of the atoms. On the large Rhlo cluster, CO is found to teraction energies appear to converge to surface values
preferentially adsorb atop. The two inequivalent Rh for clusters of the order of 20 atoms or more.
atoms of Rhlo cluster enable us to test the relation be-
tween admolecule bond energy and surface atom local
density of states bandwidth. The LDOS distribution of References see page 957
954 5 Elementary Steps and Mechanisms

Rh atom bonded to Rh atom bonded to the proper spin state is chosen [lob, 271. For example,
CO has three nearest C 0 has six nearest
neighbour atoms neighbour atoms
Neurock et al. [27] found that chemisorption energies
for atomic hydrogen and oxygen on the octahedral Pd
0 0 cluster depicted in Fig. 16 are within 15 kJ mol-' of the
C c experimental values for hydrogen and oxygen on Pd
(11 1). Figure 16 depicts the optimized structures for
Pds bare, Pds with hydrogen, and Pds with oxygen.
The bare Pd6 cluster was found to be most stable as a
triplet. This follows known evidence that the Pd dimer
is also triplet and that palladium bulk is paramagnetic.
Geometry optimization of the bare Pd6 cluster trans-
E int 86 kJimol E int = 65 kJ/mol
=
formed the starting octahedral cluster into one which
a b essentially has C4" symmetry. There are four short
planar Pd-Pd bonds of 2.63A and six long Pd-Pd
bonds of 2.76 A.
Adsorption of H or 0 forms strong bonds with the
surface palladium cluster which subsequently alters
the cluster bond lengths. The strong Pd-H and Pd-0
bonds lead to weaker Pd-Pd cluster bonds between the
Pd atoms involved in the adsorption complex.
The effect of the extended surface was examined by
optimizing a bare Pdlg cluster model and a hydrogen
Pdlg model [27]. Results depicted in Fig. 17 demon-
strate that the Pdlg structures bond by pushing the
central three palladium atoms in the surface upwards.
Qualitatively, the results are very similar to those for
Pd6. Due to constrained nature of the surface, however,
-10 -8 -6 -4 -2 EF 2 4 the changes are less dramatic for the Pdlg cluster. The
Energy (eV) elevation of the surface atoms involved in the adsorp-
tion complex is well established in surface science liter-
ature. Van Hove and Somorjai [28], for example, have

-.s clearly shown that ethylidine adsorbed on Pt leads to

longer Pt-Pt bonds and a lifting of these atoms out of
3
the surface plain by about 0.12 A.
P More generally these changes in the local geometry
o g at (or near) the chemisorption site will lead to local
J stresses which could ultimately lead to surface recon-
. . . ., l....,
n
struction effects [29].
0
C Lateral Interactions
0 a w.0. The interaction between atoms or molecules co-
-10 -8 -6 -4 -2 EF 2 4 adsorbed to a transition metal surface may be repulsive
Energy (eV) as well as attractive. Figure 18 illustrates three different
coadsorption situations for adatoms ( N and 0),adinter-
Figure 15. CO chemisorbed atop to a Rhlo cluster [25].The lo- mediates (OH and NH), and molecules (NH3 and 0 2 )
cal densities of states p of Rh 4d, CO 5a and CO 2 ~ *and , the
bond order overlap population densities RV between the rhodium on a (1 11) surface. The interaction energies were com-
and CO orbitals for onefold CO adsorption on Rhlo. Adsorption puted using density functional theory with nonlocal
on Rh (3nn) is shown on the left (a) and adsorption on Rh (6nn) is gradient corrections for both exchange and correlation.
shown on the right (b). Each graph shows: (- ) LDOS of Rh; They illustrate that the interaction energy between
(- - - - -) LDOS of CO 50; (. ' . ' .) LDOS of CO 2 ~ *(-; )
BOOPD between Rh-CO 5u: (- - - - -) BOOPD between coadsorbed atoms or intermediates is repulsive, when
Rh-CO 2R'. they share a covalent bond with a surface atom. The
repulsive interaction is significantly larger when they
share two rather than one surface atom. The nature of
Interestingly, recent results suggest that interaction en- the interaction energy is a strong function of the rela-
ergies converge at smaller cluster sizes for nonlocal tive position of the adsorbates.
density functional calculations provided that both the In the case of coadsorption of 0 and NH3 (case I),
adsorbate as well as the cluster are optimized and that the interaction energy of NH3 is increased when it is
 4:;
5.1 Chemisorption 955

/-

Pd6 dl

Pd4 Pd4

triplet doublet triplet

Pds-Triplet Pd6H-Doublet PdhO-Triplet

1-3 2.756 1-3 2.918 1-3 3.131

1-6 2.631 1-6 2.898 1-6 3.074
3-6 2.756 3-6 2.918 3-6 2.918
2-4 2.756 2-4 2.667 2-4 2.651
2-6 2.632 2-6 2.756 2-6 2.757
4-5 2.757 4-5 2.661 4-5 2.628

Pd-X 1-7 1.768 1-7 2.068

3-7 1.768 3-7 2.068
6-7 1.767 6-7 2.068
Figure 16. Structures and bondlengths (A) for geometrically optimized Pds clusters. Free hydrogen atom adsorbed and 0 adsorbed clusters
are compared [27]

Case I Case I1 Case I11

3 fold - 3 fold 3 fold - 3 fold 1 fold - 3 fold

Species Case I Case I1 Case 111

NH3 on Cu(8,3)-0 -32

NH3 on Cu(8,3)-0 -17
NH2 on Cu(8,3)-OH - -5
NH on Cu(8,3)-0 21 1 25
N on Cu(8,3)-0 30
N on Cu(8,3)-OH 170 29

Oxygen and hydroxyle are always threefold coordinated

Pd - t1 1.78 1.75
Figure 18. Interaction energies between adsorbed atoms on a Cu
surface [30].
Pd - Pd
Local- local 2.75 2.82
Local-local 2.75 2.72

Figure 17. Pdl8-H cluster: Bond distances (A) are compared for
locally geometry-optimized and not geometry-optimized cluster
atom positions. References see page 957
956 5 Elementary Steps and Mechanisms

H H
I I
H H

Mg2' Mg2'
A E int= -13.13 kJ/mol A E i n t = -49.61 klimol
CO-S'Ni
H-H H-H

-10 -8 -6 -4 -2 0 2 4
E(eV)-

Figure 19. Linear augmented plane wave results of the local

density of states of CO adsorbed on Ni(ll1) [32]:(a) unsupported
CO film; (b) CO adsorbed on nickel; (c) CO adsorbed with po- M2' Mg2'
tassium on nickel; (d) CO adsorbed with sulfur on nickel.
AE int= -21.73 kJimol AE int = -90.2 kJ/mol

Figure 20. Changes in the interaction energies of H2 with Ir4

clusters due to the presence of a Mg2+ ion [35].
bound to a surface atom next to the surface atom
Cu-0 adsorption complex. The adsorption energy is
increased by 30kJmolF' [31]. The weakening of the When a small metal particle is adsorbed next to a
Cu-Cu bonds next to the cu atom involved in the sur- cation, as in a zeolite or on an oxidic support, the
face bond with the oxygen bond results in a decreased electrostatic field of such a cation will polarize the
delocalization energy of the Cu electrons associated metal particle. This is illustrated in Fig. 20 for an Ir4
with the Cu atom to which NH3 is bonded. Lateral particle adsorbed next to a Mg2+ ion. The changes in
interactions can be also electrostatic in nature. In the the interaction energy of H2 with the Ir4 particle are
case of ammonia interacting with the coadsorbed shown. The interaction energy of H2 with Ir4 (mea-
oxygen atom, 10% of the interaction energy originates sured by DFT calculations) is weak. There is a strong
from the direct electrostatic attraction between the Pauli repulsion between the double occupied H20g
negatively charged oxygen atom and positively charged orbital and the occupied 11-4 orbitals. Bonding becomes
ammonia. The covalent interaction energies rapidly more favorable for H2 adsorbed to a single Ir atom. In
decline with distance. Within the jellium model the the presence of the Mg2+ ion, there is a polarization of
interaction energy has been found to decrease as rP3. Ir4 which removes electron density from between the
Lateral interactions can also be dominated by electro- adsorbed H2 molecule and interacting Ir atoms. As a
static interactions. This is, for instance, the case when consequence Pauli repulsion is reduced and now the
alkali atoms are coadsorbed to a metal surface. Using hydrogen atoms can approach the Ir atoms so that
the augmented plane wave approximation for CO and strong orbital overlap and develops backdonation of Ir
K coadsorbed to Ni, Wimmer et al. [32] convincingly electrons into the H2ai becomes possible. The inter-
demonstrated the existence of a strong electrostatic in- action energy of Hz with Ir is now enhanced and
teraction. This can be deduced from the relative shifts adsorption parallel to the Ir particle in threefold co-
of the Co electronic levels when CO is adsorbed to Ni ordination becomes favored.
in the presence and absence of potassium (Fig. 19).
The positive charge of potassium lowers the work
function of the metal surface and hence lowers the CO 5.1.2.4 The Surface Chemical Bond: A Summary
electronic levels compared to those of the Ni-electrons.
The result is an enhancement of the backdonation of Chemisorption causes significant changes in local elec-
electrons into the CO 2n"-orbitals. The donating inter- tronic structure, that in the case of strong interactions
action for the CO %-orbitals is reduced in the presence often leads to surface rearrangements. The structural
of coadsorbed potassium. The enhancement of the changes can often be understood as a consequence of
backdonation into the CO 2n*-orbitals changes the bond order conservation. The more bonds there are to
relative energy enough to alter the preferred CO-coor- an atom the weaker the other bonds associated with
dination sites. For instance on the Pt (111)-surface it this atom become.
has been shown that CO-shifts from the atop position The adsorbate bond strength follows from the dis-
to a high coordination site [33, 341. tribution of electrons over bonding and antibonding
 5.1 Chemisomtion 957

fragment orbitals. The interaction with the s and p lyzing changes in the interaction energy over different
metal surface valence electrons usually favors the high transition metal surfaces.
coordination site. The d valence electron interaction, A decrease in work function will favor backdonative
however, can be repulsive, which would favor low co- interactions, and hence increase the bond energy.
ordination. The adsorption energy tends to increase However, donative interactions will decrease and the
with d valence electron depletion. overall interaction result will depend on the balance of
The adsorption energy of a molecule can be consid- the two changes. For adatoms the backdonative inter-
ered as controlled by a balance of donating and back- action dominates, so that the bond energy increases.
donating interaction terms. For backdonation, the in- For molecular adsorbates such as CO, the balance is
teraction between adsorbate unoccupied orbitals and more subtle. For instance, CO binds more strongly to
the metal surface favor high coordination. For dona- Pt than to Ni, because on Pt the donative interaction
tion, the interaction favors low coordination. The d dominates. This agrees with the CO preference for atop
valence electron interaction controls the balance of coordination. On Ni, however, the backdonative inter-
these two effects. Adsorbed atoms with accessible p action dominates, resulting in a preference of CO for
atomic orbitals, favor high coordination. The prefer- higher coordination sites.
ence for site coordination is much less for adsorbed A decrease of the transition metal d valence electron
molecules. occupation will decrease the occupation of antibonding
Weak, as well as strong chemisorption locally dis- adsorbate-surface fragment orbitals and hence assist
turb the electronic structure and geometry of the the increase in bond energy when comparing bonding
surface atoms close to the adsorbate molecule. The to metals across a row (from right to left) in the Peri-
chemical bonds between surface atoms involved in odic Table. This increase in interaction energy is also
the adsorption complex and neighboring surface atoms partially due to the increase in spatial extension of the
weaken, dependent on the strength of the adsorbate- d orbital band, that favors overlap with adsorbate
surface interactions. orbital.
The substrate disturbance by an adsorbate is strongly The low reactivity of the Group IB metals (Cu, Ag,
surface or cluster-size dependent. This strongly affects Au) compared to that of the Group VIII Ni, Pd, and Pt
the overall interaction energy and leads to surface and metals stems from the repulsive interaction between
particle size-dependent interaction energies. Surface adsorbate orbitals with the filled d valence electron
relaxation effects enable adsorption complexes to take band of the IB metals. The resulting decrease in the
on geometries very similar to those in the analogous interaction energy is not compensated for by an in-
organometallic coordination complexes. crease in the backdonating interactions due to the
As the adsorbate concentration increases the intra- lowering of the work function of the latter.
atomic surface bonds become weaker. This can sub- Alloying of a Group VIII transition metal with a
sequently lead to surface reconstruction effects. The Group IB metal leads to changes in bond energies of
lateral interaction between the adsorbates give rise to adsorbates, because now mixed surface ensembles of
nonideal mixing and order-disorder transitions of the Group IB and Group VIII surface atoms are formed.
surface layer [36]. Surface atoms with lower surface New mixed-metal surface sites also exist. This may re-
atom coordination numbers tend to be more reactive duce the interaction energy of adsorbates in high co-
than surface atoms with a higher coordination numbers ordination sites, because multiple coordination to the
due to the larger electron delocalization associated with more strongly interacting Group VIII surface atoms
the latter. Atoms bind more strongly and tend to prefer can now become suppressed (secondary ensemble effect)
adsorption in high coordination sites, whereas mole- ~361.
cules adsorb more weakly with smaller differences in
the interaction energies of different coordination sites.
When donative interactions dominate and the contri- References
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The details strongly depend on the distribution of 2. D. M. Newns, Phys. Rev. 1969, 178, 1123.
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6. R. A. van Santen, Theoretical Heterogeneous Catalysis,
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van Santen, SurJ Sci. 1989,233, 233. 1983, 121, 203.
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(Ed.: A. qillard), Reidel, Dordrecht, 1986, p. 159; P. M. 35. E. Sanchez Marcos, A. P. J. Jansen, R. A. van Santen,
Boerrigter, G. te Velde, E. J. Baerends, Znt. J. Quantum Chem. Phys. Lett. 1990,167,399;A. P. J. Jansen, R. A. van
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387; D. R. Salahub, R. Fournier, P. Meynaski, I. Papai, A. Surfaces, Plenum, New York, 1991.
St. Amant, J. Ushio in Theory and Applications of Density 37. W. M. H. Sachtler, R. A. van Santen, Adv. Catal. 1977,26,
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11. M. J. Puska, R. M. Nieminen, M. Manninen, Phys. Rev.
1980, B24, 3037.
12. S. Holloway, J. K. Norskov, N. D. Lang, J. Chem. Soc.,
Faraday Trans. 1 1987, 83, 1893.
13. R. V. van Santen, A. de Koster Stud. Sut$ Sci. Catal. 1991,
64, 1. 5.2 Microkinetics
14. R. A. van Santen, M. Neurock, Catal. Rev. 1995, 37, 557.
F. Ruette (Ed.), Quantum chemistry approaches to chem-
isorption and heterogeneous catalysis, Kluwer, dordrecht,
1992; E. M. Shustorovich (Ed.), Metal-surface Reaction
5.2.1 Rates of Catalytic Reactions
Energetics: Theory and Applications to Heterogeneous Cat-
alysis, Chemisorption and Surface Diffusion, VCH, New M. BOUDART
York, 1991; R. V. van Santen, E. J. Baerends in Theoretical
treatment of large molecules and their interactions (Ed.: Z. B.
Maksic) Springer, 1991, Part 4, pp. 323-390.
15. A. Szabo, N. S. Ostland, Modern Quantum Chemistry, 5.2.1.1 Introduction
MacMillan, New York, 1982.
16. P. E. M. Siegbahn, U. Wahlgren in Metal-surface Reaction Catalysis is a kinetic phenomenon. The study of
Energetics: Theory and Applications in Heterogeneous Cat- kinetics in catalysis started early in the 20th century in
alysis, Chemisorption and surface difusion, VCH, New
York, 1991. a phenomenological mode. The first study of this kind
17. P. S. Bagus, K. Hermann, Phys. Rev. 1986, B33, 2987; P. S. dealt with the rate of decomposition of stibine SbH3 on
Bagus, F. Illas, Phys. Rev. 1990, B42, 10852. the surface of antimony, a product of the reaction act-
18. T. H. Upton, W. A. Goddard, CRC Critical Review in Solid ing as a catalyst. The kinetic data of Stock and Bod-
State and Materials Sciences 1981,261; E. A. Carter, W. A.
Goddard, J. Catal. 1980, 112, 80; E. A. Carter, W. A.
enstein [l] were fitted to what became known as an
Goddard, J. Phys. Chem. 1988,92, 2109. empirical power rate law:
19. J. Whitten in Cluster Models for Surface and Bulk phenom-
ena, (Eds: G. Pacchioni, P. S. Bagus, F. Parnigiani,) NATO u = k[SbH31n (1)
AS1 series, 375 1991, A. Chattopadhyay, H. Tang, J. L.
Whitten, J. Phys. Chem. 1990, 94 6397; H. Yang, J. L. where the rate u is proportional to the concentration of
Whitten, J. Chem. Phys 1989, 91, 126. the gas phase reactant to a fractional power n with
20. T. B. Grimley, C. Pisani, J. Phys. C. 1974, 7 , 2831; C. empirical values 0.55, 0.56, 0.63, and 0.65 at 273, 298,
Pisani, Phys. Rev. 1978, B17, 3143; R. A. van Santen,
L. H. Toneman, Iitt. J. Quantum Chem. 1977, Suppl 2, 323, and 348K, respectively. The kinetics of this his-
83. torical reaction have been discussed repeatedly [2].
21. G. te Velde, E. J. Baerends, J. Comp. Phys. 1992, 99, 84. The carly phenomenological period of catalytic
22. P. J. Feibelman, Surf: Sci. 1994, 2991300, 426. kinetics was followed by a second mechanistic period
23. E. H. Shustorovich, SurJ Sci. Rep. 1986, 6, 1. based on the findings of Langmuir. A highlight of this
24. M. C. Zonneviylle, J. J. C. Geerlings, R. A. van Santen, J.
Catal. 1994, 148, 417. period was the publication in 1931 of a very influential
25. W. Biemolt, Ph.D Thesis, Eindhoven, 1995. book by Schwab that was translated into English by
26. A. Kaldor, C. M. Cox, M. Zakin, Ado. Chem. Phys 1988, Taylor and Spence [3]. During the 1920s and 1930s,
70, 211. the kinetics used in heterogeneous catalysis were based
27. M. Neurock, G. Coulston, D. Dixon, unpublished results. largely on the Langmuir lattice model of a surface
28. U. Starke, A. Barbieri, N. Materer, M. A. van Hove, G. A. consisting of identical noninteracting adsorption sites.
Somorjai, SurJ Sci. 1993, 286.
29. J. K. Norskov, Rep. Progr. Phys. 1998, 53, 1253; J. K. These so-called Langmuir kinetics were developed first
Norskov in The Chemical Physics of Solid Surfaces and by Hinshelwood [4] and then by Hougen and Watson
Heterogeneous Catalysis, (Eds. D. A. King, A. P. Woodruff, to become a systematized tool for process research and
Elsevier, 1993, vol 6. development in the 1940s and 1950s [5]. The idea was
30. M. Neurock, R. A. van Santen, W. Biemolt, A. P. J. Jansen, to assume a reaction mechanism leading to the best
J. Am. Chem. SOC.1994,116, 6860.
31 W. Biemolt, A. P. J. Jansen, M. Neurock, G. J. C. S. van de data fitting rate equation for use in catalytic reactor
Kerkhof, R. A. van Santen, Surf: Sci. 1993,287/288, 183. design and operation. In time, the data fitting proce-
 5.2 Microkinetics 959

dure became very sophisticated [6]. By reaction mech- plotted vesus time at a given temperature. In either
anism, we mean a set of elementary steps describing the case, the available information made it impossible to
catalytic cycle. Usually, of course, there is more than reproduce the work, even if enough details were pro-
one set that comes to mind. The set that fits the data vided on the preparation of the catalyst. This tradition
best is not necessarily the correct mechanism, as was so ingrained that arbitrary units were used by
repeated many times in the literature. As a result, Beeck in a famous paper [15] reporting his extensive
the Langmuir-Hinshelwood-Hougen-Watson equa- work on evaporated metal films of transition metals
tion have often been regarded with a great deal of used as catalysts for the hydrogenation of ethene. Yet,
skepticism, in spite of their usefulness in engineering Beeck had measured the area of his films and he could
applications. Part of this skepticism is due to the have reported areal rates, i.e. rates per unit surface area
Langmuir model. Other models based on the the of the films.
theory of nonuniform surface were developed in the The measurement of areal rates on supported metal
1940s and 1950s, starting with a celebrated paper by catalysts became possible after the first attempt by
Temkin and Pyzhev [7], who first obtained a working Boreskov and Karnaukhov to obtain the area of sup-
rate equation for the catalytic synthesis of ammonia. ported metal particles by chemisorption of dihydrogen
Rate equations based on models of non-Langmuirian [16]. In this way, areal rates for silica gel-supported
surfaces were then used extensively by the school of platinum catalysts were obtained for the oxidation of
Temkin [8]. A summary of this approach can be found sulfur dioxide [17] and of dihydrogen [18]. This tech-
elsewhere [9]. Because of the facile objections against nique was then applied for the first time to y-alumina-
both models of Langmuir and Temkin, a safe return to supported platinum reforming catalysts containing a
empirical power rate equations similar to eq 1 has been much smaller weight fraction of metal. That study, in
advocated [lo], but also opposed because of the physi- the Esso (now Exxon) laboratories, revealed that the
cal content, imperfect as it may be, of the Langmuir metal clusters were about 1 nm in size [19]. Sinfelt and
[ 111 or Temkin kinetics. The matter remains unresolved co-workers at Esso then used the technique to report
[13] and will not be discussed in this chapter. A collec- for the first time areal rates on reforming catalysts [20-
tion of useful rate equations and kinetic data for 221. In fact, these were called specific rates, but this
almost 100 industrially important catalytic reactions is expression is now reserved to rates per unit mass of
available in an informative compendium [14]. catalyst. The systematic use of areal rates in comparing
Rather than the rate equation, i.e. a function that catalytic activity of metals used in the form of evapo-
tells us how reaction rate varies with temperature, rated films, large single crystals, and supported par-
pressure, and composition of the reacting system, this ticles or clusters, ushered in the era of quantitative
chapter discusses the catalytic reaction rate itself with measurements of catalytic activity. Yet, ultimately the
an emphasis on the catalytic cycle and the rate at which rate should, if possible, be referred to the number of
it turns over. General relationships between the ther- active sites, because such a rate expresses the rate at
modynamics and kinetics of catalytic reactions will which the catalytic cycle turns over: it is a turnover rate
be presented. Examples will be borrowed mostly from or turnover frequency.
heterogeneous catalysis, although the concepts apply The definition goes back to the early days of enzyme
equally well to homogeneous, enzymatic and, suitably catalysis when the rate of reaction was referred to the
modified to chain reactions. On the basis of these amount of enzyme and called turnover number. Thls
bridges between thermodynamics and kinetics, impor- appellation was unfortunate, as “turnover number” is
tant features influencing the turnover rate will be in- not a number but has the dimension of one over time.
troduced and discussed. The most important concept is In addition, turnover number in enzymatic catalysis
that of the rate determining step. Other concepts in- usually denotes the maximum value of the rate per
troduce the kinetically significant steps and the most catalytic site, at saturation of the enzyme by the react-
abundant reactive intermediates in catalytic cycles. The ing substrate, as defined by Michaelis-Menten kinetics
question of equilibrium or nonequilibrium between the [23]. This unfortunate limitation is totally unnecessary
reactive intermediates and reactants or products will and provides another cogent reason to avoid com-
then be discussed with the kinetic coupling between pletely the use of turnover number in catalysis. A
elementary steps in the cycle. qualitative comparison of the activity of a solid catalyst
with that of an enzyme in terms of a turnover number
first appeared in the literature in 1963 [24]. It appears
5.2.1.2 Turnover Rate or Turnover Frequency: that a quantitative turnover number for heterogeneous
Generalities catalysis was first used in 1968 to denote the rate of
reaction referred to the number of surface platinum
Fifty years ago, the rate of heterogeneous catalytic re- atoms titrated with dihydrogen on a supported plati-
actions was frequently expressed in so-called arbitrary
units. Activity was commonly expressed by conversion References see page 971
960 5 Elementary Steps and Mechanisms

num catalyst [25]. Subsequently, the rate referred to the found to be strictly proportional to the A1 content.
number of catalytic sites became known as turnover Clearly, all catalytic sites are identical and non-
rate, ut, or turnover frequency (TOF). It is simply de- interacting, in the range of composition covered in this
fined as the number of revolutions of the catalytic cycle study. For seven other acid-catalyzed reactions, a lin-
per unit time, generally the second [26]. It is a chemical ear correlation between activity and concentration of
reaction rate, a differential quantity depending on Br~nstedsites was also found, albeit in a more limited
temperature, pressure and concentrations. Like all cat- range of Si:Al ratios. Haag concludes: “The possi-
alytic rates, it is hard to measure. Frequently, turnover bility to synthesize zeolite catalysts with a well-defined
rate is replaced by a related, but generally not identical pre-determined number of active sites of uniform ac-
quantity, the site time yield (STY), defined as the tivity is certainly without parallel in heterogeneous
number of molecules of a specified product made per catalysis.” Haag also adds: “Turnover frequencies
catalytic site and per unit time [27]. (TOFs) for a variety of acid catalyzed hydrocarbon
The difficulty in measuring TOF is not only in de- reactions could be determined for the first time.” It
termining the rate but in counting active sites. Besides, must be noted that this achievement in catalytic science
sites may not be all identical. In spite of these experi- was driven by its many industrial applications, yet was
mental and conceptual difficulties, there are many made possible by the synthesis of pure single crystals of
advantages in attempting to report a TOF. This will be the catalytic material.
illustrated by the following examples dealing with solid Now, let us turn our attention to catalysis by metals.
acids or metallic catalysts. The situation depends on whether a given reaction is
structure insensitive or structure sensitive. An opera-
tional definition of structure sensitivity is that the areal
5.2.1.3 Examples of Turnover Rate Measurements rate of the reaction or its TOF depends on surface
crystalline anisotropy revealed by working on different
The arduous problems faced in the correct measure- faces of a single crystal or on clusters of varying size
ment of the rate of heterogeneous catalytic reactions between 1 and 10nm. Historically, the lack of effect
that are not under the influence of heat and mass of particle size was first noted for the hydrogenation
transfer, poisoning, activation and deactivation, are of cyclopropane on supported Pt [26]. The effect of
not considered in this chapter. The focus is on the de- particle size was first observed for the synthesis of
termination of the amount of catalytic sites. Clearly the ammonia on supported iron [30]. But the concept
first task is that they be identified. Next come two of structure insensitivity and sensitivity received un-
questions as to whether the sites are identical and equivocal confirmation from studies of the two above
whether they interact. Generally, there exist no un- reactions on single crystals of platinum [31] and iron
ambiguous answers, especially because identification [32], respectively.
and counting must be ideally carried out in situ, i.e. Consider the case of structure-insensitive reactions.
during the catalytic reaction. For a number of well investigated reactions catalyzed
But in spite of the difficulties, there are cases for by metal, the areal rate or the TOF under fixed con-
which true turnover rates have been determined con- ditions does not depend, or depends only slightly, on
vincingly. The first example deals with zeolites and re- surface crystalline anisotropy as expressed on clusters
actions catalyzed by their protonic Br~stedacidic sites. of varying size or on single crystals exposing different
Catalysis by zeolites is a vast subject recently sum- faces. Moreover, in many cases, identical or almost
marized in its science and technology by Haag [28]. equal values of TOF were obtained with metal clusters
Zeolites are silicoaluminates that are now available by supported on one or several carriers and on single
synthesis in the form of pure single crystals of micro- crystals of the same metal. These striking results have
metric size. Their crystallinity can be excellent. If the been discussed in detail elsewhere [26].
+
atomic ratio of A1 to (Si Al) remains small, i.e. below How is it possible to avoid significant effects of sur-
~ 0 . 1 interactions
, between A1 ions and also inter- face crystalline anisotropy on areal rates or values of
actions between their associated protons remain negli- TOF? First, the catalytic site involved in the rate de-
gible. This situation has been examined and reviewed termining step, if there is one, should consist of only
by Barthomeuf and found to depend on the topology one surface metallic atom or of two adjacent ones at
of the zeolitic framework [29]. With sodium-free ZSM- the most [33]. Otherwise, structure sensitivity should be
5 (MFI) zeolites, the lack of interaction between pro- recognizable. However, even with a catalytic site con-
tonic sites has been checked by measurements of the sisting of single metal atom, structure sensitivity might
specific rate for n-hexane cracking on samples with still be observable.
Si :A1 atomic ratios between 15 and almost 100 000, a Second, it is possible that the surface coverage during
range of almost 4 orders of magnitude [28]. In that reaction should be close to saturation and surface re-
range, rate, at constant temperature and pressure, was construction at the few remaining isolated sites might
 5.2 Microkinetics 961
~~

have erased surface anisotropy altogether. Such an ex- Consider next the case of structure-sensitive reac-
planation has been proposed to account for the structure tions. The best example is ammonia synthesis on iron,
insensitivity of palladium in the oxidation of carbon a reaction that continues to be of great industrial im-
monoxide on single crystals and supported clusters at portance. It is also another example of the decisive
pressures between lo-' and 102mbar [34]. Indeed, the results that can be obtained by studying a catalytic
surface of a Pd tip used in field ion microscopy re- reaction on large single crystals at high pressures in-
constructs as a result of CO adsorption at 1 mbar [35]. vestigated by Somorjai and co-workers [32]. Thus, it
Reconstruction of catalytic surfaces in adsorption or was reported that by far the most active face of iron
catalysis so as to minimize surface free energy was single crystals in ammonia synthesis at 20 bar was the
proposed and advocated by Boreskov as a general (1 11) plane, by more than two orders of magnitude for
principle in heterogeneous catalysis [36]. More re- the areal rate. This was attributed to special sites with a
cently, surface reconstruction has been shown to be one coordination number of seven, as suggested carlier in
of the possible mechanisms accounting for chemical work on supported iron clusters [39]. With these re-
oscillations in heterogeneous catalysis [37]. In every sults, a value for the TOF on Fe(ll1) can be obtained
case, the question is whether surface reconstruction, if and extrapolated to TOF data on ammonia synthesis
thermodynamically favored, can be reached kinetically at 1 bar on a multiply promoted industrial catalyst.
in a catalytic run. This question is reexamined below, The two TOF values agree within a factor of two [40].
in connection with structure-sensitive reactions. Because of the uncertainties in the extrapolation and in
Another explanation of structure insensitivity is the counting of iron sites on the industrial catalyst, this
based on the formation of a reactive hydrocarbon comparison suggests that the industrial catalyst exposes
overlayer on a metal surface during a catalytic reaction predominantly the optimum seven-coordinate sites that
involving hydrocarbons [38]. If, for instance, the rate are by far by far the most active ones in the reaction.
determining step in the reaction is the dissociation of If this tentative conclusion if firmed up by further
hydrogen on this overlayer, insensitivity to the sub- observations on a working industrial catalyst, it will be
jacent metal structure becomes understandable [26]. the first time that a true TOF has been reported for a
Irrespective of the true explanation of structure in- structure-sensitive reaction on a complex commercial
sensitivity when it is observed on a supported metal, metallic catalyst [41]. This will be also the first docu-
a single crystal, or both, the areal rate does not seem mented example of a structure-sensitive reaction on a
to be the best way to report the rate data. Indeed, on metal surface that is reconstructed so as to expose the
certain faces of a crystal, there may be sites that are most active sites. This reconstruction is brought about
inaccessible to reactants. Why not report a turnover or stabilized by catalyst promoters and/or by ammonia
frequency referred to the number of one or several used in the reduction of the catalyst. The surface re-
types of surface atoms? For supported metals, it is construction of supported iron clusters with appear-
not the surface area of the metal that is measured, ance of (111) facets after exposure to ammonia was
but rather the number of surface atoms counted by a reported earlier following studies with Mossbauer effect
fully described titration by chemisorption following a spectroscopy [39]. Surface reconstruction, if complete,
method that has been calibrated by means of indepen- leads again to the possibility of reporting what is be-
dent physical techniques. Such a TOF value is mean- lieved to be a true TOF.
ingful since, for a structure-insensitive reaction, all
accessible surface atoms can be considered as equally
active sites. Such a statement is strengthened if the 5.2.1.4 Comparison of Rate Data
same value of turnover frequency has been measured
for the same reaction under identical conditions on Today, rate data in arbitrary units or plots of con-
several faces of a single crystal of the same metal. The version versus time are slowly becoming the exception
availability of TOF values on single crystals at pres- rather than the rule in the scientific literature of catal-
sures equal to those used with supported metals, as ysis. With only one unit, namely the second, a value
pioneered by Kahn, Petersen, and Somorjai [31], must of turnover frequency offers a straightforward way to
therefore be regarded as a critical step forward in the compare data obtained in different laboratories. Com-
evolution of catalysis by metals toward a quantitative parisons between supported and Wilkinson homo-
science. Indeed, even with the best reproducible work geneous rhodium catalysts for the hydrogenation of
on supported metals, it is not possible to be sure that cyclohexene show very close values of TOF under
all of the possible support effects have been eliminated, similar conditions [42].
both in the measurement of rate and in the counting For the same reaction, TOF values in the gas phase
of sites. Thus, work with large single crystals becomes and liquid phase are collected in Table 1 for supported
the standard by which the quality of the work on sup-
ported metals can be judged. References see page 971
962 5 Elementarv Stem and Mechanisms

Table 1. Turnover frequency for hydrogenation of cyclohexene rials. Here again, values of TOF come to the rescue in
at 298K and H2 at atmospheric pressure for gas and liquid the form of a useful experimental criterion first pro-
phases. In the latter case, cyclohexane was the solvent, and the
rate was zero order with respect to cyclohexene. posed by Koros and Novak [50]. Thus, in the case of
supported metals, if the same value of TOF is obtained
Supported Metal exposed TOF (s-I) for a given reaction at fixed conditions on two catalytic
metal (o/O)a samples containing different amounts of metal on the
Gas phase Liquid phase porous support, the kinetic data are not disguised by
Ni
Rh
36-100
5-100
*
2.0 0.5
6.1 -t 1
0.45 k 0.15
1.3 -t 0.1
heat or mass transfer [50]. To be on the safe side, the
TOF should be measured at two different temperatures
Pd 11-76 3.2 0.8 1.5 0.2 on both samples.
Pt 14-100 2.8 k 0.1 0.6 k 0.1 Another application of TOF deals with new catalytic
"Determined by H2 chemisorption.
materials. It is frequently said that a new material is
attractive because of its high activity in a certain cata-
lytic reaction. What kind of activity is it? And how
does that activity compare with that exhibited by prior
metals: Pt [43, 441, Pd [45], Ni [46, 471, and Rh [42]. catalysts? While a comparison of specific rates may be
Two facts emerge from this comparison. First, the adequate, the use of TOF values gives a more direct
TOF values for Ni, Rh, Pd, and Pt differ by less than comparison, for instance in the case of molybdenum
an order of magnitude. Second, for a given metal, the carbide as compared to ruthenium for the hydroge-
TOF in the liquid phase is lower than that in the gas nolysis of alkanes [51]. In each case, of course, the
phase by less than an order of magnitude. method used in counting sites must be fully described,
For the oxidation of carbon monoxide on palladium, especially with new materials for which there is little
TOF values at low and high pressures and low and information on the nature of the sites.
high temperature have been compared in the case of Finally, TOF values are most helpful in assessing the
large single crystals, and of clusters supported both on role of promoters in catalysis. The classical example is
~-Al2O3single crystals and on high specific surface ammonia synthesis on metallic iron. Values of TOF
area ?-A1203 [34]. These comparisons have led to the reveal that promotion by alumina is only textural, i.e.
discovery of a new support effect consisting of the sur- it maintains high specific area without changing the
face diffusion of CO adsorbed on the support to the rate per exposed iron atom. By contrast, potassium
interface with supported palladium and subsequent oxide promoters do change the TOF for the reaction,
reaction with oxygen [48]. It is hard to imagine how per iron atom exposed, at least at high pressure and
this effect would have been identified without the use high values of conversion [41].
of TOF values. Indeed, it is because of anomalous In conclusion, TOF values are very useful. Why are
TOF values that the supply of molecules of CO by they not used more often? First, a TOF is a reaction
surface diffusion could be assessed and explained rate, i.e. a differential quality, that is always hard to
quantitatively. measure. Second, in heterogeneous catalysis, it is even
Another application of TOF values deals with the harder to measure a rate because of problems of heat
frequent occurrence of poisoning. Thus, for the hydro- and mass transfer, and catalyst deactivation. Finally, a
genation of cyclohexene, some supported Ptly-Al203 turnover rate is even harder to obtain because of the
catalysts were found to be poisoned with sulfur origi- necessity to determine or estimate the number of sites.
nating from sulfates on the support. For the hydro- If they are not all equally active, the turnover rate will
genation of cyclohexene, a typical structure-insensitive have an average value. Hence, many prudent inves-
reaction as can be seen in Table 1, values of TOF tigators omit to report a TOF even when they could
calculated by counting surface platinum atoms not estimate one because the rate may have been disguised
covered with sulfur by means of hydrogen adsorption by mass and heat transfer, or because the rate was not
were found to remain constant [49]. Again, it must measured: all that was measured was a yield. In that
be pointed out that the extensive TOF data for the case, a site time yield, STY, can still be reported. It is
hydrogenation of cyclohexene on many platinum the number of molecules of a specified product made
catalysts supported on different supports and consisting per catalytic site per unit time, real time in a batch re-
of metal clusters of size between 1 and lOnm, agreed actor or space (residence) time in a flow reactor. For
under identical conditions with TOF values obtained those who hesitate to estimate the number of sites,
on a platinum single crystal [26]. there is a last alternative, namely the space time yield,
A major obstacle in the correct measurement of in- the number of molecules of a specified product made
trinsic kinetic data in heterogeneous catalysis is the per unit volume of reactor per unit time. In the units
ubiquitous parasitic effect of heat and mass transfer, popularized by Weisz [52], the space time yield for
especially inside the pores of high specific area mate- large catalytic processes is, in order of magnitude.
 5.2 Microkinetics 963

1 pmol cmF3s-l, which translates roughly into a STY Table 2. Thermodynamics and kinetics for an elementary step i.
equal to 1 s-l, also in order of magnitude [53]. These
order of magnitude values are dictated by two limiting Ii k+ijk-i = exp(AP/RT)
IIi v + , / v - i = exp(Ai/RT)
considerations when porous catalysts are used. First, if IIIi ui = u+i [I - exp(-Aj/RZ‘)]
rates were much smaller, the reactor would have to be IVj if A,/RT c< 1: then vi = U ~ , ~ ( A , / R T )
too expensive for a given productivity. Second, if rates
were much larger, the catalyst and thus also the reactor
volume would be poorly utilized because the heteroge-
neous reaction would be confined to the mouth of the step must be taken a times, where a is the stoichio-
pores of the catalyst, as a result of diffusional limi- metric number of that step. In the example at hand, a is
tations into and out of the catalyst grains. Both con- 1, 2, or 3. Each step (subscript i ) is in principle a two-
straints give the technologist a “window on reality” way step: its net rate is
with the above value at its center [52]. ui = u+i - u-i
But, kinetically it could be one-way (or irreversible), if
5.2.1.5 Relationships between Thermodynamics and u+i >> v - i . Alternatively, it could be quasiequilibrated if
u+i and u-i are both much larger than ui. At the kinetic
Kinetics
steady state accociated with the name of Bodenstein,
These relationships are first considered for elementary aiu = v + ~- u-i (2)
steps. Then, they are generalized to the case of catalytic
cycles consisting of these elementary steps. For in- where u = v+ - v- is the net rate of the overall reaction
at the Bodenstein steady state. If the rate of every ele-
stance, a widely accepted catalytic cycle for ammonia
mentary step can be described by transition state
synthesis is as follows:
theory, the four relationships of Table 2 between ki-
Stoichiometric
netics and thermodynamics are easy to obtain [9]. For
number a
the ith step, they relate rate constants k+i and k-i, or
N2 + 2* + 2N* 1 rates u + ~and u - ~ to
, the standard affinity A:, the affinity
H2 + 2* + 2H* 3 A i and the rate of step i at equilibrium ~ i , The
~ . affinity

N* + H * + NH* + * 2 A is related to the Gibbs energy G by the definition

NH* + H* + NH2 * + * 2 Ai = -(aGi/dti),;, (3)
NH2 * +H* + NH3 * + * 2 where ti is the extent of reaction. Note that for any
*
NH3* NH3 + * 2 reaction to proceed ( u > 0), Aoneed not be positive but
A must be. Also at equilibrium Ai = 0, hence Z)+i = U - i
as follows from equation I1 in Table 2, a relationship
NZ+ 3H2 = 2NH3 attributed to De Donder [54, 551. The third relation-
Each elementary step is written as it is believed to take ship says that the net rate vi can be expressed in terms
place at the molecular level. Thus the dissociation of of the forward rate u+i and the thermodynamic poten-
dinitrogen on two adjacent catalytic sites denoted by tial A i . The last relationship, near equilibrium, is linear
the asterisk * is written as between flux and force.
These four equations are straightforward, but how
N2 + 2* + 2N* do they apply to a catalytic cycle? The answer is sim-
but not as ple: they do if the catalytic cycle contains one step,
called the rate determining step (rds), subscript d. If
;N2+*+N* there exists such a step, all the other steps in the cycle
are, by definition, in equilibrium, or at least in quasie-
as this is not a molecular event. The dissociation could quilibrium, as defined above ( U + i and U - i >> V i ) .
take place in two successive elementary steps, via the
Thus, if there exists a rds, Ai = 0 for all values of i
precursor N*N:
except for the rds. All (or almost all) of the affinity for
N2+*+N*N the cycle A is dissipated in the rds, so that
N *N + * + 2N* Ad = A / o ~ (4)
Other possibilities come to mind. Kinetically, what So, the four equations of Table 2 become those of
matters is that the sum of the elementary steps as writ- Table 3. Equation I is obtained readily form equation
ten add up to the stoichiometric equation for the over-
all reaction or catalytic cycle. In this summation, each References see page 971
964 5 Elementary Steps and Mechanisms

Table 3. Thermodynamics and kinetics for a catalytic cycle with reverse on a nickel catalyst, prior to Horiuti’s work.
od for rds. However, a later statistical analysis of the linear kinetic
data on both sides of equilibrium revealed that de-
I k + / k - = exp(AO/CdR T )
IIi v+/v- = exp(Ao/ad R T )
parture from linearity occurred considerably beyond
I11 U+ - V- = U- [eXp(Ao/CdR T ) - 11 the validity of the expansion of the exponential of
IV if A / a d RT << 1: then v = V,(A/Ud R T ) equation I11 to its first-order term [59]. The data anal-
ysis suggests that (Td is equal to 3. An appropriate rds
for the overall reaction
c6H12 = C6H6 -k 3H2
I1 if the rate equation can be expressed, within a certain
approximation, in the form of a power rate law (eq 1). might then be the desorption of H2 taking place three
In that case, from equation 11, at the standard value of times in each turnover of the catalytic cycle [60].
the concentrations v+ = k, and v- = k-. Also, A be-
comes Ao, so that equation I follows directly. Finally, 5.2.1.6 Most Abundant Reactive Intermediates and
equation I11 and IV follow from I1 in Table 3, as they Kinetically Significant Steps
do in Table 2.
Applications of the bridges between thermodynamics According to Campbell,
and kinetics, as collected in Tables 2 and 3, vary from
a check of good behavior (for I), a measure of the “Proof of a mechanism of a steady-state, solid catalyzed
approach to equilibrium (for II), the possibility of reaction lies in directly observing all of the elementary
obtaining the net rate, knowing only the forward rate reactions and their kinetics, and then folding these
or the reverse rate (for 111), and the simplicity of a lin- microkinetics into a global kinetic model for the net
ear rate law near equilibrium (for IV). reaction (. . .). The beauty of knowing a mechanism is
The equality I between the ratio of rate constants that it gives an intelligent way to extrapolate kinetics
and equilibrium constants is an expression, at equilib- to unknown condition. Also, it gives a detailed, fun-
rium, of the principle of microscopic reversibility; at a damental understanding of the reaction that might be
distance away from equilibrium it extends microscopy valuable in devising schemes for improving activity
reversibility, relying on the validity of transition state or selectivity, be they by changing reaction conditions
theory. Insofar as thermodynamic data are more ac- or by modifying the catalyst” [61].
cessible than kinetic data, the possibility of obtaining
This vibrant declaration expresses what we want to
one rate constant from its opposite and the corre-
know in heterogeneous catalysis. Fortunately, what we
sponding equilibrium constant can always be helpful.
need to know in practice to develop, control, and im-
The De Donder equation I1 will be used later in ex-
prove solid catalysts, is much less than what we want to
plaining catalytic coupling between elementary steps in
know. The reason is that few elementary steps affect
a catalytic cycle.
the turnover rate of a catalytic cycle through their rate
Finally, the linear relationship IV first obtained by
constants, forward, reverse, or both. Such steps that do
Horiuti [56] was used by him to pinpoint the rate de-
are said to be kinetically significant steps. Other steps
termining step of the ammonia synthesis on iron. If its
that are in quasiequilibrium may affect the rate of the
catalytic cycle is the one shown above and if the stoi-
cycle, but not through their rate constants. Thus what
chiometric number (Td of the rds is found equal to
may be a deplorable situation from the standpoint of
unity, the rds must be the chemisorption of N2. The
knowledge, is a great simplification in practice, with
value of CTd was obtained by measuring v near equilib-
the warning that such simplifications may not be ap-
rium and obtaining v, from the rate of the isotopic
plicable outside the scope of process variables within
equilibration
which they were invoked.
l4NI4N+ lSNH3e lsNI4N+ 14NH3 An example of the advantage of simplifying a cata-
lytic cycle is the catalytic ammonia synthesis. Suppose
taking place in a mixture of N2, H2, and NH3 at equi- that the catalytic cycle given in Section 5.2.1.5 with six
librium except for the isotopic composition, since ki- elementary steps proceeding in two directions: this is a
netic isotope effects are negligible in this situation. An- cycle with 12 rate constants and five reactive inter-
other kinetic use of equation IV in Table 3 is for the mediates. But, assume now that nitrogen adsorption-
catalytic removal of pollutants down to the ppm level, desorption is the rate-determing step in Horiuti’s sense,
since the rate described by the linear relationship IV so that all five subsequent steps are in quasiequili-
must be first order with respect to any variable meas- brium. Suppose further that the most abundant re-
uring the distance away from the end of reaction [57]. active intermediate is N*, so that
Historically, the linearity of IV was first verified [58] for
the dehydrogenation of cyclohexane to benzene and its “*I >> [NH*],“H2.1, [NH3*],[H*]
 5.2 Microkinetics 965

Then, all five quasiequilibria following the rate deter- By contrast, above T,, at low pressure, CO is ad-
mining step can be added side by side to yield an overall sorbed on the free palladium surface that is sparsely
quasiequilibrium designated by the symbol #: covered with CO, still in quasiequilibrium and CO,
diffuses to the periphery of islands of 0, where the one-
2N* + 3H2 # 2NH3 + 2* (5) way LH step occurs. Now the LH step is the only ki-
with an overall equilibrium constant K . With the two netically significant step, If we accept the proposition
assumed simplifications, the turnover rate is deter- [65] that the only kinetically significant step in a cata-
mined by the two rate constants of the rds, and the lytic cycle is still called the rate-determining step, even
equilibrium constant K . The rds with dd = 1 proceeds if not all others are in quasiequilibrium, and if the cus-
at a rate Ud = Ud+ - Vd-. The rds is the only step for tomary symbol A adopted for the rate determining step
which we can write is kept as in the case of Horiuti, below Tmaxwe have
u+ = Vd+; 0- = v& COeCOa
with v = v+ - v- as the turnover rate of the cycle. The
rds is the only kinetically significant step (kss). 02 ++ 20,
However, there exist many situations besides that COa + 0, +CO2
first recognized by Horiuti, for which there also exists
only one kss in the catalytic cycle, but not all other and above T,,,
steps are in quasiequilibrium. Consider the rate of oxi- CO +COa
dation of carbon monoxide on palladium or platinum.
Langmuir reported this kinetic study at a 1921 discus-
sion of the Faraday Society [62]. Ertl and co-workers
0 2 ++ 20,

extended all earlier studies by systematic kinetic in-

co, + 0, +co2
vestigations on large single crystals [63]. Next to the Thus the rate-determining step shifts from the first one-
two-way ammonia synthesis, the one-way oxidation of way step in the cycle to the second one as the tem-
carbon monoxide is today the best understood catalytic perature rises. Another possible way to handle the
reaction. situation would be to state that both one-way steps
With almost equimolar mixtures of CO and 0 2 , be- determine the rate of the catalytic cycle. We believe
tween 400 and 600 K, from lop6 to lo2mbar, the im- that this simple prescription carries less useful infor-
portant steps in the catalytic cycle seem to be mation than the one we favor. Consider next the case
of catalytic cycles with two, one-way steps.
Consider a one-way reaction A * B with two, one-
way steps: the entry step (in) and the exit step (out).

COa + 0, -
kLn
CO2.g
where, using the common notation of surface science,
There may exist many intermediate steps, reversible,
irreversible, or quasiequilibrated, but there is no need
to consider them explicitly if adsorbed B is the most
abundant reactive intermediate, so that [*] + [B*] =
the subscripts a and g denote surface or gaseous species [L],where [L] is the total density of sites. To obtain the
respectively. Thus, CO chemisorbed without dissocia- rate u for the overall one-way reaction, the only ki-
tion, is in quasiequilibrium (equilibrium constant K,); netically significant steps are the first and the last in the
0 2 is chemisorbed dissociatively in a one-way step (rate cycle:
constant ka); and COa reacts in one-way with 0, to kin
form COZ in a verijied Langmuir-Hinshelwood (LH) *+A+ ...
step (rate constant ~LH). Because of the existence of
two nonequilibrated steps, there is no rds in the classi-
cal sense of Horiuti. But what about the kinetics? B*k"",. * + B
Two temperature regimes are recognized: between
% 400 and z 500 K with a normal exponential increase At the quasisteady state,
of the rate with temperature, and above % 500 K (T,,,
v = Ui" = V,"t
where the rate decreases exponentially with T . Between
400 and 500K, and over eight orders of magnitude of so that, in general, the turnover rate v will depend on
total pressure [64], the chemisorption of 0 2 occurs on a both kin and kOut.
surface practically saturated with CO,. The only rate This situation is observed in the low pressure one-
constant affecting the turnover rate is k,, correspond- way decomposition of ammonia at temperatures that
ing to the chemisorption of 0 2 . The latter is then the
only kinetically significant step. References see page 971
966 5 Elementary Steps and Mechanisms

are neither low nor high, at low pressure on several stituted in them are correct and retain their usefulness,
metals [66]. Thus, according to our definition, there is even if 0 remains unknown.
no rate determining step in this general case. But at low Ultimately, as the microkinetics methodology [71-
temperatures, the rate is described simply as u = uOut 741 develops, the concept of the rate determining step
[67], with desorption of nitrogen B being the rate de- may be replaced by the tool of parametric sensitivity,
termining step, while at the other limiting case of high as proposed, without using this name, by Campbell
temperature, u = Uin [68], with adsorption of ammonia [61]. In microkinetics, a catalytic (or chain) reaction
A becoming the rate determining step. or a network of such reactions is described by a set of
There are many examples of first-order rate equa- known or plausible elementary steps; the correspond-
tions corresponding to adsorption on a sparsely cov- ing rate constants are collected from experimental data,
ered surface being the rate determining step, and of theoretical calculations, or semiempirical estimates.
zero-order rate equations corresponding to desorption The ordinary differential equations are then solved by
from a saturated surface being the rate determining computer. The activity and selectivity are obtained.
step. An example of the first kind is the oxidation of Clearly, it is important to know which steps are kineti-
propylene to acrolein [69]. An example of the second cally significant, in order to obtain a physical insight in
kind is the decomposition of germane on a germanium the fog of a very complex situation. As put by Camp-
film saturated with adsorbed H [70]. The latter example bell, a degree of rate control Xi could be obtained from
is discussed in Section 5.2.1.8. each step:
In both cases, the original definition of Horiuti can-
not be used. We could say that there exists an unknown (7)
number of nonequilibrated steps, but that does not
carry useful information. Indeed, we have no kinetic where the partial derivative of the overall rate with re-
information on intermediate steps between the entry spect to the rate constant ki of the step is taken holding
step and the exit step: some may be in quasiequili- constant the equilibrium constant for step i and the
brium, some may not be. Even in the general case rate constants k, for all other steps. Campbell notes
treated above, we may say that both the entry step and that the rate determining step as defined by Horiuti and
the exit step are kinetically significant, because they are with the extended definition being the only kinetically
nonequilibrated, but what about the intermediate ones? significant step, has a degree of rate control of unity,
How many are also nonequilibrated? What is the whereas the latter is equal to zero for all other steps.
meaning of these nonequilibrated steps? Clearly, all intermediate values of Xi are possible and
By contrast, our proposed definition of the rate de- probable in the majority of cases.
termining step is consistent with common usage, except As more microkinetic calculations are performed, it
that common usage usually lacks precision. Thus it can will be interesting to review the situation. In the mean-
be said that the rate determining step in the oxidation time, it is convenient to continue talking about a rate
of propylene to acrolein is the abstraction of a hydro- determining step in the sense of Horiuti, or perhaps
gen atom from propylene to form an allylic surface in- about a single kinetically significant step with all other
termediate. This conforms to our definition because the steps being equilibrated or not. These simplifications
measured overall rate is that of the entry step, as con- are helpful in theory and in practice.
firmed by the observed kinetic isotope effect in the ratio
of kin,H to k,,,D. The latter is equal to what is expected
if the transition state of the rds corresponds to the for- 5.2.1.7 Kinetic Coupling in Catalytic Cycles: Effect
mation of the light or heavy allylic intermediate [69]. on Rate
It must be noted that with the extended definition of
the rate determining step being adopted as being the In catalytic or chain cycles, the reactive intermediates,
only kinetically signficant step, the stoichiometric num- surface adducts or free radicals, can be in equilibrium
ber of Horiuti’s rds, C Q , must be replaced in Table 3, with stable reactants or products. Alternatively, their
by Ternkin’s [70] average stoichiometric number 0 of concentrations at the kinetic steady state can be lower
the catalytic cycle, as defined by or higher than equilibrium values. The latter situation
is the rule rather than the exception in chain reactions.
Unfortunately, in the customary approach to catalytic
kinetics, common assumptions are that the reactants
the summation applying to all the steps that are not in and products are in equilibrium with catalytic inter-
quasiequilibrium. Clearly 0 = Dd for the Horiuti sit- mediates, and the rate determining step is a so-called
uation. Unfortunately, there is no way to determine 0. Langmuir-Hinshelwood step between two such inter-
Besides, its value changes with extent of reaction. mediates. These assumptions may well be inadequate
However, the relationships of Table 3 with 0 sub- or incorrect in many situations.
 5.2 Microkinetics 967

To understand how catalytic cycles turn over, it (A! < 0), it does not mean that the cycle will not turn
is important to distinguish between equilibrium and over, as it may well do so with the help of catalytic
steady-state values of concentrations. The best example coupling. Finally, let us note that in the example of the
is borrowed from the classic work of Bodenstein and HBr reaction, while [Br],, = [Brie, the concentration
Lind [75] on the one-way thermal reaction between H2 of H atoms at the steady state, while inferior to that
and Br2 that remains one of the best understood non- corresponding to its equilibrium concentration corre-
elementary reactions. Under the conditions used by sponding to the first step (eq 6) is many orders of
Bodenstein and Lind, there is, at the steady state, an magnitude larger than that corresponding to the equi-
equilibrium between bromine atoms and molecules librium between H2 and H in the system.
[Br],, = [Br],. The propagation cycle is Let us now consider examples of catalytic reactions
where the steady state concentration of a surface spe-
k+1
Br+H2 + HBr+H cies is very different from the value expected if equi-
k-i librium prevailed between this surface species and a
HfBrzkz - + H B r + B r fluid-phase species. They will be examples of kinetic
coupling and also of a useful concept, that of fugacity
It consists of a first two-way step followed by a second of a surface species in equilibrium with a fluid phase
one-way step. The reason for the difference is that the species not at its steady state fugacity but at a different
first one is strongly endothermic while the second one virtual fugactity.
is strongly exothermic. In both cases, the change in The first example is a reaction similar to the first
entropy is very small. It follows that the extent of the catalytic reaction studied kinetically by Stock and
endothermic step will be limited by equilibrium with Bodenstein [ 11, namely, the decomposition of gaseous
the product of the reaction HBr. In fact, its standard germane GeH4 on a mirror of germanium acting as the
affinity AO is negative. catalyst for the decomposition to germanium and di-
However, the affinity A of the first step is positive hydrogen [65]. The following facts must be explained:
until the end of the reaction. Thls is due to the kinetic (i) the rate does not depend on germane or hydrogen
coupling [54] between the propagation steps, itself a pressure; (ii) decomposition of GeH4 in the presence of
consequence of the De Donder relation I1 in Table 2. D2 does not yield HD; (iii) decomposition of mixtures
Indeed, it can be shown [55] that, at the steady state, of GeH4 and GeD4 yields H2, D2, and H D but no
v1 = 02 and, at half reaction, [Hz] = [Brz] = [HBr]: GeH,D4-, species; (iv) the equilibration of H2 and D2
takes place rapidly on a germanium mirror at the tem-
perature where GeH4 decomposes on its own sepa-
rately. These observations can be explained by two,
However, according to the data of Bodenstein and one-way steps:
Lind, as interpreted by others, k2/k-1 = 10. Thus the
concentration of H in equilibrium with H2, HBr, and *+GeH4-+ ... (in)
Br in step 1, namely [H]l,ehas been reduced to a value H * +H * -+ H2 + 2 * (out)
at the steady state [HI,, by a factor of 11; this also ac- If these steps are one way and the surface is saturated
counts for a positive value A1 instead of a negative with hydrogen (or deuterium) atoms: (i) the measured
value of A!. This reduction is the consequence of rate is zero order; (ii) D2 has no access to the surface
kinetic coupling between steps 1 and 2 in the cycle: be- during decomposition of GeH4; (iii) GeH4-GeD4 mix-
cause k2/k-1 = 10, the atoms of hydrogen produced in tures yield H D but no isotopically mixed reactants; (iv)
step 1 are pumped away be step 2 ten times faster than H2-D2 mixtures equilibrate on Ge but not under de-
they return to H2 by the reverse of step 1. In other composition of GeH4. During decomposition of GeH4,
words, kinetic coupling is expressed by the fugacity of H* is very high, much higher than it
02 = 10 x u-1
would be in the presence of H2 at a steady state pres-
sure of H2 generated in the decomposition. In sum-
In the absence of kinetic coupling, step 1 would be in mary, the kinetic coupling between the in step and the
quasiequilibrium: out step results in a surface coverage by H atoms close
to unity; only a much higher virtual pressure of H2
02 = V+I = v-I, and [HI,, = [HI,,,
could lead to such saturation with H2 alone in the gas
Kinetic coupling helps a catalytic cycle to turn over, in phase. The only kinetically significant step is the de-
spite of unfavorable thermodynamics affecting one or sorptions of H2, and H2 does not inhibit the decom-
several elementary steps through the principle of Le position since it cannot compete with GeH4 for access
Chatelier: by accumulating reactants or evacuating to the surface.
products. Hence, if calculations reveal that some steps
in a catalytic cycle are thermodynamically unfavored References see page 971
968 5 Elementary Steps and Mechanisms

The second example is the platinum-catalyzed de- idea of surface fugacity of adsorbed nitrogen together
hydrogenation of methylcyclohexane (M) to toluene with the assumption that nitrogen adsorption and de-
(T) and H2. It was studied far from equilibrium and, sorption were rate determining in the sense made
indeed, the rate was found not to be inhibited by tol- clearer by Horiuti a few years later. Thus, in ammonia
uene. The data led to a catalytic cycle with, as in the synthesis, gaseous N2 is not in equilibrium with ad-
previous example, only two, one-way steps, both of sorbed nitrogen. In ammonia decomposition gaseous
them kinetically significant: N2 is not in equilibrium with adsorbed nitrogen or ab-
sorbed nitrogen that forms iron nitride Fe4N. Consider
*+M-+ ... the case of decomposition, with desorption of N* as
T* +T+* rds, N* as most abundant reactive intermediate and, as
a consequence, the reverse of eq 5 followed by the rds:
where T* is the most abundant reactive intermediate.
As chemical intuition teaches that both toluene and
2NH3 + 2 * -2N* + 3H2
benzene are more strongly held on platinum than 2N * h N 2 + 2*
methylcyclohexane, substantial amounts of benzene
were added to the feed but were found to have no ap- Since the desorption (subscript d)-adsorption (sub-
preciable effect on the rate of reaction of toluene. Thus script a) step is rate determining, with Od = 1, the
it appears that the steady state surface coverage by affinity of that step is equal to the affinity A of the
toluene is very much higher than that corresponding overall reaction
to equilibrium with gas phase toluene. Again, this is 2NH3 = N2 + 3H2
a result of kinetic coupling: it explains the absence of
inhibition by toluene at its steady state partial pressure Hence, from the De Donder equation, applied to the
as well as the absence of inhibition by added benzene. rds,
As above, everything happens as if the steady state vd
fugacity of adsorbed toluene were in equilibrium with a
- = exp(A/RT) (9)
0,
virtual fugacity of gas-phase toluene much higher than
its steady state fugacity or that of added benzene. Now, u, must be proportional to the fugacity of gas-
In a third example, the enhanced coverage at the eous N2 at the steady s t a t e f ~ ~the
, ~ ;constant of pro-
steady state as compared to an equilibrium coverage portionality is a certain function d, the value of which
could be measured quantitatively. The reaction was the depends on the fugacity of surface nitrogen at the
decomposition of ammonia at low pressure and high steady state f ~ * , ~ :
temperature on a molybdenum foil heated to high Ua = d( fNt,s) x fN2,s (10)
temperature in an ultrahigh vacuum chamber acting
as a continuous stirred tank reactor [76]. At the low Consider now that desorption at the steady state is in
pressures used, it was possible to measure adsorption equilibrium with a virtual fugacity of N2, f ~ ~i.e., the
~ ,
isotherms of N2 on Mo by determining equilibrium fugacity of gaseous N2 that would be required at equi-
surface coverage [N*] by Auger electron spectroscopy. librium to maintain the fugacity of surface nitrogen at
The latter was also used to determine the steady state its steady state valuef&. Then, for this virtual equi-
concentration "*Is during the decomposition of am- librium,
monia. The results show that "*Is >"*] at equal vd = va)v
pressures of N2. Again it appears that, because of
kinetic coupling, the fugacity df N* at the steady state where va,v is a rate of adsorption which is the product
corresponds to a virtual fugacity of gaseous N2 con- OffNz,v and the function 4 with its value at the fugacity
siderably higher than that prevailing at the steady state. of adsorbed nitrogen at the steady state. Hence:
Unfortunately, under the conditions of this work, there Ud = Ua,v = '$( fN*.s) x fN2,v (11)
are two kinetically significant steps, in and out, as dis-
cussed in Section 5.2.1.6, so that the affinity is dis- Substituting eqs 10 and 11 into 9 yields
sipated over two one-way steps and there is no way to fN2,v = fN2.s x exp(A/RT) (12)
calculate the virtual fugacity of N* to compare it with
experimental values. from which it is easy to calculate fN2,v. Indeed, eq 12
However, this comparison can be done when am- can be rewritten as
monia is decomposed over an iron catalyst at medium
temperatures and pressures. These were the conditions
for the work analyzed by Temkin and Pyzhev in their
famous paper already mentioned in the Introduction where K is the equilibrium constant for the overall re-
[7]. In this paper, Temkin and Pyzhev introduced the action
 5.2 Microkinetics 969

2NH3 = N2 + 3H2 prevailing if they are run separately with the same cata-
lyst under the same conditions. This is due to the face that
From tables, at 673 K, the value of K is 6 x 1013Pa2.
reactants or products in each reaction compete for the
The value of the virtual pressure, same sites or reactive intermediates. Hence selectivity,
or ration of rates, can be studied only in a situtation
when the two reactions proceed at the same time.
obtained from eq 13 with the use of partial pressures, A classic example is the hydrogenation in parallel of
can be checked from experimental thermodynamic two different alkyl aromatic compounds A1 and A2 on
data in the literature. This was done by lchikawa [77], a Raney nickel catalyst [81]. Separately, each com-
who used equilibrium data for two equilibria at 673 K pound saturates the surface and each rate is equal to a
andpH2 = 1.01 x 1o5Pa (1 atm): different rate constant kl or k2. However, in simulta-
iN2 + 4 F e e F e 4 N
neous hydrogenation, each compound shares the satu-
(15) rated surface as determined by two adsorption equilib-
NH3 + 4Fe Fe4N + HZ (16) rium constants K1 and K2. The ratio of rates is now the
product of the ratio of concentrations [Al]/[A2] multi-
The data give p~~= 3.10 x lo8 Pa and P N H ~ = 0.736 x plied by a selectivity factor
lo5Pa. Note that it takes a pressure of N2, more than
1000 times larger than that of NH3 to maintain Fe4N Si ;2 = ki Ki lk2K2
at equilibrium. Moreover, the calculated value of P N ~ where the kinetic coupling is determined both by the
is identical to that calculated for p ~from ~ eq. 14~using ratio of rate constants and of the ratio of equilibrium
the above values for p ~ ~ N~ H ,and ~ , K. The result is
constants. The sum of the rates when the reactions are
p ~= 3.15 ~ x, lo8~Pa, identical to the thermodynamic run separately is simply kl < k2, whereas in parallel
experimental value. hydrogenation the situation can be much more com-
The reason for summarizing here the calculations plex. Indeed, suppose that k2 < k2 but that K1 > K2.
of lchikawa is that the concept of virtual pressure, or Then the slow component A1 will monopolize most of
fugacity, first introduced by Temkin and Pyzhev and the surface, but as it reacts away, the sum of the rates
generalized later by Kemball [78], is often regarded will increase as the faster component A2 gets access to
with suspicion for the simple reason that it is called the surface. Many examples of this kind were obtained
virtual. The calculation of lchikawa vindicates quanti- by Jungers et al. in the 1950s [82].
tatively the use of virtual pressure or fugacity obtained As a second example, consider the consecutive hy-
from the De Donder equation. The concept of virtual drogenation of an alkene A1 to an alkene A2 to an
fugacity is potentially useful whenever an adsorption- alkane A3 on a heterogeneous catalyst. If K1, the
desorption step in a catalytic cycle at the steady state is adsorption equilibrium constant of A1 is much larger
not in quasiequilibrium.
than K2, the corresponding equilibrium constant for
Another application of virtual fugacity is found in a
A2, selective yields of A2 are possible even when k2, the
study of aromatization of light alkanes on a zeolite rate constant for the surface hydrogenation of A2, is
catalyst: as surface hydrogen and gas phase hydrogen much larger than that for A1. Indeed, the two reactions
are not in equilibrium at the steady state, a high are coupled kinetically as both A1 and A2 compete for
fugacity of adsorbed hydrogen leads to cracking of ad-
the same sites. A striking example of this situation is
sorbed hydrocarbon fragments and a decrease in se- shown in Table 4. As can be seen, the hydrogenation is
lectivity for aromatization [79, 801. To abate the high
not only regioselective but also stereoselective, and the
fugacity of surface hydrogen, gallium is added to the
yields. i.e. the products of conversion and selectivity,
zeolite to provide an escape route for surface hydrogen. are impressive, thanks to kinetic coupling.
In conclusion, kinetic coupling between steps in a
catalytic cycle at the steady state can result in a striking
departure of surface concentrations from their equilib- Table 4. Products of reaction between 2-butyne and deuterium
rium mode. at 287 K on palladium, from the data of Meyer and Burwell [83].

Product Yield (mol YO)

5.2.1.8 Kinetic Coupling between Catalytic Cycles: 2-Butyne 22.0
Effect on Selectivity cis-2-Butene-2,3-d2 77.2
trans-2-Butene-2,3-d2 0.7
Kinetic coupling between catalytic cycles is responsible 1-Butene 0.0
Butane 0.1
for a generally observed phenomenon, namely that,
if two catalytic reactions take place at the same time,
their individual rates will not be the same as those References see page 971
970 5 Elementary Steps and Mechanisms

As a third example, bifunctional catalysis uses kinetic Table 5. Enantiomeric selectivity ( R ) / ( S ) from the data of
coupling between catalytic cycles, but in this case the Landis and Halpern at 298 K [84].
catalytic cycles are different catalysts. An example with
kinetic details is discussed elsewhere [26], In the iso- PHI (atm) (R)/(S)
merization of n-pentane, n-C5, iso-pentane, i-C5, an 0 54
intermediate n-pentene, n-CF, is first found by de- 0.35 49
hydrogenation of n-Cs on a platinum catalyst, in close 1.1 24
proximity to an acidic catalyst, an alumina that ac- 9.07 6.6
a, 2.0
tually supports the platinum clusters. Alumina then
isomerizes n-Cy to i-Cy and the latter diffuses back to
the metal where it is hydrogenated into the final prod-
uct, i-CS. The process relies on the proximity of the two Now, the chemistry is such that, from experimental
catalytic functions. data,
A last example deals with the enantiomeric selectivity
for reaction of an alkene A with hydrogen B on a soluble
organometallic chiral catalyst *. This reaction network Given this chemistry, at all values of p~~ the favored
was studied exhaustively by Landis and Halpern [84]. product is the ( R ) enantiomer in spite of the fact
Because all six kinetically significant rate constants that the more abundant intermediate is A:. As p~~
were measured, this is perhaps the best catalytic net- increases however, the kinetic pull to the right
work with which to illustrate the effects of kinetic cou- (k2( R )/k2(4) is weakened by the relatively growing im-
pling in and between catalytic cycles [85]. There are portance of the thermodynamic pull to the left
two branches in the reaction network, left and right: ) . net result is shown it Table 5 and de-
( K i S ) / K i R )The
tails are given in the original paper [84] and a review of
the work [85]. At the intermediate values of the pres-
sure, the first step is neither one way nor quasiequili-
brated. The corresponding commonly-made approx-
On each branch, the addition with * leads to the two imations in catalytic kinetics must always be regarded
most abundant reactive intermediates A5 and AT, via a with caution, convenient as they may be.
first step that may be one-way, two-way, or quasiequi-
librated. These intermediates then react via a second
one-way step with B to give ultimately the diaster- 5.2.1.9 Conclusions
eoisomers S and R via steps that are not kinetically
significant. The two branches are kinetically coupled It will have been noted that this chapter does not con-
through the concentration of free sites *, and the two tain any rate equation except the empirical one in the
steps on each branch are kinetically coupled through introduction, as a historical tribute to Bodenstein. Of
the steady-state relationship course, this is no accident. Rate equations in heteroge-
neous catalysis are useful in the design and operation
v+1 - u-1 = v2
of catalytic reactors; how to obtain rate equations and
In particular, if 212 << v-1, the first step will be in qua- fit kinetic data properly is common knowledge [6].
siequilibrium, whereas in the opposite situation, The emphasis in this chapter has been on the rate it-
u2 >> u-1, the first step will be one way. These two ex- self rather than on the rate equation. The turnover rate
treme situations correspond to a vanishingly small is the kinetic signature of a catalyst. To understand
pressure of H2, p ~ or~an , infinite one, respectively. how the catalytic cycle turns over, a number of sim-
This is because, on each branch, 212 = k2[A*] x P H ~ . plifications can be envisaged. Beyond the steadystate
Thus, the enantiomeric selectivity, expressed as [(R)]/ approximation, these simplifications include the rate
[(S)]will depend on p ~ decreasing
~ , with increasing determining step, or a single kinetically significant step,
pressure. Why should that be? At the high pressure and the most abundant reactive intermediate. Steps in
limit, the first steps are one way and their rate con- the sequence can be one-way, two-way, or quasiequili-
stants determine the selectivity brated. Sometimes, the rate can be obtained from a
minimum of experimental knowledge. For instance, in
the case of ammonia synthesis on iron catalysts, the
At the low pressure limit, the first steps are in quasie- knowledge that the rate determining step is the ad-
quilibrium and the selectivity is determined by the sorption-desorption of nitrogen permits calculation of
equilibrium constants of the first steps and the rate the rate from the rate of desorption only by means of
constants of the second steps: equation I11 in Table 2, without any knowledge of
the rate equation. Thus it should be possible to use
temperature programmed desorption data of nitrogen
 5.2 Microkinetics 971

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89. M. Boudart, in Catalyst Design: Progress and Perspectives gas phase with a timescale typically less than 10-l2s.
(Ed.: L. L. Hegedus), Wiley, New York, 1987, Chapter 6, Two examples of such a reaction are direct dissocia-
p. 141. tive chemisorption, e.g. A2(g) + 2A(a), and the so-
called Eley-Rideal surface reaction mechanism, e.g.
A(a) + AB(g) + A2B(g). (Here, and hereafter, (a) de-
notes an adsorbed species, and (g) denotes a gas-phase
5.2.2 Dynamics of Surface Reactions species. Later in the chapter (a) is replaced by (p) or (c),
and this implies physical adsorption or chemisorption,
C.B. MULLINSAND W. H. WEINBERG respectively.) In this type of reaction, the most relevant
temperature is that of the gaseous reactant. Since the
reactant is not trapped at the surface, it cannot ac-
5.2.2.1 Introduction commodate to the surface temperature.
The other, quite different, type of reaction is a trap-
This chapter attempts to systematize much of the ex- ping-mediated surface reaction. In this case there is a
isting experimental data regarding the chemistry of “real” (bound) intermediate in the reaction, which is
surfaces within the context of a few general “rules” or usually termed a precursor. The lifetime of the pre-
concepts. In other words we shall attempt to answer cursor is usually sufficiently long compared to a vibra-
 5.2 Microkinetics 973

(a) the reaction coordinate p is shown; the potential min-

ima corresponding to the physically adsorbed Az, the
molecularly chemisorbed A*, and the dissociatively
chemisorbed A2 are noted explicitly. The two barriers,
both of which lie below the “vacuum zero” of energy
(the gas-phase A2 molecule infinitely far from the sur-
X,Y face and at rest), have associated with them two tran-
sition states which are denoted by t and $. T o the left
of the minimum corresponding to dissociative chem-
isorption in Fig. l(a), there are two branches of the
potential, one of which is denoted by i and the other
of which is denoted by 11. The Ibranch corresponds to
motion perpendicular to and into the surface, which
is repulsive due to the Pauli Principle. The 11 branch
corresponds to motion parallel to the surface, which is
periodic on a single-crystalline surface and describes
adatom hopping on the surface. A contour plot which
captures the important features of the potential energy
surface is shown in Fig. l(b). The intramolecular
(A-A) spacing is plotted on the ordinate, and the
spacing between the surface and the center of mass of
the A2 molecule is plotted on the abscissa. Note that
the three potential minima and the two barriers (tran-
sition states) are labeled in the same way as they are in
the one-dimensional representation of Fig. 1(a). The
final dissociatively chemisorbed state corresponds to
two A adatoms typically separated by one lattice con-
stant on the surface. Since this is a large separation
Figure 1. (a) One-dimensional potential energy diagram (along compared to most molecular bond lengths, one would
the reaction coordinate p ) for the hypothetical surface reaction in general expect “late” barriers to dissociative chem-
Az(g) + Az(p) + Az(c) + 2A(c). (b) Potential energy surface in isorption, i.e. barriers that are will into the exit channel
the form of a contour diagram for the reaction in Fig. l(a). The
reaction coordinate p is shown as a dashed line. Note that the of the reaction, as is indicated by the 3 in the contour
carves labeled I and 1 1 represent motions of the dissociated sur- plot of Fig. l(b).
face species, i.e. A(c), perpendicular and parallel (x, y directions) It can be deduced from Fig. 1 that trapping-medi-
to the surface, respectively, and that the transition states are de- ated dissociative chemisorption is far more probable
noted by the symbols t and $. than direct dissociative chemisorption except in un-
usual cases. In order for the A2 molecule to chemisorb
tional period of the trapped molecule perpendicular to dissociatively in a direct fashion, it must have sufficient
the surface that it accommodates thermally with the kinetic energy to scatter inelastically from the repulsive
surface. Although the elementary surface reaction rate part of the potential surface and redirect sufficient en-
coefficients will be functions of surface temperature ergy along the reaction coordinate (the A-A intra-
only, the measured reaction rate could be a function of molecular stretching mode in this case) in order for the
both the gas and the surface temperature. This is be- reaction to occur. Note that the other inelastic channels
cause the trapping probability into the precursor state, in this scattering event are dissipative and do not lead
a dynamic effect, is primarily a function of the gas to reaction. These dissipative channels include phonon
temperature. and electron-hole pair excitation in the solid, and other
The most general case of trapping-mediated dis- intramolecular energy exchange within the A2 mole-
sociative chemisorption may be written as cule, e.g. rotational degrees of freedom and trans-
A2(g) * A2(P) * A2(C) 2A(c)
+ (1)
lational degrees of freedom parallel to the surface.
Hence, a considerable apparent activation barrier to
Here, the physically adsorbed A2 molecule is a pre- direct dissociative chemisorption would be observed
cursor to the molecularly chemisorbed state, which, in experimentally for this system, although there is no
turn, is a precursor to the dissociatively chemisorbed barrier at all with respect to the vacuum zero of energy
products of the reaction. Projections of a possible for trapping-mediated dissociative chemisorption.
potential energy surface describing this reaction are
shown in Fig. 1. In Fig. ](a) the potential energy along References see puge 983
974 5 Elementary Steps and Mechanisms

Reference Energy Zero

where CiBA is the two-dimensional concentration of

“activated complexes” at the transition state on the
w potential energy surface, dp is a differential length
.-
1 S-A+S-BA
”
2
along the reaction coordinate at the transition state, I,
2s +
CL Reaction Coordinate, p
is the center of mass velocity (dpldt) of reacting species
along the reaction coordinate, andf(p) is a normalized
Figure 2. One-dimensional potential energy diagram (along the velocity distribution function.
reaction coordinate p ) for the hypothetical Langmuir-Hinshel- The concentration of activated complexes CiBAmay
wood reaction, S-A + S-BA + S-A-B-AI -+ S + A2B(g),
where S denotes a surface binding site. be evaluated from the equilibrium reaction that is as-
sumed in eq 2 via the equilibrium coefficient of this re-
action K ( T ) ,i.e.
The other previously mentioned example of a direct
surface reaction is the Eley-Rideal mechanism. This
is to be contrasted with the Langmuir-Hinshelwood
mechanism, which implies a reaction between two ad-
sorbed species, and which clearly fits into our definition where CA and CBAare the two-dimensional concen-
of a trapping-mediated reaction. It is probably fair to trations of the reactants, p is the area of an adsorption
state that the Langmuir-Hinshelwood reaction mech- site on the surface, q is a single-particle canonical en-
anism is the more correct way to describe most surface semble partition function, $, is the single translational
reactions, which is another way of saying that trap- degree of freedom of the ABA complex along the re-
ping-mediated reactions are usually more important action coordinate, and the prime on (qaBA)’reminds us
than direct reactions. In the next section some simple that the one degree of freedom along the reaction co-
theoretical arguments are presented that put this con- ordinate (4;) has been removed from this partition
clusion on a firmer foundation. function, i.e. there are 3n - 1 (not 3n) degrees of free-
dom in (qaBA)’,where n is the number of atoms per
activated complex. For example, if A and B are taken
5.2.2.3 Transition State Theory of Surface Reaction to be atoms in this example, then there are eight de-
Rates grees of freedom in (qaBA)’.The degree of freedom
contained in ( q i ) can very loosely be thought of as
In this section the rates of Langmuir-Hinshelwood and what would be the frustrated translational degree of
Eley-Rideal surface reactions are formulated within freedom perpendicular to the surface of the ABAl
the context of an elementary, equilibrium statistical complex were it bonded to the surface in our usual
mechanical treatment of transition state theory. This picture of adsorption.
allows a quantitative assessment of the relative impor- Writing eq 4 as
tance of these two mechanisms: the trapping-mediated
Langmuir-Hinshelwood reaction versus the direct
Eley-Rideal reaction.

A Langmuir-Hinshelwood Reaction Mechanism and substituting eq 5 into eq 3 allows us to write, for

Consider the following surface reaction which obeys the rate.
the Langmuir-Hinshelwood mechanism:
S-A + S-BA + ( S . . . A . . . B . . .A)’ + A2B(g) (2)
where S denotes a surface binding site. The one-
dimensional potential energy diagram along the re- In order to evaluate ( b ) , we perform the averaging
action coordinate p is shown in Fig. 2 for this activated with the properly normalized Maxwell-Boltzmann
and (assumed) exothermic reaction. The rate of the re- distribution function and the rate expression of eq 6
action is just the rate (usually written as a flux) at becomes
which the reactants cross (irreversibly) a hypothetical
surface at the saddle point of the potential energy sur-
face (the barrier in Fig. 2) which separates the reactants
from the products. Hence, it follows that
 5.2 Microkinetics 975

In order to evaluate qb, we make use of the classical where AU; = U i - 170 > 0. We might, for complete-
phase integral for the one-dimensional translation ness, multiply the right-hand side of eq. 16 by ( K ) ,
along p which gives the so-called dynamical correction to transition-state
theory [l], which taken into account the possibility of
barrier recrossing by the product molecule.
We can write the reaction rate (in units of flux,
where A is an effective de Broglie wavelength. Sub- recall) in terms of a Langmuir-Hinshelwood reaction
stituting eq 8 into eq 7 allows us to write the rate of rate coefficient as
reaction as RL-H -
kLPHCAC J ~ A (17)
where

If, as is essentially always the case, the reactants oc- kL-H =

- k(0)L-He-AUi/kBT, (18)
cupy specific sites, then this localization implies that
In order to obtain a “physical feeling’’ for the mag-
each of the partition functions that appears in eq 9 is a
nitude of the preexponential factor of the Langmuir-
vibrational partition function. This gives
Hinshelwood reaction rate coefficient, let us assume
that T, = 400 K, p = 6.7 x cm2 (a site concen-
tration of 1.5 x 1015cm-2), and the ratio of the vibra-
and tional partition functions (with the factor involving the
zero-point energy having been extracted) is approx-
imately unity. In this case we find that

where we have assumed that the vibrational degrees k(o)L-H

z 5.6 x 1 0 - 3 ( ~ ) ~ m
s-l2 (19)
of freedom are separable, and the electronic ground
and (K) < 1. Hence, a “normal” value of the pre-
states are nondegenerate. The “Boltzmann factors”
exponential factor would be expected to be approx-
that result from the electronic partition functions con-
imately lop3cm2 s - l . When “unusual” values of the
tain the potentials Ut and U which are defined in Fig.
preexponential factor are observed experimentally,
2. Within the harmonic approximation, the individual
vibrational partition functions are given by they are frequently rationalized in terms of various ad
hoc assumptions concerning the localization or deloc-
e - h ~ i / 2 kTs
~ alization of the reactants and the transition state.
qv,i = 1 - e-hvi/kBT, (12) In fact, most experimentally observed “unusual” pre-
exponential factors are probably not unusual at all.
We define a new vibrational partition function qv,i as
Rather, they are generally a consequence of an artifact
follows:
in the analysis of the data. The root of the problem lies
Q , = (1 - e-hvi/kBTs in something known as the compensation effect, which
V,I - 1-l (13)
has been explained recently in terms of a temperature-
and we include the zero-point-energy contribution ex- dependent distribution of reacting surface configura-
plicitly in the Boltzmann factor, i.e. tions [2, 31.

B Eley-Rideal Reaction Mechanism

and We shall now derive an expression for the rate of an
Eley-Rideal reaction in order to compare it with the
results of eqs 17 and 18 for the rate of a Langmuir-
Hinshelwood reaction. In this way, we shall be able to
Combining eqs 10-15 into eq 9 gives assess the relative contribution of each under different
experimental conditions. The Eley-Rideal analog of
the reaction given in eq 2 may be written as

8 S-A + BA(g) * ( S . .. A . . . B . . . A)i + S + A2B(g)

r=l (20)
X

References see page 983

976 5 Elementary Steps and Mechanisms
~~

Recall that this is a direct reaction since BA is not Reference Energy Zero
adsorbed on the surface. The rate of this Eley-Rideal
reaction is defined to be (in flux units, as before)

‘
where e A / & the ratio of the fractional surface coverage
of A to the site area, is the two-dimensional concen- S+A p W
Reaction Coordinate, p
tration of A, CBA,g is the three-dimensional (gas-phase)
density of BA, and kE-R is the Eley-Rideal reaction Figure 3. One-dimensional potential energy diagram (along the
rate coefficient (in units of volume divided by time), reaction coordinate p ) for the hypothetical Eley-Rideal reaction,
which may be written as +
S-A + BA(g) --t (S-A-B-At + S A>B(g),where S denotes a
surface binding site.
kE-R - k(0)E-Re-AUit/kBT8
(22)
where T, is the gas-phase temperature. Since it is not
quite clear what the appropriate temperature ( T s , T,,
or something intermediate between the two in non-
isothermal systems) is to use in connection with the where the notation is the same as that employed earlier,
partition function of the activated complex, in what and (ti), the dynamical correction to transition-state
follows we shall assume T, = Tg = T when evaluating theory is included explicitly here. The one-dimensional
the preexponential factor of the Eley-Rideal reaction potential energy diagram along the reaction coordinate
rate coefficient. We shall, however, use T, in the for this reaction is shown in Fig. 3. Note, by comparing
Boltzmann factor for this direct chemical reaction, al- eqs 21 and 27, that the Eley-Rideal reaction rate co-
though this also is clearly an approximation. efficient is given by
We next introduce the probability of reaction
Pr(BA),which is a function of the fractional surface
coverage of A, as follows:
where q B A in this case refers to the single-molecule
canonical ensemble partition function of a gaseous BA
molecule. If we assume that BA is an ideal gas, we can
where F ‘ B ~is the impingement flux of BA onto the replace C B A by
, ~ P B A / k B T ; we also extract one of the
surface. Assuming that BA is an ideal gas and equating translational degrees of freedom from qBA in eq 27, i.e.
the two expressions for the reaction rate in eqs 21 and one factor of qt,BA given by eq 25. This allows us to
23 allow us to write the rate coefficient of the Eley- rewrite eq 27 as
Rideal reaction as follows:

where the primes on the partition functions remind us

where j,as before, is the area of an adsorption site of that one degree of freedom has been extracted.
reactant A, and q r , B A is the canonical ensemble parti- As in the case of the Langmuir-Hinshelwood
tion function of a single translational degree of free- mechanism discussed earlier, we assume that both the
dom of a BA molecule, which in this case is given by reactant A and, of course, the transition state are
localized. This allows us to write

The rate of this Eley-Rideal reaction may also be

written, in units of flux, as
and

in exactly the same way the Langmuir-Hinshelwood

rate was written in eq 3. Following the same derivation where the potentials associated with the electronic part
presented earlier in eqs 4-8, we find that the Eley- of the partition function (the Boltzmann factors) are
Rideal reaction rate may be written as shown in Fig. 3, and qf,BAis the partition function of
 5.2 Microkinetics 977

the two rotational degrees of freedom. Extracting the and we note that, whereas P, is a function of e A , the
zero-point energy from the various vibrational partition ratio P r ( e A ) / d A is not a function of I ~ A .Using our
functions, as was done in connection with eqs 12-15, same assumptions concerning qt,BA, p, and T that were
allows us to rewrite the Eley-Rideal reaction rate as introduced earlier, and making use of the order-of-
r 1 magnitude estimate for kE-R given by eq 35, we find
that

which, of course, could have been written down di-

rectly from eq 33. If we ignore (i.e. take to be unity) the
e A in the denominator on the left-hand side of eq 37,
where AUA is defined below eq 16, and the subscript
for the reasons discussed below eq 33, eq 37 gives the
zero implies that the zero-point energy is included in
this potential. initial probability of chemisorption of the BA mole-
In order to obtain a physical feeling for the pre- cule. Furthermore, this order-of-magnitude estimate,
exponential factor of the rate coefficient implied by eq which applies to a localized transition state, is not just
32, which in this case is dimensionless, let us assume valid for direct chemisorption. It also applies to trap-
that the ratio of the vibrational partition functions ping-mediated chemisorption (with the gas temperature
is unity, T = 400K, p = 6.7 x cm2, and BA is replaced by the surface temperature in the Boltzmann
taken to be carbon monoxide whch implies that factor), and to both molecular and dissociative chem-
I/qtBA z 2.7 x 10-'*cm2 and q:,BA x 150. With these isorption. Indeed, depending on where the potential
assumptions, eq. 32 becomes curves cross with respect to the reference energy (the
vacuum zero), i.e. the curves for physical adsorption
REPR% 2.7 X 10-5(K)e-AUalikBTg6AFBA (33) and molecular chemisorption for the case of molecular
It is important to note that eq 33 is of nearly the same chemisorption or for molecular adsorption and dis-
form that would be derived for the initial rate of sociative chemisorption for the case of dissociative
chemisorption of BA with a localized transition state, chemisorption, A @ could be either greater than or less
but with an additional factor of 6~ on the right-hand than zero; e-Aui/ksTcould be either less than or greater
side. This, of course, is as it should be since the chem- than unity. When the Boltzmann factor e-Aui/kBT is
isorption reaction can occur at any unoccupied site on greater than unity, which corresponds to unactivated
the surface, whereas the Eley-Rideal reaction can only chemisorption with respect to the gas-phase energy
occur at a site that is occupied by an A adatom. zero, then it would appear that the probability of
The Eley-Rideal reaction rate coefficient, given by chemisorption (see eq 41) could exceed unity. This is,
eq 28, may be written as of course, not the case. When the probability, calcu-
lated from an expression such as eq 37, appears to
exceed unity, then its value is in fact just unity, and the
adsorption reaction is flux limited. In this case an

[ 1
-% equilibrium approximation, implicit in the derivation
':=l qv,ABA.i e-A u,'/kB Tg
(34) of the probability of chemisorption that is analogous to
(7fi3_1qv,A,j)(q:,BAq?,BAqV,BA)
eq 37 for the Eley-Rideal reaction probability, simply
If we make the same assumptions as in the previous breaks down.
paragraph concerning the temperature (400 K), the
value of l / q t . B A ( 1.6 x cm), the value of q;,BA
(1 50), and the cancellation of the vibrational partition C Langmuir-Hinshelwood versus Eley-Rideal
functions, eq 34 becomes Reaction Rates
It is possible to compare quantitatively the rates of the
Eley-Rideal and Langmuir-Hinshelwood mechanisms
by taking the ratio of eqs 32 and 16. Noting that
for the physically relevant case of a localized surface
Ci= ei/p, and if we assume that T, = Tg= T , equiv-
reactant and a localized (at the saddle point of the po-
alent dynamical corrections to transition state theory
tential energy surface) transition state. The reaction for both cases ( K ) and that the activation energies
probability contained in eq 24 may be written as of the reaction AU: are the same for the Eley-Rideal

References see page 983

978 5 Elementary Steps and Mechanisms

and the Langmuir-Hinshelweed mechanisms, we find even worse than implied by this argument based on
that attempt frequencies, because there is a “loss of entropy”
1 of one of the reactants in forming the transition state
in the Eley-Rideal mechanism. This loss of entropy is
reflected, for example, by a prefactor of 2.7 x
(rather than unity) in eqs 33 and 37. This argument can
also be couched in terms of “effective” or “virtual”
pressures of an adsorbed molecule. For example, satu-
Next, we make the same assumptions that we made ration coverage (0 = 1) on a lattice, the site concen-
earlier, namely that T = 400 K and that BA is a carbon tration of which is 1.5 x 1015cm-2, corresponds to an
monoxide molecule, which implies that q$A = effective three-dimensional pressure of an ideal gas at
2.7 x 1 0 - l ~cm2 and x 150. If we furthermore 400 K of approximately 3000 atm!
assume that the ratio of vibrational partition functions We can write eq 40 in an alternate pedagogic form
in eq 38 is approximately unity, then we find that if we make the approximation that the adsorption-
desorption equilibrium of the BA molecule is not per-
RE-R
turbed significantly either by the Langmuir-Hinshel-
RL-H wood or Eley-Rideal reactions or by the presence of
the A adatoms. Furthermore, if the surface temper-
with the flux in units of cm-2 s-’. If the flux is in units ature is sufficiently high that ~ B A= 1, which is in the
of site-’ s-I, and assuming that z 1.5 x 1015cm-2 spirit of our trying to decide when the Eley-Rideal
is the site concentration, then eq 39 may be written as mechanism would be most competitive with the Lang-
RE-R
-
RL-H = 3.2 x lo-”( 2) (40)
muir-Hinshelwood mechanism, we may write
F~~ ~ B A
BA(g) BA(a) (41)
With the flux on a per site basis,a pressure of 10-6T, ~ , B A

for example, corresponds approximately to FBA = where 5BA is the probability of trapping of the BA
1 site-‘ s-l. molecule into the chemisorbed state, and kd,BA is the
The implication of eqs 39 and 40 would seem to be rate coefficient of desorption of the adsorbed BA. In
that the rate of the direct Eley-Rideal reaction is the pseudoequilibrium, physical situation we are imagi-
always completely negligible compared to that of the ning
trapping-mediated Langmuir-Hinshelwood reaction.
In fact, except in rather unusual cases, the Langmuir- ~QBA
--
dt
- FBA~B
-A
Hinshelwood reaction rate dominates that of the Eley-
Rideal reaction; however, the domination is not quite which implies that
so dramatic as that which seems to be implied by eqs
39 and 40. Let us next try to understand intuitively why (43)
our calculated ratio REPR/RLpHis so very small, and
then we shall examine our derivation more carefully The rate coefficient for desorption kd,BA, may be writ-
in order to decide when the Eley-Rideal rate could ten in a Wigner-Polanyi form as
become important compared to the Langmuir-Hin-
shelwood rate. (44)
When two reactants are adsorbed adjacent to one
another, as in the Langmuir-Hinshelwood mechanism, where a normal value of k d(0), B A , the preexponential
they can attempt to react on the order of 10’2-10’3 factor of the first-order desorption, rate coefficient, is
times each second. Think of this as either an asym- approximately 1013s-’, Ed,BA is the activation energy
metric atom surface stretching frequency or as a frus- of desorption of the adsorbed BA molecule, and the
trated translational frequency of an adsorbed molecule temperature that appears in the Boltzmann factor is the
parallel to the surface. In a direct reaction, such as the surface temperature. Substituting eqs 43 and 44 into
Eley-Rideal mechanism, this “attempt frequency” is Eq. 40 gives
replaced by the impingement flux which, for example,
is approximately 1 site-’ s-l at lop6Torr. Such high (45)
pressures would be required to overcome this limita-
tion, that adsorption (perhaps even condensation) of Within the context of eq 45, we can now inquire into
the reactant would become extremely important, thus when might the direct Eley-Rideal reaction become
favoring the Langmuir-Hinshelwood mechanism. We competitive with the trapping-mediated Langmuir-
shall return to this point later. Indeed, the situation is Hinshelwood reaction. Clearly, within the approxima-
 5.2 Microkinetics 979
~~~ ~

tions inherent in eq 45, which have been delineated Thus, trapping-mediated chemisorption, even in the
explicitly, the crossover from the Langmuir-Hinshel- case of activated dissociative chemisorption, will almost
wood rates being greater to the Eley-Rideal rates being always be far more important than direct chemisorp-
greater occurs at tion. In both cases, the form of the rate will involve
a preexponential factor multiplied by a Boltzmann
SBAeEd,BAlkBTs M 3.2 x (46) factor. The preexponential factor will be larger for the
and the Eley-Rideal rate becomes more significant at trapping-mediated case, however, due to the loss of
lower values of (BAeEd’BA1kBTs. entropy in going from the reactant to the transition
When might we expect rBAeEdBAlkBTs to be suffi- state in the direct reaction. Moreover, the apparent
ciently small for the Eley-Rideal mechanism to be- activation energy will be greater for the direct reaction
come important? The answer to this question is when since the barrier almost always lies in the exit channel
the AB molecule is bound very weakly to the surface on the potential energy surface, see Fig. 1. In this case
and the surface temperature is very high (which tends also, direct (dissociative) chemisorption would only be
to make eEdBAlkBTssmaller), and when both the surface expected either within the context of a translationally
and especially the gas temperature are sufficiently high hot supersonic molecular beam experiment or when the
to make SBA very small indeed. It has been observed trapping-mediated barrier is sufficiently large that the
experimentally on numerous occasions that the trap- necessary surface temperature to surmount it precludes
ping probability decreases slightly with increasing sur- a sufficient lifetime of the trapped reactant.
face temperature and decreases precipitously with in- Since essentially all industrial catalysis is trapping
creasing gas temperature [4-161. Hence, we tentatively mediated rather than direct, we shall concentrate al-
conclude that very high gas temperatures would tend to most entirely on describing and quantifying this kind of
emphasize the Eley-Rideal mechanism. Indeed, if the surface reactivity in the remainder of this chapter.
gaseous reactant were supplied with a very high trans-
lational energy and also a very narrow translational
energy distribution, then it is possible that the reaction 5.2.2.4 Trapping-Mediated Surface Reactions
might only follow the Eley-Rideal mechanism. For
example, we could picture the surface temperature be- A Trapping
ing sufficiently low that the rate of the Langmuir- Since trapping at a surface is the first step in all trap-
Hinshelwood reaction is negligible, whereas the gas ping-mediated reactions, it is important to have a rea-
“temperature” could actually be greater than the ac- sonably complete picture concerning this dynamical
tivation energy of the reaction. Although this peculiar phenomenon. The reason we refer to trapping as a dy-
set of experimental conditions could lead to a greater namical phenomenon is because it involves momentum
relative rate of the Eley-Rideal mechanism compared and energy exchange between the gas-phase atom or
to the Langmuir-Hinshelwood mechanism, we would molecule and the repulsive part of the gas-surface po-
nevertheless expect the absolute rate of the direct re- tential (see Fig. l(b)). Tentatively, we might expect that
action to be quite low. an atom or molecule is trapped at the surface if it ex-
An equivalent way of considering this issue is to changes sufficient energy in the gas-surface collision to
imagine that the barrier for reaction is sufficiently high have negative total energy (kinetic plus potential) after
with respect to the binding energy of the adsorbed re- the collision - negative with respect to our usual zero
actant that the surface temperature would have to be so of energy which is the gas molecule infinitely far from
high in order to allow the surface reaction to occur that the surface and at rest. A schematic picture that helps
the lifetime of the adsorbed reactant would be too short clarify this discussion is shown in Fig. 4, which depicts
both to accommodate to the surface temperature and, a gas with a three-dimensional Maxwell-Boltzmann
of more importance, to execute even one successful velocity distribution interacting with a one-dimensional
hop on the surface. A physical situation to which this potential of (say) physical adsorption. Only the dis-
argument may apply is the direct versus the trapping- sipative collision of a molecule with the most probable
mediated dissociative chemisorption of methane on the velocity is shown explicitly, but keep in mind that each
Ni(l11) surface [17-191. A critical assessment of the molecule with its own particular velocity (kinetic en-
assumptions that lead to eqs 39, 40 and 45 is presented ergy) collides with the repulsive barrier and undergoes
in Ref. 20. energy exchange.
The arguments above tell us that any contribution of There are a number of dissipative (inelastic) channels
a direct reaction is almost always negligible, even under available in the gas-surface collision. If the impinging
the most favorable circumstances. In almost all tech- gas-phase particle is an atom, e.g. a rare gas atom, then
nological applications, one can ignore the direct chan-
nel of the reaction compared to the trapping-mediated ~ ~~

channel. References see page 983

980 5 Elementary Steps and Mechanisms

1.o

.8
-
f
z0
n
2 .6
n
0
C

.4

2
UI

Figure 4. Illustration of the trapping mechanism of gas-phase .2

atoms or molecules (represented by the Maxwell-Boltzmann dis-
tribution of kinetic energies f(T ) a t a surface via inelastic inter-
actions with the repulsive part of the surface potential (curve 0
shown on the left). 0 .2 .4 .6 .8
E cos la6 eI
Figure 5. Trapping probability of xenon on Pt(ll1) as a function
of E, cos’ 0, (in eV) at a surface temperature of 85 K (note that
the “inelasticity” is restricted to the solid. Electronic 1 eV is approximately equal to 96.8 kJ mol-’).
excitations of the rare gas are considered to be in-
accessible. In this case, the principal inelastic channels
are phonon excitations and electron-hole pair creation,
i.e. vibrational and electronic excitations. The detailed
nature of the substrate, e.g. the Debye temperature and
the densities of phonon and electronic states. will dic-
tate the dynamics of the individual collisions. If the
impinging gas-phase particle is a molecule, then there
are additional dissipative channels that are available.
In this case, there can be intramolecular energy transfer
that converts translational energy to either rotational
or vibrational energy. Hence, to first order we can
define the thermally averaged trapping probability to
be the fraction of molecules in the Maxwell-Boltzmann
distribution of Fig. 4 that lose sufficient energy to fall
below the zero of energy.
Rettner et al. [21], employing molecular beam tech- Figure 6. One-dimensional potential energy diagram (along the
niques, measured the trapping probability of xenon on reaction coordinate p ) proposed for the dissociative chemisorp-
Pt( 11 1). Numerous kinetic energies were employed at tion of Nz on W(100).
three different angles of incidence, to determine the
trapping probability at a surface temperature of 85 K. B Example of a Trapping-Mediated Surface Reaction
The experimental results are shown in Fig. 5. Not sur- The potential energy of the reaction
prisingly, the trapping probability decreases strongly
with increasing translational energy (gas “temper-
ature”). Notice also, however, that the trapping prob-
N2(g) 2 N2(P) 4 2N(c) (47)

ability has a strong dependence on the angle of in- along the reaction coordinate on W(100) is similar to
cidence, increasing with increasing angle of incidence. the solid curve of Fig. 6 . If the potential curves for the
It has been found that the normal component of mo- physical adsorption of molecular nitrogen and for the
mentum of a gas-phase particle frequently has signif- chemisorption of two nitrogen atoms do indeed cross
icantly more importance than the parallel component below the zero of energy, as indicated in Fig. 6, this has
and, thus, increasing the angle of incidence increases an important qualitative consequence on the proba-
the probability of trapping [5, 21-30]. There are only bility of dissociation of an impinging nitrogen mole-
minor deviations in the trapping probability as a func- cule, namely, if the surface temperature is increased,
tion of surface temperature relative to the variations then the reaction probability should decrease. This
that are observed with changing gas temperature (in- statement can be rendered quantitative by considering
cident kinetic energy) [ S , 231. Thus, to first order, we the initial probability of dissociative chemisorption of
can think of the trapping probability as only a function nitrogen, i.e. the reaction probability on a clean sur-
of the gas temperature. face. If the surface temperature is sufficiently high that
 5.2 Microkinetics 981

the concentration of physically adsorbed nitrogen is P y + t in the limit of low T, 1

negligibly small, then a pseudo-steady state approx-
imation implies that

- --
dt
+
dep <F - (kd k,)6, % 0
(However, T, must not be so low that E, cannot be
surmounted!)
where 6, is the fractional surface coverage of the
It is apparent from eq 51 that the reaction proba-
physically adsorbed nitrogen, [ is the trapping proba- bility is composed of two different ingredients: a “dy-
bility of molecular nitrogen into the well for physical
namics” part describing the gas-surface collision (em-
adsorption, F is the impingement flux of nitrogen (on a
bodied by 5 ) and a surface “kinetics” part describing
per site basis), and kd and k, are the rate coefficients for
the competing dissociative chemisorption and desorp-
molecular desorption and reaction (dissociative chem-
tion reactions (embodied by kd/k,). The dissociative
isorption), respectively.
chemisorption of N2 on the W(100) surface has been
From eq 48 we find that the pseudo-steady state
studied with the aim of both verifying the assumptions
fractional coverage of physically adsorbed nitrogen on inherent in the derivation of eq 51 and determining the
the surface is given by
parameters of fundamental ph sical significance con-
tained therein, namely 5 , kd(0) l k70)
, , and Ed - E,. These
(49) results are summarized next.
Rettner et al. [31] employed a method similar to the
and the reaction rate is given by
-)kr
reflectivity technique of King and Wells [32] to measure
R, = k,6, = < F ( the initial probability of dissociative chemisorption of
kr + kd nitrogen on the W( 100) surface as a function of impact
energy, parametric in surface temperature. The results
Note that the form of eq 50 is intuitively predictable, of these measurements for surface temperatures be-
namely the rate of the reaction is given by the rate of tween 300 and lOOOK, and impact energies up to
production of reactants ( ( F ) multiplied by the rate % 116 kJmol-’ (1.2 eV) are shown in Fig. 7. The first
coefficient for reaction, which is normalized by the sum thing to notice in Fig. 7 is that there is a minimum
of the rate coefficients of reaction and desorption for P,(Ei). Below approximately 50 kJmol-’ (0.5 eV), P,
this two-channel “reaction”. The probability that an decreases with increasing Ei, whereas above this impact
impinging nitrogen molecule adsorbs dissociatively is energy, P, increases with increasing Ei. At lower values
simply the rate of reaction divided by the impingement
flux, as defined above, i.e.
1.0 - I I I I I
-
N2/W( 100)
ei=oo
-
.
The form of eq 51 proves our earlier assertion that
for the potential energy diagram of Fig. 6, the reaction .- 300K
probability decreases as the surface temperature in- n 800K
? 0.6 A1000K -
creases. Since both rate coefficients are of the Polanyi-
Wigner form, namely t
0.4

then eq 51 can be written as follows: 0.2

0.01 I , I I I 1
0.0 0.4 0.8 1.2 1.6
Kinetic Energy (eV)
Since Ed > E, in this case, the second term in the de-
Figure 7. Initial probability of dissociative chemisorption P, of
nominator becomes progressively smaller as the surface Nz W(100) as a function of impact energy E, at variable sur-
temperature decreases, which gives rise to a larger face temperatures (note that 1 eV is approximately equal to
value of the reaction probability. The corresponding 96.8 kJmol-’)
maximum and minimum values of the reaction proba-
bility for the case when Ed > Er are given by References see page 983
982 5 Elementary Stem and Mechanisms

of the impact energy, the dissociative chemisorption is

dominated by the trapping-mediated mechanism, and NdW(100)
is a strong function of the surface temperature, as may
be seen in Fig. 7. At higher impact energies, the prob-
ability of dissociative chemisorption increases because 1 '
the "direct" mechanism of chemisorption dominates in
this regime. At sufficiently high impact energies, where -7
0'
the trapping probability approaches zero, only the di- I

rect channel contributes, and the probability of chem- VP -1

isorption is approximately independent of temperature.
2
v

This regime is being approached at the highest impact 5 -2

u
energies in Fig. 7. Indeed, at surface temperatures far in
excess of 1000 K, there is very little trapping-mediated -3
chemisorption at any impact energy and, therefore,
data of this type would allow us to assess the relative
importance of the two channels (trapping mediated and I I I
direct) at the other surface temperatures as a function 0 1 2 3 4
of the impact energy. We should also note that the 1000/ TI (K-')
minimum in P,(Ei) moves to lower impact energies as
the surface temperature increases (see Fig. 7) because Figure 8. Verification of the trapping-mediated mechanism pro-
posed in eq 51 for the dissociative chemisorption of N2 on W(100).
the probability of the direct reaction is not a significant
function of surface temperature, whereas the proba-
bility of the trapping-mediated reaction decreases rap- surface:
idly with increasing surface temperature. Ed - E, = 15.5 kJmol-' (56)
Rettner et al. [33], with further experimentation and and
modeling, have determined that for impact energies less
k r ) / k i o )= 25 (57)
than 9.7 kJ mol-' (0.1 eV) there is no detectable con-
tribution from the direct channel to chemisorption. where there is an uncertainty (one standard deviation)
Thus, if we restrict our analysis to an incident energy of k1.9 kJ mol-' in the difference in the activation en-
less than 9.7 kJ mol-' (0.1 eV), then a strong test of the ergies, and an uncertainty of &8 in the ratio of the
validity of eq 51 can be made, insofar as its proposed preexponential factors. Since the rate coefficient of de-
description of trapping-mediated chemisorption is con- sorption of nitrogen in the precursor state has not been
cerned. For this purpose we rewrite eq 51 as follows: measured, the rate coefficient of the elementary surface
reaction involving rupture of the molecular nitrogen
_5 _ 1 = -kd (55) bond cannot be determined precisely. It is clear from
n
r r 4 Fig. 6 that the potential curves cross, in this case,
and we note that 5 and P, have not been measured 15.5 kJ mol-' below the gas-phase energy zero, and
independently. Mullins and Weinberg have performed that the apparent activation energy with respect to this
similar studies of the trapping-mediated dissociative latter energy zero is -15.5 kJmol-I.
chemisorption of C2H6 on the Ir(ll0) surface in which The fact that kf'jk!') > 1 for this reaction is com-
the trapping probability 5 and the chemisorption prob- pletely expected [37]. Using the formalism developed in
ability were independently measured [34-361. However, Section 5.2.2.3, the ratio of the preexponential factors
Rettner et al. [23] have shown 5 to be a weak function of desorption and reaction may be written as
of surface temperature. If eq 55 is valid, then a plot
of In(E/P, - 1) as a function of reciprocal surface
temperature should be linear with a slope equal to
-(Ed - E , ) / ~ B
and an intercept equal to ln[kd , 1.
(0)/ k (0) where both the electronic part of the partition functions
The data of Fig. 7 are plotted in this Arrhenius form in (the Maxwell-Boltzmann factor) and the zero-point
Fig. 8, assuming 5: = 0.6, and a straight line is observed energy contribution of the vibrational partition func-
over the temperature range employed, 300-1000 K. tions have been extracted from the two transition-state
This result validates the simple model that was employed partition functions that appear in eq 58. Whereas the
to describe the trapping-mediated chemisorption see constrained and localized partition function for re-
eqs 48-54. action (qi): will contain four degrees of vibrational
The slope and intercept of Fig. 8 imply that the fol- freedom we expect that the partition function for de-
lowing rate parameters describe the trapping-mediated sorption (qJ); will contain two rotational degrees of
dissociative chemisorption of nitrogen on the W( 100) freedom (with one degree of freedom being vibra-
 5.2 Microkinetics 983

this is that methane typically has both quite large en-

ergy barriers for activation (with respect to the gas-
NdW(1OO) T=, 800 K phase energy zero, i.e. Er - Ed > 0 for methane) as
well as quite small well-depths for physical adsorption,
of the order of 17 kJ mol-’ or so, on most transition

-
2 0.60 - x r 00
.-
0 0 m450 metal surfaces. For example, consider the interaction
a 0 =60°
2
n of methane with a surface at a temperature of l000K
c
._ 0.40 - (gas temperature equal to surface temperature in
.- ::o a “bulb” rather than a “beam” experiment). At this
p T
5
temperature and with a well-depth for physical ad-
a
sorption of 17 kJmol-*, the residence time of the
0.20 - 0 methane on the surface is only about seven vibrational

0.00
t’ i periods, i.e. of the order of 1 ps. On a time-scale that is
this short, the concept of a trapping-mediated reaction
0 1 2 3 4 5 6
becomes ill-defined, and we would expect significant
Kinetic Energy (eV) contributions from the direct channel, i.e. the direct
reaction of methane molecules in the high-energy tail
Figure 9. Initial probability of dissociative chemisorption via of the Maxwell-Boltzmann distribution. This is an in-
the direct mechansim of N2 on W(100) as a function of impact
energy E, at a surface temperature of 800K, parametric in in- efficient way for the molecule to react, but in the case
cident angle. The trapping-mediated component of chemisorption of methane this is likely to be the only path. We must
has been subtracted from the total chemisorption probability to emphasize, however, that this is an exceptional case.
construct this plot [32] (note that 1 eV is approximately equal to Very few chemical reactants have a binding energy on
96.8 kJmol-’)
a catalytic surface which is as small as that of methane
(or, more precisely, there are very few systems for
tional). On this basis, for a nonspherically symmetric
which Er - E d is as large as that of methane).
reactant we would expect k!’/k(O’ to lie between ap-
proximately 10 and 1000 (in the absence of any quan-
titative information concerning the relative magnitudes 5.2.2.5 Synopsis
of (Kd) and (K~)). The measured value of k?’/k(’) is The concepts of trapping-mediated and direct surface
completely consistent with this expectation. reactions were defined and discussed in Section 5.2.2.2
Finally, we note that Rettner et al. [33] have mea- of this chapter, and we argued intuitively that trapping-
sured the initial probability of direct dissociative mediated reactions should be observed with greater
chemisorption of nitrogen on W(100) at a high surface frequency. These arguments were quantified in Section
temperature (Ts= 800 K) (the contribution from the 5.2.2.3 within the framework of elementary transition
trapping-mediated channel was subtracted). These re- state theory, and the trapping-mediated channel (the
sults are shown in Fig. 9, where the initial probability Langmuir-Hinshelwood mechanism) was shown to
of chemisorption is plotted as a function of impact dominate the direct channel (the Eley-Rideal mecha-
energy. Notice that the threshold value of the normal
nism) under industrial catalytic conditions. Finally, in
energy required for detectable direct reaction is ap-
view of the importance of trapping-mediated reactions,
proximately 9.7 kJ mol-’ (0.1 eV), which is approx-
trapping dynamics and the dissociative chemisorption
imately 25 kJ mol-’ greater than the minimum energy
dynamics of N2 on W(100) were discussed in the limit
pathway from reactant to product (i.e. the trapping- of low surface coverages in Section 5.2.2.4.
mediated mechanism). The reason for this is clear from
Fig. 1, and it was discussed in connection with that fig-
ure. In the direct mechanism excess total energy is References
necessary in order to transfer sufficient energy to the
reaction coordinate in order for the reaction to occur, 1. A. F. Voter, J. D. Doll, J. Chem. Phys. 1985, 82, 80.
i.e. for there to be “funneling” of reaction products 2. K. A. Fichthorn, W. H. Weinberg, Langmuir 1991, 7, 2539.
into their final ground state, rather than a reflection of 3. H. C. Kang, T. A. Jachimowski, W. H. Weinberg, J , Chem.
Phys. 1990, 93, 1418.
the reactants from the repulsive wall of the potential. It 4. C. T. Rettner, E. K. Schweizer, H. Stein, J. Chem. Phys.
is for this reason that most of the surface chemistry 1990, 93, 1442.
that occurs in the “real world” is trapping mediated 5. C. B. Mullins, C. T. Rettner, D. J. Auerbach, W. H. Wein-
rather than direct. berg, Chem. Phys. Lett. 1989, 163, 11 1.
As mentioned in Section 5.2.2.3, one of the few 6. A. V. Hamza, H.-P. Steinruck, R. J. Madix, J. Chem. Phys.
1987, 86, 6506.
exceptions to this general rule is likely to be the dis- 7 . C. B. Mullins, Y. Wang, W. H Weinberg, J. Vuc. Sci. Tech-
sociative chemisorption of methane. The reason for nol. 1989, A7,2125.
984 5 Elementary Steps and Mechanisms

8 A. C. Luntz, M. D. Williams, D. S . Bethune, J. Chem. Phys. and reaction system is therefore characterized by the
1988, 89,4381.
9. H. P. Steinruck, R. J. Madix, Surf: Sci. 1987, 185, 36. rates for different elementary steps in the reaction, and
10. S . L. Tang, J. D. Beckerle, M. B. Lee, S . T. Ceyer, J. Chem. the theoretical modeling of catalytic reactions must
Phvs. 1980. 84. 6488. therefore, as the end product, have the calculation of
11. M.’ P. D’Evelyn, H. P. Steinruck, R. J. Madix, Surf: Sci. the kinetics.
1987, 180. 41. The kinetics of a catalytic reaction is usually mea-
12. J. Harris,’A. C. Luntz, J. Chem. Phys. 1989,91, 6421.
13. P. Alnot, A. Cassuto, D. A. King, SurJ Sci. 1989, 215, 29. sured in a reactor under conditions relevant to the
14. K. D. Rendulic, A. Winkler, H. Karner, J. Vac. Sci. Technol. industrial process. The measured overall rates can then
1987, A5, 488. be fitted to a mathematical model, the macroscopic
15. C. R. Arumainayagam, M. C. McMaster, G. R. Schoofs, R. kinetics. This is extremely convenient for process design
J. Madix, Surf: Sci. 1989,222, 213. purposes [l].
16. B. E. Hayden, D. C. Godrey, Surf: Sci. 1990,232, 24.
17. M. B. Lee, Q.Y. Yang, S. L. Tang, S. T. Ceyer, J. Chem. If the aim is to explore the mechanism of the re-
Phys. 1986,85, 1693. action and to understand which are the important
18. M. B. Lee, Q.Y. Yang, S. T. Ceyer, J. Chem. Phys. 1987,87, parameters of the catalyst determining the activity,
2724. then a microkinetic model is needed. A microkinetic
19. T. P. Beebe, Jr., D. W. Goodman, B. D. Kay, J. T. Yates, Jr.,
J. Chem. Phys. 1987,87, 2305.
model is based on a detailed mechanism and indepen-
20. W. H. Weinberg in Dynamics of Gas-Surface Interactions dent information about the rates of the elementary
(Eds: C. T. Rettner, N. W. R. Ashfold), Royal Society of steps involved and the stability of the intermediates. It
Chemistry, London, 1991. can be said that the microkinetic model is the synthesis
21. C. T. Rettner, D. S. Bethune, D. J. Auerbach, J. Chem. Phys. of all the basic knowledge about a reaction over a
1989, 91, 1942.
22. G. Comsa, R. David, Surf: Sci. Reports 1985, 5 , 145. given catalyst.
23. C. T. Rettner, E. K. Schweizer, H. Stein, D. J. Auerbach, The input into a microkinetic model is usually mea-
Phys. Rev. Lett. 1988, 61, 986. sured rates of elementary steps and measured heats of
24. K. C. Janda, J. E. Hurst, Jr., C. A. Becker, J. P. Cowin, L. adsorption together with thermodynamic data for
Wharton, D. J. Auerbach, Surf: Sci. 1980, 93, 270. the gas (or liquid) phase above the catalyst. The input
25. C. T. Campbell, G. Ertl, H. Kuipers, J. Segner, Surf: Sci.
1981,107, 220. parameters may be measured over the catalyst [2]. This
26. C. T. Rettner, E. K. Schweizer, C. B. Mullins, J. Chem. Phys. gives information of direct interest for the catalyst sys-
1989,90, 3800. tem considered, but often the interpretation of the
27. J. E. Hurst, Jr., C. A. Becker, J. P. Cowin, K. C. Janda, L. experiments is difficult because the state of the active
Wharton, Phys. Rev. Lett. 1979,43, 1175.
28 K. C. Janda, J. E. Hurst, Jr., C. A. Becker, J. P. Cowin, D. J.
surface is not known and may vary with the conditions
Auerbach, L. Wharton, J. Chem. Phys. 1980, 72, 2403. of the experiment. Alternatively, the input can be taken
29. L. K. Verheij, J. Lux, A. B. Anton, B. Poelsema. G. Comsa, from measurements on model systems. If the structure
Surf: Sci. 1987, 182, 390. of the catalyst is known and there is a suspicion which
30. C. T. Rettner, C. B. Mullins, D. S . Bethune, D. J. Auerbach, is the active phase, then it is possible to isolate this
E. K. Schweizer, W. H. Weinberg, J. Vac. Sci. Technol. 1990,
A8, 2699. phase, usually in the form of a single-crystal surface
31. C. T. Rettner, H. Stein, E. K. Schweizer, J. Chem. Phys. and do experiments on this model using the chemical
1988,89, 3337. and structural characterization tools available to sur-
32. D. A. King, M. G. Wells, Surf: Sci. 1972, 29, 454. face science [3]. A third possibility for obtaing input
33. C. T. Rettner, E. K. Schweizer, H. Stein, J. Chem. Phys. has become available during the early 1990s. Electronic
1990, 93, 1442.
34. C. B. Mullins, W. H. Weinberg, J. Vac. Sci. Technol. 1990, structure theory has developed to a point where realis-
A8, 2458. tic bond energies and activation barriers can be calcu-
35. C. B. Mullins, W. H. Weinberg, J. Chem. Phys. 1990,92,3986. lated [4]. Typically, the model catalysts used in such
36. C. B. Mullins, W. H. Weinberg, J. Chem. Phys. 1990,92,4508. calculations are even more idealized than in the surface
37. C. T. Campbell, Y.-K. Sun, W. H. Weinberg, Chem. Phys.
Lett. 1991, 179, 53.
science experiments (perfect surfaces, ordered over-
layers etc.), but the insight into the details of the po-
tential energy surface of the reaction is much greater.
The modeling of a surface chemical reaction can
5.2.3 Theoretical Modeling of Catalytic take place at many different levels of complexity.
Reactions Section 5.2.3.2 gives an overview of the various ap-
proaches ranging from a complete description of the
J. K. N 0 R S K O V AND P. STOLTZE dynamics of the reaction over simulations which in-
clude the adsorbate-adsorbate interactions to the sim-
plest mean field approaches. The latter is by far the
5.2.3.1 Introduction most widespread in use and in Section 5.2.3.3 a de-
tailed description is given of this approach using the
A catalyst is a substance which modifies the rate or the synthesis of ammonia over an iron catalyst to exem-
selectivity of a chemical reaction. A particular catalyst plify the concepts introduced. Finally, Section 5.2.3.4
 5.2 Microkinetics 985

I
I
Full dynamics
I
I

1 neglect details
ofdynamics
2.25

I Monte Carlo description I

1.I5
mean field
approximation

Continuum description
’ 0.6 0.8 1 1.2 1.4
neglect adsorbate-
adsorbate interactions

Langmuir-Hinshelwood
Figure 2. A calculated ab initio potential energy surface for H2
description on Cu(l11). The contours of constant potential energy are shown
in a plane containing the distance of the molecule (lying parallel
Figure 1. Hierarchy of methods for treating surface reactions. to the surface perpendicular to the bridge site) above the first Cu
plane, and the H-H bond length.

briefly points to a few examples of reactions that have

been treated in this way. the molecule over the surface and the H-H distance.
There are another four Hz degrees of freedom plus all
the degrees of freedom of the surface atoms for a
complete description, but the two degrees of freedom
5.2.3.2 Different Approaches to Simulations of
included in the cut contain the most important in-
Surface Reaction Kinetics formation [8, 91. The barrier for dissociation is about
0.7 eV (or 70 kJ mole-’) and the vibrational excitation
As mentioned above, it is possible to attack the prob- of the incoming molecule will help surmounting the
lem of simulating the rate of a surface chemical re- barrier (this follows from the fact that the barrier is to a
action at several different levels of complexity [ 5 ] . At
substantial extent along the H-H coordinate).
the most fundamental level the time development of
Both conclusions are in agreement with detailed
the reaction system is followed in detail, and at the
molecular beam studies [lo]. From the potential the
most approximate level only gross averages are con- dissociation probability Q,d,v , j : T,) can in prin-
sidered. The hierarchy of methods for dealing with ciple be calculated as a function of the translational
surface reactions is illustrated in Fig. 1, and the fol-
energy &n, angle of impact (0, d), vibrational state v,
lowing discusses the different levels individually.
and rotational statej of the incoming molecule, and the
temperature T, of the surface [l 11. At this level of detail
A The Full Reaction Dynamics it is possible to see whether the reactivity may be
At the most fundamental level the time development enhanced by selectively exciting the vibrational or
of the system is followed in detail. The reactants are rotational degrees of freedom of the reactants.
started in a specific initial (quantum) state and the If we are only interested in the rate for a gas in
equation of motion are propagated to give the final thermal equilibrium at a temperature T over a surface
state. The equation of motion of the system is the time- of the same temperature, the adsorption rate can be
dependent Schrodinger equation, or, if the atoms in- calculated as
volved are heavy enough (not H or Li), Newton’s
equation. The starting point is the adiabatic potential
energy surface on which the process takes place. For
some reactions, electronic excitations during the reac-
tion are important and must be included in addition to XS(Ekin,e,d,v,j, T)sinedQdddEkin (1)
the electronically adiabatic dynamics [6]. Such a detailed description could in principle be
The adiabatic potential energy surface is the ground- made of every elementary step in a given reaction,
state electronic energy of the system as a function of all while a dynamical simulation of a whole chemical
the degrees of freedom of the system. Figure 2 shows as process including several elementary steps is usually
an example a two-dimensional cut, through the poten- impossible. Typically, intermediates in a reaction can
tial energy surface for Hz dissociation on a Cu( 1 1 1) sur-
face 171. The two dimensions shown are the distance of References see page 990
986 5 Elementary Steps and Mechanisms

have lifetimes which are many orders of magnitude

larger than typical times for a dynamical simulation (a
,I<
"1 adsorption
cfldesorption
few picoseconds). Another point is that if the aim is to
obtain an elementary reaction rate for a system at a
given temperature, the full dynamical approach may be
too detailed. Clearly, the Boltzmann factor in eq 1 will
single out only the lowest energy processes, that is, the
processes involving molecules with energies just around Figure 3. A schematic overview of the five elementary steps in a
surface reactions: adsorption, dissociation, diffusion, recombina-
the minimum barrier E,. A determination of the bar- tion, and desorption.
rier will therefore usually give the rate as

y ( T ) = AePEa/lkT (2) 2). Since the detailed configuration during each event is
Estimating the prefactor is in principle not an easy known, the actual activation energy including all local
task, but often simple absolute rate theory suffices [12]. interactions can be calculated and used. Adsorption
Given a rate expression as in eq 2 for the elementary processes will have a rate where the prefactor is related
steps, it is possible to simplify the description of the to the gas-phase pressure.
rate problem substantially. If the interaction energies are known from indepen-
dent experiments or calculations, this will give a very
B The Kinetic Monte-Carlo Approach detailed description of the process. The computational
The main difficulty in setting up a set of rate equations effort needed is, however, very substantial compared to
for a surface chemical reaction based on rate expres- the simpler mean-field description described in the next
sions such as eq 2 for the elementary steps is that the section. At low temperature, where diffusion is slow
activation energies and prefactors may depend strongly and ordered structures appear, this is the only possible
on the surroundings of the reacting molecule. This is a accurate description of the system. At temperatures
well-known problem in gas- and liquid-phase reactions, high enough that diffusion is fast and the adsorbates
but it is even more severe for surface reactions. The are evenly and randomly dispersed over the surface,
reason is that when atoms and molecules are con- such an approach is usually not necessary [ 13, 151.
densed onto a solid surface they are forced into a
framework with a typical spacing between adsorbates C The Continuum Description
of only a surface unit cell dimension. The interactions Instead of considering the detailed configuration of the
between adsorbates can therefore be quite substantial, system as outlined above, a considerably simpler mean-
leading to ordered adsorbate structures at low tem- field description is possible. Here, only average prop-
peratures. The best procedure is therefore to include erties are considered. The rate of a given elementary
the interactions between the adsorbates as directly as step involving adsorbates A and B are assumed, given
possible. by
If the surface can be viewed as a lattice on which the
reaction proceeds, then the problem can be formulated R = reAeB (3)
in the following way. Instead of considering the posi- where OA and d B are the coverages of A and B, respec-
tion of the adsorbates on the surface as a continuous tively, and the rate constant r is given by an expression
variable we can associate each adsorbate to a lattice such as eq 2. The activation energy and prefactor may
site. This is often possible even when adsorption leads still depend on the surroundings, but only in an aver-
to a reconstruction of the surface. There are basically age way through the coverages.
five kinds of processes that can take place on this lat- Even at this level the kinetics may become quite
tice: adsorption, dissociation, diffusion, recombination, complex. There are several examples [16, 171 where the
and desorption. Figure 3 shows schematically the pos- adsorption probability of one of the reactants depends
sible processes. At each lattice site the configuration of strongly on the coverage of another. This can lead to a
surrounding adsorbates will determine the activation strongly nonlinear set of equations for the total rate of
energies for the different processes, if the form and a reaction and to very interesting phenomena such as
strength of the interactions are known. kinetic oscillations and chaos [13, 15-17].
The kinetics can then be calculated using the kinetic
Monte-Carlo method [5, 13-15]. In this method the D Langmuir-Hinshelwood Description
different processes discussed above are now simulated At the simplest level even the coverage dependence of
on the lattice by randomly letting adsorbates arrive the parameters entering the rate constants is neglected.
on the surface, dissociate, diffuse, recombine or desorb. This is obviously an oversimplification, but is still an
For each attempted process the probability of a suc- extremely useful way of analyzing a reaction, and it has
cessful event is taken to be proportional to the rate (eq been shown in a number of cases to work remarkably
 5.2 Microkinetics 987

well. The next section discusses this approach in more At equilibrium the kinetic equation must go
detail. smoothly into the appropriate equilibrium equation.
The rate constants k+ and k-, and the equilibrium
constant K, are thus related by
5.2.3.3 Simplest Mean-Field Approach
(9)
This section first discusses in some detail how to con-
struct a microkinetic model at the simplest level, where and the activation energies E i and E!, and the energy
interaction between adsorbates are only included of reaction AE, are related by
through the saturation coverage. The use of such a
model is then considered. E$ - EL = AE (10)
The kinetic model be formulated using kinetic equa-
A Constructing the Model tions for all steps or using equilibrium equations for all
To make the following discussion more explanatory, but the slowest steps. The latter approach reduces the
ammonia synthesis is used as an example as this is one computational effort and leads to a kinetic expression,
of the simplest catalytic reactions from a modeling which is far easier to analyze. However, if a step, which
viewpoint: is slow in reality, is modeled by an equilibrium equa-
+
N2(g) * + N2* tion, the microkinetic model becomes unrealistic and it
may in some cases be the simplest to treat a problem-
+
N2* * + 2N* atic step by a kinetic equation.
N* + H a + NH* * + For the NH3 synthesis the kinetic scheme has been
NH* + H* + NH2* + * (4) treated by both approaches, [21-261, and identical
NH2* + H* + NH3* * + results are obtained [26], when the same set of input
parameters is used.
NH3* + NH3(g) +* When the mechanism has only one slow step, the
H2(g) + * + 2H* system of equilibrium equations and the rate equation
may be solved with respect to 8* and the coverages by
In this mechanism, the second step is known experi- intermediates may be expressed by 8, and the partial
mentally to be slow [18-201. pressures of the reactants and products. If the mecha-
The competition for adsorption sites is very im- nism has two or more slow steps [27-291, the solution
portant for the kinetics of a heterogeneous catalytic for the coverage by free sites is more difficult. For three
reaction. For this reason sites, *, are included as a re- or more slow steps, numerical solution is likely to be
actant in the kinetic model. As a site must be either free the only option.
or occupied by one of the surface intermediates, there is The equilibrium constants are expressed in terms of
a conservation law for the coverages, the molecular partition function, e.g.
C8x=1 (5)
where 8x is the coverage by the intermediate X.
In writing this equation it is implicitly defined that The molecular partition function Z is a product of
8x = 1 represents saturation. With this convention, contributions from each mode for the molecule. The
coverages may be interpreted as probabilities. number and nature of the modes is known from the
Each of the equilibrium steps gives an equilibrium symmetry of the intermediate.
equation, e.g. The enthalpy of formation for reactants and inter-
PNz = 8 ~ ~ *
K1-8* mediates may be calculated from the expression for the
(6) partition function
PO
A slow step gives a kinetic equation, e.g. dln Z
H = kBT2-
2 dT
r2 = k + 2 8 ~ ~ ,-
&k-28N* (7)
The enthalpy obviously depends on temperature.
which expresses the net rate r as the difference between However, even at T = 0 the enthalpy of an inter-
the forward rate r+, and the backward rate r - . mediate may differ substantially from the electronic
The condition for equilibrium is that both the for- binding energy due to contributions of iAo from the
ward and the backward rate are much larger than the zero-point motion in vibrational degrees of freedom.
net rate
Ir, - r-1 << min(r+,r - ) (8) References see page 990
988 5 Elementary Steps and Mechanisms

Simulation of adsorption is an important tool for the

determination of rate constants. Complicated adsorp-
tion experiments may be simulated through a numer-
ical integration of the relevant part of the reaction
mechanism once the parameters in the model are
known.
However, for determination of parameters it is pos-
sible to obtain an expression for the sticking coefficient
0, by equating the rate of adsorption in the kinetic
model to the conventional expression used to define 0.
For instance, the sticking coefficient for N2 at zero
coverage, 00, is
10-3 1
Experimental output
Figure 4. Comparison of calculated and measured ammonia
production over a commercial iron-based catalyst for a broad
range of temperatures, pressures, N : H ratios and gas flows; from
Ref. 23.
where d is the density of adsorption sites and m is the
mass of a Nz molecule, and the activation energy for 00
is While the number of parameters may be large, only
a few of the parameters are usually significant. The
significant parameters are easily determined by calcu-
The first term comes from the thermodynamics of the lation of the sensitivity of the calculated rate at typical
molecular precursor, the second term is the activation conditions to a small variation in the value of each
energy for the dissociation, while the third term comes parameter. For NH3 synthesis, for instance, the rate of
from the temperature dependence of the flux. The acti- dissociation of Np and the binding energy for N* are
vation energy for the rate determining step is obviously the most significant parameters and the kinetics of de-
significantly different from the activation energy for the sorption of N2 in a temperature programmed de-
sticking coefficient. sorption (TPD) experiment is rather closely related to
While sticking coefficients and more generally the the kinetics of NH3 synthesis [30, 311.
kinetics of adsorption is an important source for rate Fragments of the kinetic model may be tested by
constants, simulation of desorption experiments is the detailed simulation of the same experiments as have
primary source of binding energies, e.g. been used to determine the parameters in the model.
Failure to reproduce these experiments is entirely pos-
sible if a wrong reaction mechanism has been assumed.
A sensitive test can be made by simulation of a re-
for N2 desorption in the limit of infinite pumping actor through numerical integration of the rate ex-
speed. The ground state energy for N* is calculated pression. This will test the model at higher pressures,
from K2 after K2 has been determined from experiment. frequently at higher coverages, in the presence of all
Simulation of more complicated desorption mecha- reactants, intermediates and products, Fig. 4.
nisms such as disproportionation is possible through The model can be further tested for internal con-
numerical solution of the relevant equations. sistency. Steps treated through kinetic equations should
In the case where there is one slow step in the re- be slow at least under some conditions or the model
action mechanism, the solution for the rate of the cat- may obviously be simplified. The significant parame-
alytic reaction is straightforward [24, 251: ters should obviously be determined rather directly
from experiments. The coverages of the intermediates
calculated under reaction conditions should not be
greatly different from the coverages in the experiments
used to determine the parameters.
The parenthesis has a simple interpretation in terms of Once the kinetic model passes the tests, the model
the thermodynamics of the gas phase while the inter- may be used to understand details of the catalytic re-
esting part of the kinetics comes from the factor 6:. action, such as the origin of the macroscopic activation
When the reaction mechanism has more than one energy, the reaction orders, or the structure of empiri-
slow step [27-291, the solution for the rate is more cal kinetics.
complicated, but the final expression is remarkably The activation enthalpy for the catalytic reaction may
similar. be calculated from the microkinetic model as [24, 251
 5.2 Microkinetics 989

For a mechanism with a single slow step, the activation

enthalpy for the catalytic reaction equals the activation
energy for the slow step plus the averaged binding en- -01
ergy for the intermediate. The average binding energy
is formed by weighing the desorption energy for each Elel
intermediate through equilibrium steps with the cover-
age for the intermediate. Intuitively, these two con-
tributions represent the increase in the reaction rate at
- 02 i-1
1
iI
increased temperature through increase in the rate lim- I ~

iting step and increase in the number of free sites, re-

spectively. For models with more than one slow step
[27-291 the contribution to the average desorption en-
ergy is further weighted by the relative rates of the slow
steps.
As the desorption enthalpy for the intermediates de- 0 5 10
pends on temperature (eq 12), and as the coverage by Number of d electrons
intermediates may vary significantly with the operating
conditions for the catalyst, the microkinetic model will Figure 5. Trends in dissociative energies and activation energies
for dissociation as a function of the number of d electrons. The
often predict regions of operating conditions where the results are calculated in the Newns-Anderson model including
activation enthalpy is significantly larger than usual. the coupling between an adsorbate level E, and the metal d band.
Except at conditions where the coverage of all inter- All energies are measured relatively to the Fermi energy in units
mediates is negligible, the activation enthalpy for the of the d-band width and E, = 1.5 corresponds to a chemisorbed
atom with a level well below the d band, whereas E, = 0.0 corre-
catalytic reaction will be larger than the activation en- sponds to a dissociating molecule with its antibonding level par-
thalpy for the slow step. tially filled around the Fermi level.
B Using the Model
In the preceding section we developed the simplest
methods for building a microkinetic model using the instance) are known to change the stability of the in-
ammonia synthesis as an example. For this reaction it termediates and, by including such changes in the
turns out that if all input data are taken from surface- model, one can immediately see if these changes also
science experiments on single crystal Fe(ll1) surfaces account for the observed effects of promoters in the
[20] and the catalyst is characterized only by the active real catalyst system. This turns out to be the case for
Fe area, then the model gives a reasonable account of the potassium promotion of the iron-based catalysts
the kinetics of the real catalyst under industrial con- used for the ammonia synthesis, where it is the K-
ditions [23-251. Due to its simplicity, the model is far induced lowering of the barrier for N2 dissociation and
from perfect; several details of the kinetics are not accu- lowering of the NH, stability on the surface which
rately described. Also, the quantitative aspects of the dominates [30].
model calculation are no more accurate than the input The model can also be used to begin understanding
parameters. For the ammonia synthesis reaction, for in- which metals are active and which are not. It is known
stance, there is still some uncertainty about the sticking roughly how the stability of the intermediates and the
probability and about the absolute value of the nitro- barrier for Nz dissociation varies through the periodic
gen binding enthalpy [20, 30, 32, 331. Also, the mea- system [34]. Figure 5 shows the result of a simple model
sured values for the adsorption rate are known only for calculation of these variations as a function of the
low coverages. While the former problem does not ap- number of d electrons in the metal. If these variations
pear to affect the results significantly [30], the effects of are included in the kinetic model, variations in the
the latter are still not understood in detail [31]. ammonia activity shown in Fig. 6 are obtained. The
In spite of the shortcomings of the modeling, the real modeling clearly shows the volcano shape, which has
strength is that it can be used to understand variations been observed experimentally for many reactions [35].
in the catalytic activity from one system to another. For elements to the left of Fe, the kinetics is similar
The stability of the intermediates and the activation to the kinetics of Fe, but the rate is low due to the
barriers are among the input parameters for the mi- strong bonding of N*. For elements to the right of Fe,
crokinetic model, and it is straightforward to calculate the rate is low due to the low sticking coefficient for N2,
the effects of changes in stability for some or all the
intermediates. Adsorbed promotors (alkali atoms, for References see page 990
990 5 Elementarv Stem and Mechanisms

7 observed for the catalyst and the microkinetic models

0.30 X

thus suggest that the active structure in the catalyst is

the basal planes of metallic Cu.

References
1. J. Rostrup-Nielsen, in Elementary Reaction Steps in Hetero-
geneous Catalysis, Kluwer Academic Publishers, 1993, p 441.
2. J. A. Dumesic, D. F. Rudd, L. M. Aparicio, J. E. Rekoske,
A. A. Trevino, The Microkinetics of Heterogenous Catalysis,
The American Chemical Society, 1993.
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3. G. A. Somorjai, Introduction to Surface Chemistry and Cat-
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5 6 7 8 9 1 0 4. R. A. van Santen, Theoretical Heterogeneous Catalysis,
Number of d electrons World Scientijic Lecture and Course Notes in Chemistry,
Word Scientific, 1991, vol. 5.
Figure 6. The calculated ammonia production for a fixed set of 5. H. Chuan Kang, W. H. Weinberg. Surf: Sci. 1994, 2991300,
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7. B. Hammer, M. Scheffer, K. W. Jacobsen, J. K. Nsrskov.
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8. D. Halstead, S. Holloway, J. Chem. Phys. 1990, 93; 2859.
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the other elements with approximately seven d elec- 389.
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J. Chem. Phys. 1993, 98, 8294.
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pointers to some examples. 18 P. H. Emmett, S. Brunauer. J. Am. Chem. Soc. 1934, 56, 35.
Microkinetic modeling has been applied in mecha- 19 M. Grunze in The Chemistry and Physics of Solid Surfaces
and Heterogeneous Catalysis, (Eds: D. P. Woodruff, D.
nistic studies of the synthesis of HCN [36], the hydro- King.) 1982, Vol 4, p. 413.
genation of ethylene over Pt [37] the reactions CO + 0 2 20 G. Ertl in Catalysis Science and Technology (Eds: J. R.
and CO + NO over Rh [38], the reaction between NO, Anderson, M. Boudart) 1983, Vol 4, p. 209.
and NH3 [39], and the oxidation of CH4 over oxides 21 M. Bowker, I. Parker, K. C. Waugh. Appl. Catal, 1985, 14.
101.
[2]. Microkinetic modeling of nonisothermal reactions 22 M. Bowker, I. Parker, K. C. Waugh. SurJ Sci. 1988, 197,
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of H2 and 0 2 over Pt [15, 40-431 and the highly exo- 23 P. Stoltze J. K. Narskov. Phys. Rev. Lett. 1985, 55, 2502.
thermic partial oxidation of CH4 [44, 451. 24. P. Stoltze. Phys. Scr. 1987, 36, 824.
Microkinetic modeling of the oxidation of CO over 25. P. Stoltze, J. K. Nsrskov. J. Catal. 1988, 110, 1.
26. J. A. Dumesic, A. A. Trevino. J. Catal. 1989, 116, 119.
Pt [16, 17, 46, 471 has demonstrated quantitatively that 27. C. V. Ovesen, P. Stoltze, J. K. Nsrskov, C. T. Campbell. J.
reconstruction of the Pt surface under reaction con- Catal. 1992, 134, 445.
ditions leads to a coupling between reactivity and 28. P. B. Rasmussen, P. M. Holmblad, T. S. Askgaard, C. V.
coverages by intermediates, which causes the reaction Ovesen, P. Stoltze, J. K. Nsrskov, I. Chorkendorff. Catal.
Lett. 1994, 26, 313.
condition to display deterministic chaos. 29. T. Askgaard, J. K. Nsrskov, C. V. Ovesen, P. Stoltze. J.
The catalytically active structure for the Cu-based Catal. 1995, 156, 229.
catalysts used in the water-gas shift reaction and, in 30. P. Stoltze J. K. Nsrskov. Topics in Catal. 1994, I , 253.
particular, in methanol synthesis, has been contro- 31. L. M. Aparicio, J. A. Dumesic, Topics in Catal. 1994, 1 ,
versial. Recent microkinetic models of these reactions 233.
32. C. T. Rettner, H. Stein. Phys. Rec. Lett. 1987, 59, 2768.
[27-29, 481 starting from experimental data for Cu 33. C. T. Rettner, H. Stein. J. Chem. Phys. 1987, 87, 770.
single crystals, show a good agreement between the re- 34 S. Holloway, B. I. Lundquist, J. K. Narskov in Proc. In?
sults calculated by the microkinetic model. The kinetics Congr. Catalysis, Berlin, 1984, Vol. 4, p. 85.
 5.2 Microkinetics 991

35. J. K. Nerrskov, P. Stoltze. Surf: Sci. 1987, 1891190, 91. adsorption. This can change the nature of the limiting
36. N. Waletzko, L. D. Schmidt. AZChEJ. 1988,34, 1146. step and in some cases lead to desorption-limited
37. J. E. Rekoske, R. D. Cartright, S . A. Goddard, S . B. Sharma, kinetics. The optimum is, therefore, a balance of the
J. A. Dumesic. J. Phys. Chem. 1992, 96, 1880.
38. S. H. Oh, G. B. Fisher, J. E. Carpenter, D. W. Goodman, J. adsorbate-surface chemical bond strength; the reac-
Catal. 1986, 100, 360. tants readily adsorb and the products desorb. This is
39. J. A. Dumesic, N. Y. Topsere, T. Slabiak, P. Morsing, B. S . the well-known Sabatier’s principle where the hghest
Clausen, E. Tornquist, H. Topsere in Proc. loth Znt. Congr. reaction rates are achieved at intermediate adsorbate-
Catal., Budapest, 1992.
40. B. Helsing, B. Kasemo, V. P. Zhdanov. J. Catal. 1991, 132, surface chemical bond strengths. It is the basis for
210. Volcano-structure-reactivity plots which depict a
41. M. Fassihi, V. P. Zhdanov, M. Rinnemo, K-E. Keck, B. maximum in reactivity at a given metal-adsorbate
Kasemo. J. Catal. 1993, 141, 438. bond strength.
42. W. R. Williams, C. M. Marks, L. D. Schmidt. J. Phys. Chem.
1992,96, 5922.
The direct extrapolation of detailed information on
43. M. P. Zum Mallen, W. R. Williams, L. D. Schmidt. J. Phys. surface chemical bonds to predications about the over-
Chem. 1993, 97, 625. all catalytic reactivity, while useful, must be done with
44. D. A. Hickman, L. D. Schmidt, AZChEJ. 1993,39, 1 164. extreme caution so as to properly account for all rele-
45. D. A. Hickman, L. D. Schmidt, Science, 1993,259, 343. vant competing phenomena. The surface science com-
46. K. Krischer, M. Eiswirth, G. Ertl. J. Chem. Phys, 1992, 96,
9161. munity has been very careful in their attempts to bridge
47. K. Krischer, M. Eiswirth, G. Ertl, J. Chem. Phys, 1992, 97, well defined single crystal results, performed at ultra-
302. high vacuum (UHV) conditions, to results for real
48. C. T. Campbell, Topics in Catal. 1994, I , 353. catalytic surfaces at operating conditions. Schlogl [ 11
has cited differences in the surface structure (materials
gap), reactor operating pressures (pressure gap), re-
actor transport phenomena (transport gap), and the
5.2.4 Theory of Surface-Chemical single-crystal model of the polycrystalline surface
Reactivity (model gap) as important issues in mapping funda-
mental information on the nature of the adsorbate-
R. A. VAN SANTEN
AND M. NEUROCK surface interaction to quantitative kinetic descriptions
of real catalytic phenomena.
While there are still a number of issues which need to
5.2.4.1 Introduction be resolved, we are moving closer towards narrowing
these gaps. There is a growing number of examples
The relationship between the overall rate of reaction whereby the gaps have actually been closed. Ertl [2],
and the reactivity of a catalytically active surface is Goodman and co-workers [3], and Nsrskov [4],for
complex due to competing phenomena at the elec- example, have been instrumental in demonstrating how
tronic, atomic, and molecular levels. The catalytic re- well-defined surface science data and theoretical de-
action is a cycle composed of a series of fundamental scriptions of the binding and reactivity of adsorbates
elementary steps in which the state of the active surface on surfaces can be used to predict real catalytic systems
is maintained by regenerating active surface sites upon under operating conditions for various example sys-
each cycle turnover. The chemical state of individual tems. Ertl demonstrated the well-established ammonia
reaction sites and the overall active surface are readily synthesis mechanism from a series of probing UHV
altered as a function of reaction conditions. Surface experiments. Goodman and co-workers [3] presented
coverage, for example, can change with conversion. a number of relevant catalytic examples, for both
This affects the distribution of vacant sites available structure-insensitive and structure-sensitive reactions,
for reaction, and can subsequently lead to surface re- whereby a pressure-modified UHV chamber was used
construction. Temporal changes in either the chemical to resolve pressure-gap issues. Some examples include
state or the surface coverage ultimately alters surface CO methanation, CO oxidation, alkane adsorption,
reactivity. and hydrogenolysis on different metal surfaces. N0r-
The overall reaction rate of a catalytic cycle is con- skov [4]applied statistical mechanics to predict ammo-
trolled by a delicate balance of the strength of the nia synthesis production on an iron-based potassium-
adsorbate-surface interaction. A strong interaction promoted catalyst over various temperatures and up to
between the reactant and surface tends to favour the 300 atm, and water-gas shift kinetics on copper.
initial activation of the adsorbate and its subsequent While high-pressure designed UHV chambers, such
dissociation. This is desirable for systems which are as that described by Goodman, allow us to probe
activation-limited and have no secondary decomposi- binding and surface reactivity of molecular adsorbates
tion routes. By increasing the reactant adsorption,
however, we are also likely to increase the product References see page 1004
992 5 Elementary Steps and Mechanisms

on transition metal surfaces from experiments, careful of the catalytic cycle, and actual specifics about the
first-principle quantum chemical calculations coupled controlling reaction mechanism. As was suggested,
with atomic reactivity simulations provide a comple- coupling of first-principle electronic and kinetic de-
mentary computational approach to modeling pressure- scriptions enable us to begin to bridge some to the
gap concerns. A fundamental understanding of (i) the pressure gap and material gap issues discussed. By way
nature of the adsorbate-surface interaction and (ii) of illustration, we examine overall reaction cycles
how reaction probabilities change as a function of sur- as well as the controlling reaction coordinates for vari-
face composition changes is therefore essential. Both ous reaction mechanisms for various types of surface
of which can be gained from advanced computations. chemistries.
Surface coverage changes lead to changes in the nature Historically, most of the theoretical efforts aimed at
of the active surface which can ultimately alter the heterogeneous catalysis have focused on small mole-
nature of the rate limiting step of the catalytic reaction cule reactivity over different transition metal surfaces.
cycle. There has been a wealth of valuable information from
The selectivity of a reaction is controlled by both the formal chemisorption theory, semiempirical and ab
energetics of the available reaction channels, as well as initio studies on the principles that govern chem-
the temporal surface composition. By way of illus- isorption. Collectively, these systems provide a very
tration, consider the balance between elementary dis- valuable resource and qualitative description of the
sociation and desorption events. At low surface cover- relevant principles which control the nature of the sur-
ages, the step with the lowest energy barrier proceeds. face-adsorbate bond and small molecule reactivity on
At higher coverages, however, the number of available clean transition metal surfaces.
vacant sites become a critical concern. For dissociation In Section A.5.1.2 we focused on the information
to proceed, there must be at least on vacant site ad- and insights derived from formal chemisorption theory,
jacent to the adsorbed species. Dissociation is, there- tight-binding approaches, and current first-principle
fore, highly dependent upon surface concentration. The results for these systems. The explosive growth of both
reaction rate of an isolated molecule is then an explicit methods development as well as the computational
function of surface coverage. hardware capabilities today enable us to examine sig-
Surface coverage or surface composition can also act nificantly larger transition metal systems, as well as
indirectly and change surface reactivity by electroni- more complex adsorbates, and provide quantitatively
cally altering the adsorbate-chemical bond strength reliable values for adsorption energies and activation
through lateral surface interactions. Lateral surface in- barriers. In addition to CPU advances (which enable
teractions lead to nonideal mixture properties. Effective larger cluster calculations) recent two- and three-
attractive interactions can lead to ordered-disordered dimensional density functional theory (DFT) codes are
phenomena, whereas effective repulsive interactions enabling the first-principles treatment of real extended
can lead to phase separation with surface island for- transition metal surfaces and slabs and their inter-
mation. In the latter case, the overall reaction rate is actions with adsorbates [7].
significantly reduced because reactions between adsor- Our knowledge about transition metal reactivity and
bates can only occur at the boundary of the islands the current success of fmt-principle calculations now
formed. put us in a favorable position to begin to answer ques-
Island formation is usually accompanied by surface tions posed at the chemistry of other complex mate-
reconstruction [ 5 ] . Interestingly, Ertl and co-workers rials, such as transition metal sulfides and transition
[6]have demonstrated that, at least at UHV conditions, metal oxides. In many respects, the chemistry of these
“hot” ad-surface atoms generated by dissociation of systems is considerably more challenging due to the
an adsorbed molecule can migrate over an 80 8,distance unknown surface structures, the ease of surface re-
before finally adsorbing. The energy released by dis- construction, and the ill-defined nature of the active
sociation dissipates slowly on the time-scale of transla- centers. Current first-principle attempts at modeling
tional motion of the “hot” atoms, and thus allows these systems are discussed.
these species to move considerable distances before We, therefore, structure this chapter around the im-
finally chemisorbing. portant elements that help to define surface reactivity
In this chapter we examine a set of important con- and subsequently present recent examples from (i)
cepts of the adsorbate-surface chemical bond deduced classical small molecule-transition metal surface re-
from quantum chemical calculations and how these activity, (ii) transition metal sulfide reactivity, (iii)
fundamental ideas can be coupled with statistical me- transition metal oxide reactivity, and (iv) well-defined
chanics to provide energetic and kinetic analyses. Cur- metal oxide (zeolite) reactivity. This diverse scope in
rent first-principle quantum chemical analyses com- chemistry provides a more comprehensive treatment of
bined with transition-state theory can help to elucidate the theory of surface reactivity, whereby we extend our
overall reaction pathways, competing elementary steps knowledge base and cover important elementary cata-
 5.2 Microkinetics 993

lytic steps such as C-0 dissociation, C-H activation, In the follow-up section, we illustrate the utility of
C-S bond scission, O-mediated bond activation, metal reaction energy diagrams in identifying slow reaction
atom insertion, and proton transfer pathways. steps and estimating the surface composition of the re-
acting surface overlayer. In the ammonia oxidation
example, the reaction energy diagram is used to exam-
5.2.4.2 Outline ine the N2 versus NO production.
Some of the simple ideas discussed for adsorbates on
The first part of this Section describes the electronic metals are then applied to sulfide catalysis. The analy-
and structural features that determine the rates of dis- sis of very small adsorbates on transition metal surfaces
sociation and association reactions on transition metal to the treatment of larger adsorbates, such as thio-
surfaces. We elucidate the lowest energy reaction paths phene, dihydrothiophene, butadiene, on model tran-
and discuss the utility of two important theoretical sition metal sulfides relevant in hydroprocessing sys-
concepts for analyzing transition metal surface chem- tems is expanded. The use of the reaction energy
istry. The first is the principle of least metal atom diagram for the analysis of thiophene activation by the
sharing which helps to describe adsorbate bonding on Ni3SZ is extended. This example nicely illustrates the
transition metal surfaces and provides a qualitative de- importance of including complete structure relaxation
scription of minimum energy reaction paths over sur- for adsorbates, as well as clusters in establishing the
faces. The second is the concept of negative ion for- controlling intermediates and reaction pathways.
mation. In various systems, barriers for dissociation can The final section covers recent studies on different
be substantially reduced if the dissociated adsorbate- amorphous reducible transition metal oxides and well-
surface species is allowed to take on a negative charge. ordered crystalline metal oxides. The current status
Both surface structure and surface electron delocali- of theoretical calculations on transition metal oxide
zation play important roles in controlling surface re- selective oxidation catalysis is assessed and proton
action rates. We discuss how changes in delocalization transfer chemistry in zeolites is examined. The latter
of the metal s, p, and d valence electrons affect re- illustrates the concept that the intermediate geometries
activity. A more in-depth analysis is provided in Sec- in surface reactions often bear little resemblance to
tion A.5.1.2, on chemisorption, and elsewhere [8, 91. In analogous gas-phase intermediates. Reducing the acti-
addition, we analyze the adsorbate-surface structure at vation barrier on a surface typically requires a sig-
various active sites and how it changes along operative nificant interaction between the reactant and active
reaction coordinates. The Brernsted-Polanyi relation- surface site and thus substantial adsorbate-surface re-
ship is discussed in terms of relating changes in the construction. In the proton transfer reaction, a charge
activation energy with changes in reaction energy to separation energy has to be minimized.
predict trends in the reaction rate constants. CO and Most of the theoretical results referred to in this chap-
NO are used as prototype adsorbates for bond activa- ter are based on the use of first-principleelectronic struc-
tion and dissociation. Their dissociation paths are an- ture calculations. The details for these calculations are
alyzed in terms of transition state reaction rate theory described in more detail in their original references. We
to determine surface reaction rate constants. focus instead upon the chemical concepts of reactivity.
The fundamentals of X-H bond activation is con- The current status of first-principle computational
sidered next and analyzed in terms of methane and quantum chemistry is such that interaction energies can
ammonia activation. A dissociating molecule that is be predicted within reasonable accuracy, i.e. about
coordinatively saturated initially has a repulsive inter- 20kJmol-', for systems of catalytic interest [8]. Such
action with the surface which is only overcome when theoretical results are typically accurate for the cluster
the molecule deforms itself. Hydrogen, for example, chosen as a chemical model. Discrepancies between the
requires a significant activation of the H-H bond be- calculations and experiment then represent differences
fore it will coordinatively bind to a transition metal in the chosen model and the actual experiment.
surface. On surfaces of low reactivity, reaction with This includes deviations due to limited-size models
coadsorbed oxygen, either atomic or molecular, can (clusters) of bulk phenomenon, as well as deviations
provide low energy paths to drive the dissociation due to competing phenomena inherent in the actual
which would otherwise not proceed. This is discussed experiment. A critical discussion on the use of different
in terms of ammonia activation by oxygen over copper. quantum chemical methods and cluster-size effects is
We examine both precursor atomic and molecular given in Ref. 8. We have chosen to discuss selected ex-
oxygen surface species. Coadsorption of ammonia with amples of the surface-chemical reactions representative
oxygen (either atomic or molecular) demonstrate sig- of main classes of surface chemistry and reactivity in
nificant lateral attractive surface interactions. In addi- heterogeneous catalysis.
tion, we comment on the repulsive lateral interactions
for adsorbates bound too close to one another. References see page 1004
994 5 Elementary Steps and Mechanisms

Cu, the results of a series of first-principle density

P i / O - functional calculations on a Cu(9,4) model of the Cu

i
C
(100) surface indicate the same low energy metal-metal
I 0 bond crossing reaction path [Ill. A minimum energy
barrier for dissociation requires CO or NO bond
bending stretching
weakening to be made possible by electron transfer
from the surface into the antibonding 271* CO or NO
,o orbitals. The position of the molecular CO axis over a
c” I
surface atom allows for the overlap of one of the two
C- I Rh
0 Rh
271* orbitals with surface atomic orbitals of the same
symmetry, i.e. the d,, or dyzmetal orbitals.
If, however, the CO axis is placed perpendicular,
over a metal-metal bond, both 2n’ bonds can become
no yes activated via the interaction with the asymmetric sur-
face d atomic orbitals. The overlap of the 271* orbital
FCC(I I I ) normal to the surface, as well as the activation of the
C - 0 bond, however, are now somewhat less.
The energy barrier for C - 0 activation can be low-
E,,, = I80 kJImo1 ered by lowering the work function of the metal.
Clearly, the lower the work function, the easier it is to
FCC(100) form a negative ion surface species. This acts to en-
hance surface reactivity. This observation agrees well
E,,, = 140 kJimol with experiment. More open surfaces, which corre-
spond to lower work function surfaces, tend to be more
reactive. Coadsorption of promoters, such as alkali
Figure 1. Dissociation paths of CO (schematic): (a) bonding and species or oxides which act to lower the work function,
stretching of the CO bond; (b) CO dissociates not along a metal- also help to enhance CO dissociation.
metal bond the C and 0 atom generated by dissociation require
~
In Section A.5.1.2, the relevance of the d valence
a surface ensemble; (c) dissociation paths and activation energies band width and the degree of electron delocalization
on Rh(ll0) and Rh(ll1) surfaces.
to adsorption energetics and surface reactivity is dis-
cussed. We note here that the adsorbate-surface
chemical bond strength tends to increase with an in-
5.2.4.3 Transition Metal Surface Chemistry crease in the degree of coordinative unsaturation of the
surface atoms. The greater degree of coordinative sur-
A Dissociation of CO and NO face unsaturation reduces the delocalization of surface
Semiempirical ASED extended Huckel calculations electrons and narrows the d valence band width. Ad-
were used to provide the low-energy CO dissociation sorption energies thus increase accordingly.
paths over Rh(l1 l), Rh(100), and Rh(ll0) surfaces The surface reaction energy is a function of the ad-
as modeled by large 50 atom clusters [lo]. Some of sorbed initial state, the adsorbed dissociated products,
the more favorable dissociation paths determined are and the transition-state surface complex. This situation
illustrated in Fig. 1. CO binds end-on with the carbon can be simplified by applying the Brmsted-Polanyi
atom attached to one or several surface metal atoms. relationship which indicates a linear correspondence
In order to dissociate, CO bends in such a way that between the activation energy and the overall reaction
both the carbon as well as the oxygen develop stabiliz- energy:
ing bonds with the metal surface atoms. On the (1 1 1)
and (100) surfaces, the lowest energy path involves 6Eact t AEreact (1)
stretching the C - 0 bond over a metal atom center with The reaction energy depends only on the overall dif-
a combined reduction of the 0-C-surface angle. The ference in energy between the adsorbed initial state and
result is an intermediate with a C-0 bond nearly par- the final reaction state, the adsorbed dissociated prod-
allel to the surface. The carbon and oxygen atoms uct fragments.
produced move towards the higher coordination ad- Due to the compensating changes in donating and
sorption sites that share only a single surface atom backdonating interaction terms, the changes in the
center. An alternative path was found on the (1 10) surface atom reactivity affect the adsorption energy for
surface. Here the ASED calculations indicate a re- molecules much less than the changes in the binding
action path in which the CO molecule crosses over a energies for the corresponding adatom products. Hence
metal-metal surface bond. For NO dissociation over on a more reactive surface, the reaction energy for dis-
 5.2 Microkinetics 995

sociation tends to be more favorable. A comparison of the rate of dissociation is much lower than that of de-
the reactivity of the nickel surface with the corre- sorption, even though their activation energies are
sponding platinum surface, for instance, indicates that close to one another. This is the case, for example, for
CO binds more strongly to Pt than Ni, but that the rate the Rh(l11) surface [lo]. It also helps to explain the
of CO dissociation is faster on Ni. The lower work low sticking coefficients that are found for dissociative
function of Ni results in significantly larger C and 0 adsorption. At low surface coverage the apparent rate
atom binding energies to Ni than to Pt. This favors a constant for dissociation is
lower dissociation barrier on Ni than on Pt.
Whereas molecules such as CO and NO usually ad- kdiss(app;6 << 1) = kzif X &ds (2)
sorb perpendicular to the surface, chemisorbed oxygen The apparent activation barrier is the intrinsic barrier
or nitrogen molecules chemisorb parallel to the surface. minus the energy for adsorption. The apparent barrier
The increased backdonation of electrons results in a is, therefore, significantly lower due to adsorption. In
significant negative charge and population of bond- some instances the apparent barrier can even become
weakening antibonding orbitals. The parallel binding negative. Despite this lowering of the barrier, the rate
geometry further enhances the increase in backdona- of dissociation is still often a limiting step in the over-
tion. The molecular bond can now stretch considerably all catalytic reaction cycle. An example of this is the
to accommodate the increase in backdonation and in- dissociation of N2 on Fe for the ammonia synthesis
teract more strongly with different metal surface atoms. reaction. The low rate in this system is attributed to the
The activation energy for the dissociation of different low preexponent factor for the rate constant for dis-
diatomics from this state is low. Examples include the sociation [13].
dissociation of 0 2 on the (110) surface of Ag [12], and Reaction paths for dissociation require an ensemble
dissociation of N2 on the (111) surface of Fe [13]. of surface atoms to carry out the dissociation, so that
Based on calculations with the N2 dimer, Blomberg the adatoms generated as reaction products have sites
and Siegbahn [14] proposed that N2 would dissociate whereby they can strongly adsorb. Dissociation reac-
by crossing perpendicularly over the metal-metal tions are suppressed when the availability of suitable
bond. surface ensembles is reduced due to site blocking from
Transition-state reaction rate theory can be used to coadsorbate species or additives. Alloying the metal
predict reaction rate constants from computed vibra- surface with an inert has the same effect and also acts
tional frequencies of ground state and transition state to reduce available reaction sites and measured dis-
structures. Computed preexponents for dissociation sociation rate constants.
from the adsorbed state are typically [l 11 Because of their short lifetimes (femto- to pico-
seconds), transition state complexes are only indirectly
AdkS
pre z 10" s-l
accessible to experiment. Detailed molecular beam and
Surface recombination of adatoms to form an adsorbed high resolution spectroscopic techniques can be used
molecular intermediate results in a preexponential to probe the vibrational, rotational, and translational
value of the order of velocity distribution of molecules that recombinatively
desorp from a surface, to elucidate structural evidence
1013 s-l on different surface transition-state complexes. Using
Pre
A typical value for the preexponent of the rate-con- infrared emission spectroscopy, Coulston and Haller
stant of desorption from the same immobilized state as [ 151 were able to deduce information on the elementary
used for dissociation is reaction path on the structure of the transition state for
CO oxidation on Pd, Pt, and Rh foils. From differences
AdeS
pre 1015s-l in the measured vibrational-rotational emission spec-
tra, they were able to conclude that the transition state
The preexponent value of 1013 for the recombination is a bent COi- complex on Pd, whereas on Pt and Rh
reaction indicates that the entropy of the transition the complex is nearly linear. The work functions of
state complex for the recombination path is close to the each of these metals are surprisingly similar, and is
entropy for the adsorbed atoms. The situation is there- therefore not a likely explanation these differences. The
fore described as a tight transition state. The consid- density of states at the Fermi level, however, is nearly
erably elongated molecular intermediate has very lim- three times higher for Pd than for Pt or Rh and was
ited mobility due to its strong interaction with the suggested as the reason for the change in transition-
surface. This is in contrast with the transition state for state surface structure. The higher density of state for
desorption where the molecule is freely rotating and Pd increases the amount of charge transfer to the
has two translational degrees of freedom. The large
difference in the preexponents of the rate constants
for desorption and dissociation help to explain why References see page I004
996 5 Elementary Steps and Mechanisms

Figure 2. Transition state for dissociation of CH4 molecule on

Nil3 cluster [16].
Figure 3. Contour plot of the electron density difference for
threefold adsorption of Mg2+, p(Mg2++Ir4)-p( Ir4- p(Mg2').
Dashed lines show a decrease, solid lines an increase of the elec-
weakly bound COz adsorbate. In an effort to accom- tronic density, except for the solid lines next to dashed lines which
modate the higher negative charge, the bound COz depict nodal surfaces [ 181.
distorts and, therefore, takes on a more bent structure.
The speculated reaction path on each of these metals is
considered to be the same, and one in which the CO
The weak initial interaction of CH4 with the metal
migrates atop an adsorbed surface oxygen.
surface is due to the strong repulsive interaction be-
tween the occupied metal and methane orbitals. The
B CH4 and NH3 Dissociation unoccupied methane orbitals are very high in energy
The activation energy of a surface dissociation reaction and have little orbital overlap with the occupied metal
is minimized by the interaction of the dissociation orbitals. Attractive interaction terms are therefore very
products with the surface. The tetrahedral carbon atom small, and the interaction is predominantly repulsive.
in methane is physically shielded from the surface As discussed in Section A.5.1.2, for the interaction of
atoms by its outer shell of hydrogen atoms. Only by H2 with small Ir clusters, the polarization of such a
deforming the molecule (or the outer hydrogen shell) particle by a charged cation will pull charge towards
by stretching one of the C-H bonds is the carbon the cation and deplete the atomic orbitals located in
allowed to approach the surface with an attractive atoms opposite the Mg2+ ions, as shown in Fig. 3 [18].
interaction. This is clearly seen in the computed tran- This reduces the electron density between H2 and co-
sition state complex of CH4 on a Nickel cluster, shown ordinated Ir atoms. The hydrogen molecule can now
in Fig. 2 [16]. While the C-H bond is significantly more closely approach the cluster and lead to a sub-
stretched, the rest of the molecule is essentially un- stantial increase in the attractive interaction energy.
altered and maintains its rotational freedom. The Protons or cations adsorbed in zeolites, near to small
methyl radical and hydrogen atom products have sig- metal particles can in the same way promote alkane
nificantly less interaction with the surface metal atoms activation.
than that of the oxygen and carbon adatom frag- Activation of the N-H bonds in ammonia is more
ments from CO dissociation (some 250 kJ g-atom-'vs. facile than the activation of C-H bonds in CH4, be-
600 kJ g-atom-'), and hence the dissociating molecule cause of the basic nitrogen atom with its free lone pair
in the transition state maintains considerable mobility. orbital, and the hydrogen atom of the molecule which
The computed preexponent for dissociative adsorp- can now interact with the surface atoms. Ammonia
tion is only 0.1 times the hard sphere collision rate. binds more strongly to transition metals to the left in
the weak adsorption energy of CH4 implies a high the periodic table primarily due to their substantially
activation energy for dissociation (= 80 kJ mol-I). lower work functions and unfilled d valence electron
Dissociation then occurs by direct activation of the bands. Under conditions of higher temperature many
colliding molecules or, when adsorbed, by the energy of these surfaces will readily dissociate ammonia. Am-
transfer from the impacting molecules [16]. An ex- monia binds much more weakly, however, to transition
tensive study of CH4 and CH, activation in general by metal surfaces to the right of the periodic table with
transition metal atoms and surfaces can be found in the highly filled d bands, such as Cu [19] and Pt [20]. Dis-
work of Siegbahn and co-workers [17]. sociation over these surfaces is much more difficult.
 5.2 Microkinetics 997

Surface Reactants A E = 0 kJimol A E = 0 kJ/mol

I
2 28
2.17
2.05k2.17

A E = 67 kJimol
Transition Complex AE = 132 kJ/mol
0.98
1.853,

A E = -25 kJimol
Surface Products A E = +48 kJimol 0.99

9 P p0.98

Figure 5. Transition states for the dissociation of NH3 by

Figure 4. Transition states for the dissociation of NH3 by co- molecular oxygen.
adsorbed atomic oxygen.

Coadsorbates, such as adsorbed oxygen can, how- primarily due to the enhanced stabilization of the
ever, considerably facilitate the dissociation. On both stretched N-H bond by the interaction with the closer
Cu and Pt, Roberts and co-workers [19, 201 have oxygen atom from the molecularly adsorbed oxygen.
shown that with coadsorbed oxygen the ammonia dis- At low coverage, the effective activation energy is the
sociation occurs quite readily even at room temper- activation energy of the surface reaction minus the heat
ature to form NH, fragments. As discussed in Section of adsorption (eq 2). Notwithstanding the higher acti-
B.4.6.1, such a reaction with an adsorbed oxygen is vation energy for the activation of ammonia by atomi-
quite common for acidic adsorbate protons, as for the cally adsorbed oxygen, the effective activation energy
hydroxylic protons of CH30H or CH3COOH. It is for this process may be lowest! Molecular and atomic
probable that CH4 oxidation by Pt is also promoted by oxygen have both been cited as a possible precursor in
an initial reaction of CH4 with adsorbed oxygen. Both ammonia oxidation over Cu(ll1) [19].
atomic as well as molecular oxygen precursors have The overall reactivity of higher alkanes is larger than
been suggested in promoting NH3 dissociation. We that of methane, mainly because of their larger heats of
considered both and examined the dissociation reaction adsorption. The higher heats of adsorption act to de-
path of NH3 over Cu(ll1) using nonlocal density crease the apparent activation energy for C-H bond
functional calculations [21]. Figure 4 depicts the com- scission with respect to that of the gas phase (eq 2). The
puted transition state complex for the reaction with barrier is thus more substantially reduced for the lon-
atomic oxygen, whereas Fig. 5 shows the complex with ger alkanes than than for methane.
molecular oxygen. The activation energy of the latter is
nearly half that of NH3 with atomic oxygen. This is References see page 1004
998 5 Elementary Steps and Mechanisms

Table 1. Recombination and dissociative adsorption activation

energies for the recombination of adsorbed hydrogen and methyl
species and CH4 on Cox and Nix [16a].
C +3H
Metal Recombinative Dissociative 21 27
desorption adsorption
(kJ mol-‘) (kJ mol-‘
CH3 CH+ZH
Cluster size 7
co 81 199
Ni 71 86
Cluster size 13
co 95 92
Ni 86 104

32
C +3H
The activation of the C-H bonds in alkenes is easier
than in alkanes for two reasons. First, for molecules
CH3
I CH+ZH IT-
larger than ethylene, ally1 formation is possible. This
weakens the C-H bond. Secondly, alkenes bind more Figure 6. The relative energies of CH, species chemisorbed on
strongly to surfaces as witnessed by both their greater (a) a Nil3 and (b) a Col3 cluster [16b].
adsorption energies and their closer approach to the
metal surface. This promotes a stronger interaction
with the transition metal surfaces which acts to lower methyl fragments to form methane over Ni and Co
the barrier for dissociation. As was the case for alka- clusters, and the barrier for the recombination of an
nes, the coadsorption of oxygen can support C-H adsorbed carbon atom with a CH2 surface fragment.
bond activation in alkenes. One example is the activa- The cluster size dependence is discussed in Section
tion of ethylene over Ag by the coadsorption of oxygen A.5.1.2. The rate of formation of CH4 on Co is signif-
PI. icantly slower on Co than on Ni due to the higher sta-
Adsorbed ethylene and other alkenes can react in bility of the reactant CH3 and H fragments on the Co
consecutive reactions via various different routes on surface. The lower rate of methanation of surface car-
transition metal surfaces. Highly reactive metal sur- bon on Co favors the chain growth reaction.
faces can further dehydrogenate the absorbed ethylene Interestingly, in a set of experimental studies on the
(alkene) to form vinyl surface species or ethylidine reactivity of CH3 groups generated by low temperature
which can undergo further dehydrogenation to form bombardment of adsorbed CH4, Ceyer and co-workers
acetylene. In addition, the C-C bond scission path [24] found that the decomposition of CH3 on Ni is
also becomes accessible. In the presence of hydrogen, an activated processes, but upon further increasing
adsorbed ethyl fragments can react to form ethane the temperature, the CH species become the preferred
provided the transition metal surface can dissociate H2. intermediate. Six CH surface intermediates can sub-
The mechanism of C-H scission or C-H bond for- sequently recombine on the transition metal surface to
mation in alkenes is similar to that for CH4 activation. form benzene when the temperature remains low. To
C-H activation is favored by a reaction path such that help elucidate the reactivity of CH, species, Burgh-
the barrier to bond stretching is weakened by electron graaf [16c] used nonlocal DFT calculations to examine
back-donation from the surface. The most favorable the relative stability of CH, species on Ni and Co. The
reaction path for the dissociating C-H bond is that results are depicted in the reaction energy diagram
which crosses atop over a surface metal atom so that shown in Fig. 6. This figure clearly shows that CH3 as
the asymmetric d atomic orbitals can contribute to the well as CH activation are endothermic, but CH2 de-
activation of the C-H bond for cleavage. composition is exothermic. This agrees with the low
The C-C bond scission of alkanes by transition “CH2” concentrations observed on surfaces covered
metals can only occur after one of the C-H bonds has with CH, species.
been cleaved. The activation energy for these reactions
decreases with the hydrogen content of the hydro- C Reaction Energy Diagrams
carbon fragment. This is primarily due to the reduction
of the steric repulsion of the C-H bonds by the metal a Ammonia Synthesis
surface. A reaction energy diagram provides an important
Table 1 compares DFT computed activation barriers overview of the energy changes that accompany each
for methanation verses carbon chain growth. Reported elementary step. It provides a concise pictorial sum-
are the barriers for the recombination of hydrogen and mary of the energetics of the complete overall catalytic
 5.2 Microkinetics 999

I
--
N+3H

I I
J l
314

--
I I29
i -
c
s
-400 -

I
389
Y -600 -
NH2 +H P8
-960

I I
1400 ti
-800 -
,1000 -
543 460
1 I
-1200

Figure 8. The reaction energy diagram corresponding to the re-

action skips shown in Fig. 9 [21]:
SR1 NH3.ads + Oads + NH2ads + OHads
Figure 7. A scheme for ammonia synthesis on Fe(ll1) at low SR2 : NH2.ads + Oads + NHads +O h d s
nitrogen coverages; energies in kJ mo1-I [13].
SR3 : NHads + Oads + Nads f OHads

reaction cycle and leads to insights about the control-

ling mechanism and how it may change under various
2 q g s J & + 2 AE = -96 kJ
operating conditions. For the ammonia synthesis re-
action catalyzed by the (1 11) surface of Fe, a complete

-2e
diagram has been established based on the vast number
of fundamental experimental studies aimed at resolv- 3 - 3
ing the controlling steps [13]. This diagram is shown in AE = -44 kJ
Fig. 7.
Decomposition of N2 is found to be exothermic,
whereas the steps involved in the formation of NH, 2
A E = +96 kJ
species by hydrogen addition are endothermic. The first
hydrogen addition step is the most difficult. The acti-
vation energy of N2 dissociation with respect to the gas
phase is only a few kilojoules per mole. Notwithstand- 2
ing this apparently low barrier, N2 dissociation is con- j
A E = +I2 kJ 2 *
sidered to be rate limiting and competes with NH3 de-
sorption. The low rate of nitrogen dissociation here is
attributed to entropic considerations where there is a 2
+ 2
low preexponent for dissociative adsorption, as was A E = -96 kJ
discussed in Section 5.2.4.2.

b Ammonia Oxidation 2 - 1
A DFT-computed overall reaction energy diagram for
AE=-214 kJ
ammonia oxidation by Cu(ll1) is shown in Fig. 8 [21].

3e
In Fig. 9 the corresponding elementary steps are
-+
shown. While only the overall reaction energies are
depicted here, the diagram still provides a very useful
summary of the chemistry and a tool for examining
6
+ A E = + I 17 kJ
changes in this system. The results indicate that the
coadsorption of oxygen and ammonia increases the
Figure 9. A catalytic cycle of elementary reaction steps of the
binding of ammonia by z 40 kJmol-'. This is attrib- 02,NH3 oxidation reaction catalyzed by Cu.
uted to the weakening of the surface complex Cu-Cu
bonds by adsorbed oxygen, and the subsequent
strengthening of the neighboring Cu-N bond. Ammo-
nia prefers to adsorb atop. In the presence of chem- References see page 1004
1000 5 Elementary Steps and Mechanisms

isorbed oxygen, ammonia situates itself at a neighbor- was found for the N2 interaction with Cu. This drives
ing Cu site to enhance the attractive through-metal N2 formation to become endothermic on these metals.
surface interaction. Dissociative adsorption of oxygen
is highly exothermic. At low concentrations, the prod-
uct oxygen atoms prefer to sit in threefold coordination 5.2.4.4 Transition Metal Sulfide Catalyzed
sites which do not share any surface Cu atoms. The Desulfurization
strong interaction of the oxygen atoms with the Cu
surface may ultimately lead to surface reconstruction The theoretical study of desulfurization reactions cata-
to form ordered adsorbed oxygen arrays. This is seen lyzed by sulfidic catalysts has been limited by both the
experimentally [27]. As discussed in subsection B above difficulty in defining the active surface and active sites
coadsorbed oxygen influences the surface dissociation for hydrodesulfurization (HDS) as well as the lack of
paths. While the oxygen site is clearly the favored relevant model systems. Recent fundamental experi-
site for dissociated hydrogen in terms of the overall mental evidence is now providing a more complete
thermodynamics, does it play a role in the actual picture of the working catalytic surface [28-311. This
mechanism or kinetics? Ammonia dissociates by atom- catalytically active site corresponds to a distribution of
ically adsorbed oxygen. The endothermicity for am- small Co&like or Ni3Sz-like particles along the edges
monia dissociation is lowered by 128 kJ mol-' (from of MoS2 basal planes. Studies on highly dispersed sul-
176 kJ mol-' for the reaction NH3+ds + NH2.adst Hads fide particles formed on carbon [31a-c] and those
to 48 kJ mol-') when atomic oxygen is introduced into deposited in the microporous framework of a zeolite
the reaction mechanism [21]. [31d-f] have demonstrated that small metal sulfide
The first step of ammonia dissociation is the ab- particles themselves are active HDS components.
straction of hydrogen by oxygen, which is endothermic. Previous theoretical studies have, for the most part,
Subsequent NH2 and NH dissociation steps, however, been aimed at understanding the electronic structure of
become progressively easier, whereby NH2 is essen- bulk metal sulfides and how thiophene, a probe HDS
tially thermoneutral and NH dissociation is exothermic species, interacts [32]. Nearly all of these studies have
in the presence of adsorbed atomic oxygen. The favored been performed at the semiempirical level and have
adsorption sites for the NH, intermediate species been aimed at qualitative trends. The recent experi-
change as the value of x changes. Those with a higher mental evidence, which suggests small transition metal
value of x (NH3) prefer lower coordination sites, sulfide particles as active components, as well as the
whereas those with a small value of x prefer higher advances in computational quantum chemistry cited
coordination sites. earlier, have motivated first-principles-based analyses
Due to the relatively weak Cu-N bond, associative of this chemistry. We report on a series of density
nitrogen recombination and desorption is exothermic. functional studies aimed at elucidating the reaction en-
However, the relatively strong Cu-0 interaction leads ergy diagrams for different postulated reaction schemes
to an endothermic recombinative desorption of NO. for thiophene desulfurization over a model Ni$2 clus-
The free surface is regenerated by the recombination ter, and also on a plausible mechanism for C-S bond
of 2(0H),d, to remove H20. Once again, there is a scission [32, 331.
competition between dissociative adsorption (of NH3) The overall catalytic cycle for thiophene HDS in-
and desorption processes (HzO). The large entropic volves a number of different sequential and competing
changes associated with recombinative desorption help elementary steps. To elucidate controlling paths, we
to favor water desorption as the temperature is in- examined a number of different plausible cycles [33].
creased. The change in entropy for the ammonia sur- The two most relevant systems are depicted in Fig. 10.
face dissociation step is quite small and not likely to The first is considered to dominate at very low surface
enhance the dissociation energetics. This step is there- coverages whereby thiophene adsorbs in a parallel-like
fore likely to be rate-limiting. The selectivity for the arrangement on the surface. DFT calculations indi-
formation of N2 versus NO is determined by their rel- cated that the q4 mode for the adsorption of thiophene
ative rates for recombination as well as their proba- is more favorable than the completely parallel qs mode.
bility of finding the corresponding ensemble of ad- The cycle involves the adsorption of thiophene which
sorbed surface atoms. Higher surface coverages of is highly exothermic, the coadsorption of hydrogen,
oxygen preferentially favor the formation of NO. Se- hydrogenation to form the stable 2,5-dihydrothiophene
lectivity is, therefore, expected to be a strong function intermediate, scission of the C-S bonds to form buta-
of surface coverage. One predicts an increase in nitro- diene which desorbs from the surface, subsequent
gen production with increasing conversion. In the Ost- hydrogenation, and the associative removal of H2S to
wald ammonia oxidation process, a Pt-Rh alloy in the regenerate the starting Ni& cluster. Inspection of the
form of a thin gauze is used to carry out this reaction. reaction energy diagram (Fig. 11) indicates that both
These metals have a stronger interactions with NZ than the adsorption of thiophene and the hydrogenation of
 5.2 Microkinetics 1001

thiophene are highly exothermic processes which are

likely to occur quite readily. The C-S bond scission
and associative removal of H2S (sulfur removal), how-
ever, are highly endothermic processes and likely to be
rate-limiting steps in the overall cycle. This is consistent
with experimental evidence which has cited both
of these steps as rate-limiting candidates at different
operating conditions [29, 341.
From the single-crystal studies of Gellman and
Somorjai [35] there appears to be a change in the
favored adsorption site and possible surface recontruc-
tion as the sulfur coverage is increased beyond 0 > 0.67
of a monolayer of coverage.
DFT calculations predict a similar change in surface
structure as the sulfur coverage in increased. Threefold
bound sulfur species move to twofold positions in an

ji
effort to lower repulsive interactions.
Figure 10 depicts thiophene as y' adsorbed. This is
+ Butadiene(g) to be compared with y4 adsorption when no hydrogen
is coadsorbed. Coadsorption of hydrogen atoms also
weakens the interaction energy in the thiophene by
almost 6kJmolp1. Wiegand and Friend [36] find a
7 7
similar change in the binding and energetics when
going from a clean Ni surface to one saturated with
sulfur. The binding mode of 2,5-dihydrothiophene is
t also through the I?' mode at higher surface coverages.
Both the C-S bond scission and the sulfur removal
steps are again highly endothermic. Which of these
steps controls the reaction kinetics is highly dependent
upon the operating conditions.
In both situations there is strong competitive ad-
Figure 10. Catalytic hydrodesulfurization cycle via q' adsorbed sorption between H2, HIS, thiophene, and DHT. This
thiophere and dehydrothiophere intermediates. illustrates the complexity of hydrodesulfurization cat-
alysis. Strong inhibition effects due to vacancy sup-
pression of reactant or product molecules also exist due
the inhibition for the dissociation of DHT. Although
0
the metal-sulfur bond ultimately appears to control
both of these situations, the optimum metal-sulfur
-62
bond strength is actually highly dependent upon the
-40
reaction conditions and the operative surface coverage.
- This is consistent with the ideas brought forth by both
z
h
3
Chiannelli and Harris [29] which indicate the optimal
i
5 : -74 metal-sulfur bond strength is an intermediate M-S
-80
E 3:
-
bond, and Nmskov et al. [34] who describe the optimal
metal-sulfur bond as the weakest M-S bond.
6 ;F'
'U

-I

-120
\ -81 /+70
5.2.4.5 Reactivity of Oxidic Surfaces
-160
A Reactivity of Coordinatively Unsaturated Oxide
Surfaces
Electrostatically neutral oxidic surfaces expose both
-200 cation as well as oxygen atom anion sites. Whereas in
Reaction Path the bulk the formal charge on oxygen can often be
Figure 11 The reaction energy diagram corresponding to Fig.
I0 [33]. References see page 1004
1002 5 Elementary Steps and Mechanisms

considered to be equal to -2, this is not the case on a to a bridging oxygen centre. The carbenium ion inter-
metal or metal oxide surface. The decreased Madelung mediate formed from the organic molecule which is
energy on the surface makes charge transfer between initially complexed with the cation converts to a o-
cation and anion on the surface less favorable. This can bonded state with another bridging oxygen. This leads
give rise to reactive 0- sites, or in the case of the ad- to a surface alkoxy intermediate, quite analogous to
sorption of 0 2 , 0; anions which are active in non- the o-bonded carbenium ion intermediates found in
selective combustion paths for reacting hydrocarbons zeolites (as is discussed in the next section). In the
[37]. Dehydrated surfaces have both Lewis acid cat- reducible oxide case, the bridging oxygen can incor-
ionic sites as well as Lewis base anionic sites. Water will porate into the hydrocarbon. In this elementary step, a
physisorb at low temperatures and readily dissociate on second hydrogen atom needs to be activated. It can
nonpolar surfaces. This occurs on reducible as well as then recombine with an already present OH group on
nonreducible oxides. Protons attach at bridging oxygen the surface to produce H20. The catalytic cycle is
sites and behave as Brsnsted acids, whereas the OH- closed by the dissociative adsorption of oxygen. This
fragments adsorb to the cation sites and behave as does not necessarily occur at the same sites where C-H
Br~nstedbases. This is readily deduced from Pauling's activation or selective oxidation reactions occur.
valency rules [9]. Oxides, such as MgO, when heat
treated can activate H2 via a heterolytic dissociation B Proton Transfer in Zeolites
path at vacancy positions. More reactive oxides, such The zeolitic proton is bound to a lattice oxygen atom
as ZnO, can form hydroxy groups and metal hydrides that bridges two tetrahedrally-coordinated lattice cati-
(ZnH) under mild conditions. This is the analog of the ons each of different valency. The first is the Si4+ ion of
heterolytic chemistry reported in the previous section the framework, while the second is a trivalent cation
for Ni3S3, where H2 heterolytically splits to form both such as A13+ which has substituted and Si4+framework
the metal sulfhydryl and the metal hydride fragments. site. Acidic protons are generated at the cation bridg-
A review of quantum chemical studies applied to the ing surface oxygen sites by the splitting of H20, as
analysis of selectivity of reducible metal oxides has re- discussed in the previous section. These zeolitic protons
cently been reported by Witko [37]. We summarize behave as Brsnsted acids. Quantum chemical calcu-
here the main conclusions which are primarily the re- lations indicate a strong covalency between the hydro-
sult of a series of earlier theoretical studies by the gen and oxygen, with a small dipole moment [40]. The
Witko and Haber groups. Active selective oxide cata- proton charge is estimated as xO.1e.u. The highly
lysts, such as Moo3 and V205, contain reducible cati- acidic nature of the proton becomes apparent when it is
ons which have close to octahedral coordination. Five disturbed by an adsorbed basic molecule. Due to the
oxygen atoms are shared with other cations while the repulsive interaction between the lone-pair nitrogen
sixth oxygen is end-on coordinated. This oxygen atom atom and the OH electrons, the OH electrons polarize
often acts as a spectator, a nonreactive oxygen atom, away with a significant increase in the proton charge.
because of its strong triple M=O bond character. It The zeolitic proton remains attached to the framework
helps to promote the reactivity of the bridging oxygen oxygen, as indicated by the short 0 - H distance, and
sites. Calculations [38] show that the negative charge of forms hydrogen-bonding interactions with the acetoni-
the end-on 0 atom is significantly larger than that for trile. The interaction energies of the base-proton pair
the more reactive bridging oxygen atoms. In many se- follow the protonation values of their counterpart gas-
lective oxidation routes, the bridging oxygen is thought phase species.
to be more readily inserted into the reacting organic The low dielectric content of a zeolite implies a high
molecule. This is then subsequently followed by a facile energy cost for charge separation. Reaction paths for
rearrangement of coordination polyhedra resulting in proton activation with reactant molecules are con-
the formation of shear planes [39]. This is the analog of trolled by the need for minimum charge separation of
the surface reconstruction effects observed for many of the lattice basic oxygen and the protonated inter-
the transition metal surfaces when atoms or fragments mediates [40]. We illustrate this by using methanol
adsorb strongly at higher concentrations. This is also adsorption and activation as a motivating example.
analogous to the cluster reconstruction effects dis- Infrared spectroscopy and DFT quantum chemical
played by the metal sulfide clusters when sulfur was analyses demonstrate that CH30H is hydrogen bonded
either added or removed, as discussed in Section to a zeolitic proton in the coordination geometry de-
5.2.4.4. picted in Fig. 12. The zeolitic proton is coordinated to
Activation of the adsorbate C-H bonds associated the oxygen atom of methanol while the proton asso-
with alkanes is proposed to occur by an oxidative ciate with the OH bond of methanol is coordinated the
addition of the hydrocarbon to a reducible cation neighboring Lewis base oxygen atom that bridges the
site. The hydrogen atom becomes bound as a proton A1 and Si. Hydrogen-deuterium exchange between
 5.2 Microkinetics 1003

---T
A

B
t
A

/
1
h

oe
A1 Si C
*
0

Figure 12. Methanol dehydration: (A) groundstate adsorption mode (end-on); (B) transition state for transition A-C; ( C ) intermediate
adsorbed state (side-on); (D) Transition state for dehydration; (E) Product state of methoxy and physisorbed HzO [41].

protonated zeolite and the deuterated methanol occurs TS"

very rapidly, because of the low energy of the sym-
fi\
iI \
metrical transition state corresponding to protonated
methanol, which is only a few kilojoules per mole

\
higher in energy than the ground state structure.
Methanol can also undergo a dehydration path to
form water and the CHT carbenium ion. This reaction, Cluster+
. -.

however, is highly activated. The DFT computed bar-

~

CH,OH ~
+H,O
Methoxide
rier is ~ 2 1 kJmol-'
2 (Fig. 13). The corresponding .......

transition state, structure D in Fig. 12, is very different

from the structure found for the hydrogen-deuterium
exchange reaction. What is similar, is that the zeolitic
proton is directed towards the methanol oxygen. The complex
structure of the activated CH; species is planar and / complex
"side-on
remarkably similar to that of the free CHT species. The "

positive charge that develops on the bound CH: spe-

cies is stabilized by electrostatic interactions between
the carbon atom and a Lewis basic oxygen. In the final 7
... ............
state (structure E), the CH: ion becomes covalently adsorption
com pIex
bound to the bridging oxygen and forms an adsorbed "end-on''
methoxy species. It is important to distinguish the sta-
ble o-bonded ground states of carbenium ions and the Figure 13. The reaction energy diagram corresponding to Fig.
excited carbenium transition states. The protonation of 12
ethylene [42], for example, proceeds in three distinct
steps. In the first, ethylene interacts with the proton to
form a weakly n-bonded intermediate. The ethylene is
then protonated and proceeds through a transition References see page 1004
1004 5 Elementary Steps and Mechanisms

state where the Lewis basic oxygen stabilizes the pos- Acknowledgments
itive charge that develops on the nonprotonated carbon
atom. In the third and final step, the formed ethyl MN wishes to acknowledge Dr. George W. Coulston
fragment and the lattice oxygen atom combine to form and Dr. David A. Dixon from DuPont Central Re-
a stable ethoxylate intermediate. search and Development for their helpful discussions.
The identification of carbenium ions with activated
transition states also helps to elucidate the nature of
free carbonium ion intermediates. Carbonium ions are References
protonated saturated hydrocarbon intermediates which
can carry out a host of different chemistries [4]. Such 1. R. Schlogl, Angew. Chem., Int. Ed. Engl. 1993, 32, 3, 381.
ions have been identified in the gas phase by mass 2. G. Ertl, Angew. Chem., Int. Ed. Engl. 1990,29, 1219.
spectrometry. In the zeolite, however, they are to be 3. (a) D. W. Goodman, Surf Sci. 1994, 299/300, 237; (b) S. H.
Oh, G. B. Fisher, J. E. Carpenter, D. W. Goodman, J. Catal
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imately 1250 kJ mol-' , whereas the protonation energy 5 . (a) J. K. Nerrskov, Rep. Prog. Phys. 1990, 53, 1253; (b) G. A.
of a hydrocarbon is only a few hundred kJmol-'. Somorjai, M. van Hove, Prog. Surf: Sci. 1991, 30, 201; (c) D.
A. King, Surf Sci. 1994, 299/300, 698; (d) T. Gritsch, D.
Carbonium ion formation only becomes possible be- Coulman, R. J. Behm, G. Ertl, Phys. Rev. Lett. 1989, 63,
cause of the stabilizing electrostatic interaction between 1086.
protonated alkane and negatively charged zeolite 6. H. Brune, J. Wintterlin, R. J. Behm, G. Ertl, Phys. Rev. Lett.
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7. (a) G. te Velde, E. J. Baerends, Phys. Rev. B 1991, 44, 7888;
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1992, 69, 1971.
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11. M. A. van Daelen, Y. S. Li, J. M. Newsam, R. A. van
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face site atoms that is needed to provide the reaction 13. (a) G. Ertl, Solid State and Material Science, CRC Press,
path of lowest energy. Another important feature is the Boca Raton, 1982, 349; (b) G. Ertl, in Catalytic Ammonia
strong influence of coadsorbates, not only the adsorp- Synthesis, Fundamentals and Practice, (Ed.: J. R. Jendings),
tion energies, but also on the relative geometries of the Plenum Press, 1991.
14. M. R. A. Blomberg, P. E. M. Siegbahn, J. Am. Chem. SOC.
adsorbed molecules, with important consequences for 1993, 115, 6908.
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The use of reaction energy diagrams enables the 16. (a) H. Burghgraef, A. P. J. Jansen, R. A. van Santen,
illustration of the kinetically competitive behavior of J. Chem. Phys. 1993, 98, 8810; (b) H. Burghgraef, A. P. J.
Jansen, R. A. van Santen, Chem. Phys. 1993, 177, 407; (c)
surface reactions versus desorption. Due to the large H. Burghgraef, Ph. D. thesis, University of Eindhoven, 1995.
change in entropy, desorption reactions become fast at 17. (a) P. E. M. Siegbahn, U. Wahlgren, E. Shustorovich Metal-
high temperatures, whereas surface reactions tend to Suvface Reaction Energetics: Theory and Appli-cations to
become rate-limiting. At low temperatures desorption Heterogeneous Catalysis, Chemisorp t ion, and Surface D f-
can become rate-limiting. fusion, VCH, New York, 1991; (b) P. E. M. Siegbahn, M. R.
A. Blomberg, M. Svensson, J. Am. Chem. Soc. 1993, 115,
Theory can be used to compute reaction energy dia- 4191; (c) M. R. A. Blomberg, P. E. M. Siegbahn, J. E.
grams for proposed mechanisms of catalytic reaction Backvall, J. Am. Chem. SOC.1987, 109, 4450; (d) M. R. A.
cycles. Blomberg, P. E. M. Siegbahn, M. Svensson, J. Phys. Chem.
Computational techniques are approaching the sta- 1994, 98, 2063; (e) M. R. A. Blomberg, P. E. M. Siegbahn,
M. Svensson, J. Phys. Chem. 1992, 96, 5783; (f) P. E. M.
tus of experimentalists tools. Extensions of current Siegbahn, Theor. Chim. Acta 1994, 87, 277; (g) M. R. A.
capabilities to systems of increasing complexity is Blomberg, P. E. M. Siegbahn, U. Nagashima, J. Wenner-
highly desirable. berg, J. Am. Chem. SOC.1991, 113, 424; (h) J. E. Backvall,
 5.2 Microkinetics 1005

E. E. Bjorkman, L. Pettersson, P. Siegbahn, A. Strich, J. Am. 36. B. C. Wiegand, C. M. Friend, Chem. Rev. 1992,92,491-504.
Chem. SOC.1985,107, 7408; (i) P. E. M. Siegbahn, I. Panas, 37. M. Witko, J. Mol. Catal. 1991, 70, 277.
Surf: Sci. 1990,240, 37. 38. J. N. Allison, W. A. Goddard ACS Symp. Ser. 1985,279,23.
18. E. Sanchez Marcos, A. P. J. Jansen, R. A. van Santen, Chem. 39. A. Bielanski, J. Haber, Catal. Rev.-Sci. Eng. 1992, 19, 1 .
Phys. Lett. 1994, 167, 399. 40. R. A. van Santen, G. J. Kramer, Chem. Rev., in press.
19. (a) M. W. Roberts, J. Mol. Catal. 1993, 74, 11; (b) B. Afsin, 41. S. Blazkowski, R. A. van Santen, J. Phys. Chem., in press.
P. R . Davies, A. Pashusky, M. W. Roberts, D. Vincent, Surf: 42. V. B. Kazansky, I. W. Senchenya, J. Catal. 1989, 119, 108.
Sci. 1993, 284, 109; (c) A. Boronin, A. Pashusky, M. W.
Roberts, Cat. Lett. 1992, 16, 345; (d) B. Afsin, P. R . Davies,
A. Pahuski, M. W. Roberts, Surf: Sci. Lett. 1991, 259, L724;
(e) B. Afsin, P. R . Davies, A. Pashuski, M. W. Roberts,
D. Vincent, Surf: Sci. 1994, 284, 109.
20. T. S. Amorelli, A. F. Carley, M. K. Rajumon, M. W. Rob- 5.2.5 Isotopic Labeling and Kinetic Isotope
erts, P. B. Wells, Surf: Sci. 1994, 315, L990.
21. M. Neurock, R. A. van Santen, W. Biemolt, A. P. J. Jansen, Effects
J. Am. Chem. SOC.1994, 116, 6860.
22. R. A. van Santen, J. P. E. Kuipers, Ado. Catal. 1987, 35, K. TAMARU
AND S . NAITO
265.
23. R. A. van Santen, A. de Koster, T. Koerts, Catal. Lett. 1990,
7, 1.
24. S. T. Ceyer, J. D. Beckerle, M. B. Lee, S. L. Tang, Q. Y. 5.2.5.1 Introduction
Yang, M. A. Hines, J. Vac. Sci. Techn. 1987, A5, 501; M. B.
Lee, Q. Y. Yang, S . L. Tang, S. T. Ceyer, J. Chem. Phys. Isotopes are defined as elements having the same
1986,85, 1693.
25. M. C. Wu, D. W. Goodman, J. Am. Chem. SOC.1994, 116, atomic number but different atomic weight, and are
1364; M. C. Wu, D. W. Goodman, G. W. Zajac, Catal. Lett. divided into two categories: radioactive and stable iso-
1994,24, 23; M. C. Wu, P. Lenz-Slomm, P. W. Goodman, J. topes. Since their chemical properties are practically
Vac. Sci. Techn. 1994, A12, 2205. identical, it is possible to label particular molecules by
26. G. Ertl, S. B. Lee, M. Weiss, Surf: Sci. 1982, 114, 515. isotopes and follow them through a sequence of chem-
27. (a) D. J. Coulman, J. Wintterlin, R. J. Behm, G. Ertl, Phys.
Rev. Lett. 1990, 64, 5432; (b) F. Jensen, F. Besenbacher, E. ical or physical changes. This method is known as the
Laegaards, I. Steensgaard, Phys. Rev. B 1990, 41, 10233; (c) isotope tracer technique. It is applied in many research
F. Jensen, F. Besenbacher, E. Laegaards, I. Stensgaard, Surf: fields, such as chemistry, physics, biology, and medical
Sci. Lett. 1991, 259, L774; (d) F. Jensen, F. Besenbacher, I. science. In early research, a great variety of radioactive
Stensgaard 1992, 2691270, 400.
28. H. Topsoe, B. S . Clausen, Catal. Rev.-Sci. Eng. 1984,26,395- isotopes were applied in tracer experiments because
420; N. Topose, H. Topsoe, J. Catal. 1993, 139, 641-651. of the facility of tracing them with a Geiger counter.
29. (a) R. R. Chianelli, Catal. Rev.-Sci. Eng. 1984, 26, 361-393; Recent development of high-resolution mass spectro-
(b) S. Harris, R. R. Chianelli, Chem. Phys. Lett. 1983, 101, meters has enabled the application of stable isotopes
603-605; (c) S. Harris, R. R. Chianelli, J. Catul. 1984, 86, in tracer experiments, which are much more easy to
400-412; (d) S. Harris, R. R. Chianelli, J. Catul. 1986, 98,
17-31. handle than radioactive isotopes.
30. (a) S. P. A. Louwers, R. Prins, J. Catal. 1992, 133, 94. In the study of chemical reaction kinetics, isotope-
31. (a) V. H. J. de Beer, J. C. Duchet, R. Prins, J. Catal. 1981, labeled reactants are frequently employed to follow a
72, 369; (b) J. C. Duchet, E. M. van Oers, V. H. J. de Beer, reaction pathway and to determine the reaction mech-
R. Prins, J. Catal. 1983, 80, 386; (c) J. P. R. Vissers, J. P. R.,
C. K. Groot, E. M. van Oers, V. H. J. de Beer, R. Prins, Bull. anism. By applying this technique, it is possible to
SOC.Chim. Belg. 1984, 93, 813; (d) Vissers, J. P. R., V. H. J. identify the position of bond scission in chemical re-
de Beer, and R. Prins, J. Chem. SOC.,Faraday Trans. I 1987, actions. Polanyi and Szabo [l] have employed ‘*O-
83, 2145; (e) W. J. J. Welters, G. Vorbeck, Zandbergen, J. W. labeled water to determine the position of bond scis-
de Haan, V. H. J. de Beer, R . A. van Santen, J. Cutal. 1994, sion in the hydrolysis of esters as follows:
150, 155; (f) T. I. Koranyi, L. J. M. van de Ven, W. J. J.
Welters, J. W. de Haan, V. H. J. de Beer, R. A. van Santen,
Cat. Lett. 1993, 17, 105-116.
RCOO-R’ + HO*-H + RCOOH HO*R’+
32. (a) A. B. Anderson, J. J. Maloney, J. Yu, J. Catal. 1988, 112, RCO-OR’ + H-O*H -+ RCOO*H + HOR’
392-400; (b) A. B. Anderson, J. Yu, J. Catal. 1989,119, 135-
145; (c) R. P. Diez, A. H. Jubert, J. Mol. Catal. 1992, 73,65- Only ‘*O-labeled carboxylic acids were obtained and
76; (d) M. C. Zonnevylle, R. Hoffmann, S. Harris, SurJ no ‘*Owas detected in alcohols, clearly indicating that
Sci. 1988, 199, 320; (e) F. Rouette, N. Valencia, R. Sanchez- the reaction takes place through the second reaction
Delgado, J. Am. Chem. SOC.1989, 111, 40-46; (f) J. Ro-
driguez, Surf: Sci. 1992,278, 326-338. path.
33. M. Neurock, R. A. van Santen, J. Am. Chem. SOC.1994,116, It is known that the isotopic mass of an atom in the
4427. reactant molecule has an influence on the reaction rate
34. J. K. Nsrskov, B. S . Clausen, H. Topsoe, Catal. Lett. 1992, as well as on the reaction equilibrium. The change in
13, 1-8.
35. A. J. Gellman, M. E. Bussell, G. A. Somorjai, J. Cutul. 1987,
107, 103. References see page 1012
1006 5 Elementary Steps and Mechanisms

reaction rate with the substitution of an isotope is

called the kinetic isotope effect and is distinguished
from changes of equilibrium constants, called equilib-
rium isotope effects. It is possible to design isotope-
labeling experiments to test a postulated mechanism in
which a particular bond is broken in the transition
state. If such bond breaking is involved in the rate de-
termining step, the ratio of the rate constants between
light and heavy isotopes would become large.
In the first part of this article, several examples of
isotope-labeling experiments will be described, which
have provided some important conclusions in under-
standing the mechanisms of heterogeneous catalysis.
In the second part, the theoretical background of the
T i m e (min.)
kinetic isotope effect is discussed and some examples of
relevant research are described, which successfully elu- +
Figure 1. "CO H2 reaction on I3C-preadsrobed Ni film at
cidated the postulated reaction mechanisms. A more 523K: 0 I3CH4; 0 I2CH4; 0 I2CO2 (from Ref. 2).
thorough review of this field is also available [2].

directly to methane, Araki and Ponec [3] employed

5.2.5.2 Isotope Labeling in Heterogeneous Catalytic carbon-13 isotopes as a tracer. First of all, 13C0 was
Reactions admitted at 573K to a clean Ni film and the dis-
proportionation
Modern techniques for surface analysis, such as elec-
tron spectroscopies, have enabled investigation of the 2 I 3 c o -+ 13c(a) + l3 C O ~
structure and electronic state of surfaces under reaction
conditions. Adsorbed species during the reaction can took place to form surface carbon-13. After evacuation
also be observed by various surface techniques such of the system at 573 K to remove adsorbed 13C0 from
as high resolution electron energy loss spectroscopy the surface, "CO and H2 were introduced onto the
(HREELS) and infrared reflection absorption spectro- surface at 523K. As shown in Fig. 1, the first prod-
scopy (IR-RAS). However, the adsorbed species which uct appearing from this mixture was 13CH4, and the
exist on the surface during the reaction are not always formation of "CH4 and l2CO2 was accompanied by
the reaction intermediates. Sometimes, stable adsorbed an induction period. These facts demonstrate clearly
species present on the surface during the reaction are that surface carbon is used for methanation rather
byproducts, which have no relationship with the re- than CO from the gas phase, and that surface carbon
action pathway. The isotope tracer technique is a use- does not recombine easily with 0 into CO and COz
ful method with which to investigate whether the molecules.
observed surface species is the reaction intermediate To clarify the role of adsorbed CO for higher hy-
or not. One of the adsorbed species is labeled by an drocarbon formation, Biloen et al. [4] carried out sim-
isotope atom (D, 13C, "N, l8O, etc.) and its rate of ilar experiments over silica-supported Ni, Co, and Ru
disappearance is followed by some kind of surface catalysts. Surface carbon-13 was deposited on the sur-
spectroscopy. At the same time, its rate of appearance face of these catalysts via the disproportionation re-
in the product molecule is followed by mass spectro- action of I3CO. Subsequent exposure of these catalysts
scopy. When both rates are identical, it can be con- to I2CO and H2 led to the abundant formation of
cluded that the observed adsorbed species is the reac- 13CH4 and of hydrocarbons containing several 13C
tion intermediate. atoms within one molecule. These results indicate that
oxygen-free species CH, (x = 0 to 3) are possible in-
A Hydrogenation of Carbon Monoxide termediates in methanation and that they are capable
Because of the need to develop effective catalysts for of being incorporated into growing hydrocarbon
the conversion of synthesis gas (CO-H2) to liquid fuels chains.
(Section B.3.6), a great many studies have been carried The detailed mechanism of this surface carbon in-
out on the mechanism of the Fischer-Tropsch reaction. corporation process over Ru/SiO2 was investigated by
During the hydrogenation of CO over Group VIII applying the isotope tracer technique as well as infra-
metal catalysts, infrared spectroscopy demonstrates red spectroscopy during the reaction [5, 61. During the
that most of the surface is covered by adsorbed CO. CO-H2 reaction, the accumulation of long straight-
To investigate whether or not the adsorbed CO goes chain hydrocarbons on the Ru surface was demon-
 5.2 Microkinetics 1007

0
1
60
Time
I20
(min.)
I80 ' 1.

Figure 2. I3C content in each hydrocarbon product having dif-

ferent carbon numbers during l2 C 0 + H2 reaction at 423 K after
the accumulation of 13Csurface hydrocarbon x C I ; 0 C2-C3; 0
c 4 - C ~ ;A C S- C ~ ;0 c4Cc (from Ref. 4). Figure 3. Carbon isotope distribution in products during
"CO + H2 reaction at 393 K over a Rh/SiOz catalyst after
I3CO+ H2 reaction at 392 K (from Ref. 8).

strated by infrared spectroscopy. In order to investigate

the role of these accumulated hydrocarbons in the to completely dissociate to adsorbed C and 0 atoms
overall reaction, carbon-13 labeling experiments were which then recombine statistically to produce ethanol.
carried out. After the accumulation of I3C surface hy- To explain these results, they proposed the mechanism
drocarbon species from I3CO-H2 reaction at 423 K, of CO insertion into an adsorbed carbene followed by
I2CO was introduced and the molecularly adsorbed isotopic scrambling in the adsorbed intermediate.
CO was replaced by l 2 C 0 at room temperature. Then The mechanism of acetaldehyde and ethanol for-
a H2-I2CO reaction was carried out at 423 K and the mation from CO + H2 below atmospheric pressure has
I3C content in the hydrocarbon products was analyzed been investigated by combining infrared spectroscopic
with time. As shown in Fig. 2, 13C content in the re- measurements and 13C0 and C'*O isotopic tracer
action products was reduced with time, but could be studies with reaction kinetics [9]. The rate of acetalde-
extrapolated to 100% at the initial stage of the reaction. hyde and ethanol formation are markedly dependent
Moreover, the I3C content in each of the hydrocarbon on the nature of the metal precursors employed. The
products having different carbon numbers did not addition of sodium cations depresses the total catalytic
exhibit any difference, suggesting that all the hydro- activity, while the selectivity for acetaldehyde increases
carbon products are formed from common building considerably. In order to study the mechanistic rele-
blocks and no l2C0 insertion is involved in the chain vance between acetaldehyde and hydrocarbon forma-
growth. The role of the accumulated hydrocarbon spe- tion, isotopic tracer experiments were carried out as
cies in the overall reaction was shown to be a reser- follows:
voir of carbon atoms which may be supplied as CI
species through the scission of their carbon-carbon (i) the 13CO-H2 reaction was carried out at 393K
bonds. over freshly reduced Ru/SiO2, and I3C surface
Another set of key products in CO+H2 reactions species (hydrocarbon and acetate species) were
are oxygenated compounds such as methanol and accumulated on the catalyst;
ethanol. The reaction intermediates of these reactions (ii) the catalyst was cooled to room temperature and
were also investigated applying the isotope-labeling a sufficient amount of I2CO was introduced to re-
technique. Takeuchi and Katzer [7, 81 have studied the place the molecularly adsorbed 13CO;
mechanism of methanol and ethanol formation from (iii) a 12CO-H2 mixture was introduced and the cata-
CO + H2 over Rh/Ti02 catalysts. When the hydro- lyst was heated to 393 K as rapidly as possible;
genation of an equimolar amount of 13C160 and (iv) the 13C distribution in the products was analyzed
12C1s0was carried out, the isotopic distribution in the with time.
produced methanol was 13CH3160Hand 12CH3NOH,
indicating that methanol synthesis occurs by a non-
As shown in Fig. 3, the 13C distribution in the methyl
dissociative mechanism. On the other hand, the iso-
group of the acetaldehyde exhibited almost the same
topic distribution in the produced ethanol was com-
behavior as for the hydrocarbons and was extrapolated
pletely different from that of methanol and fits the
isotopic composition predicted for a fully dissociative
model. In this model all CO molecules are assumed References see page 1012
1008 5 Elementary Steps and Mechanisms

group, indicating the initial removal of a hydrogen

atom from the methyl group to form an ally1 inter-
mediate which subsequently reacts at either end with
equal probability. Confirmation and extension of this
mechanism was obtained by Adams and Jennings [ 141
employing deuterium-labeled propenes. The same iso-
topic ratios were obtained in the deuterated acrolein
products from 1-propene-ld and l-propene-3d, again
indicating the symmetric allylic intermediates.
Keulks [15] used 1 8 0 2 in an attempt to determine
the mode of oxygen atom incorporation into oxygen-
Time (min.) containing products formed in the catalytic oxidation
of propene on bismuth molybdate catalysts. Before
Figure 4. Gas phase composition for the reaction of propene studying the oxidation of propene with " 0 2 , the iso-
with ' * 0 2 over bismuth molybdate at 698 K (from Ref. 9). topic exchange process of the oxygen atoms of the bis-
muth molybdate with gaseous oxygen (lSO2) was
checked. No exchange in the gas phase composition
to the isotopic purity (90%) of the 13C0 used at the was noted at the temperature range of propene oxi-
initial stage of the reaction. On the other hand, the 13C dation. On the contrary, when propene oxidation was
distribution in the formyl group of acetaldehyde dif- carried out with 1 8 0 2 , the main products were
fered markedly from those of hydrocarbons, and de- C3H4160 and Cl6O2, and "0-containing products
creased rapidly to the natural abundance of 13C(1.1%). were only 2-2.5% as shown in the gas phase. These
This indicates that during the steady state CO+H2 results strongly suggest that not only the oxide ions
reaction, there exist common C1 intermediates through in the top layer but also oxide ions in the subsurface
which hydrocarbons and the methyl group of ace- layers may participate in the reaction. Moreover, the
taldehyde are formed, and acetaldehyde is formed via diffusion of oxide ions between the surface and the bulk
CO insertion into these C1 intermediates. must be rapid, and gaseous oxygen, once adsorbed,
must be able to undergo this diffusion into the bulk.
B Oxidation of Propene Wragg et al. [16] have confirmed this conclusion by
The catalytic oxidation of hydrocarbons has been in- using "0-enriched bismuth molybdate catalysts.
vestigated extensively because of its practical impor-
tance in the chemical industry. In particular. oxidation C Propene-Deuterium Addition and Exchange
(Section B.4.6.2) and ammoxidation (Section B.4.6.6) Reaction
of propene to acrolein and acrylonitrile, respectively, is The catalytic exchange of hydrocarbons with deute-
the most thoroughly studied catalytic system from the rium is one of the oldest and most extensively studied
viewpoint of processes catalytic compositions, kinetics, reactions in the isotopic tracer experiments. The inves-
and mechanisms over various oxide catalysts such as tigation of these processes provides valuable informa-
Cu20 and bismuth molybdate (Fig. 4). tion on the adsorbed state of hydrocarbons and the
In the early stages of these studies, radioactive 14C mechanism of C-H and C-C bond activation on the
propene was employed as a tracer. Isaen and co-work- catalytic surfaces, which have been reviewed by Kem-
ers [lo, 111 showed that carbon dioxide was formed ball [17].
from both propene and acrolein, and that an organic Since microwave spectroscopy has extremely high
film was formed on the catalyst during reaction, which resolution and high sensitivity, it can be applied to
appeared to be constructed from the outermost meth- analyze the composition of the mixture of isotopic
ylene carbon in propene. Radioactive tracers are isomers, which are formed during isotope-labeling
sometimes powerful for the investigation of surface experiments. For example, in the case of the propene-
layers, which are not so easy to detect by certain sur- deuterium exchange reaction, four isomers of propene-
face spectroscopic techniques [ 121. Isotopic-labeling dl and seven isomers of propene-d2 can be analyzed
experiments using I3C, deuterium, and l S 0 , have re- quantitatively at the same time by this technique [ 181.
vealed the reaction pathway, the structure of the re- Fig. 5 summarizes the possible reaction intermediates
action intermediates, the rate determining step, and the of the propene-deuterium exchange reaction leading to
source of oxygen in the acrolein product. Voge et al. the isotopic distribution of propene-dl isomers as in-
[13] employed propene, 13C-labelled in the methyl dicated. Sometimes it is difficult to distinguish the re-
group, in the oxidation over cuprous oxide and exam- action intermediates only from the isotopic distribution
ined the isotopes in the produced acrolein. Half of the patterns, especially when more than two intermediates
13C in the acrolein product was found in the carbonyl are operating at the same time. Accordingly, separate
 5.2 Microkinetics 1009

( i ) A s s o c i a t i v e mechanism
1- marized in Table 1. When these metals were alloyed
with copper, the distribution patterns became similar to
each other and resembled that over Cu, whereas the
/ reaction rates were more than two orders of magni-
H,C - CH +
I tudes larger than that of Cu and the activation energies
*I I , r
were still close to those of the individual metals. From
S, S, CHD-CH-CH,
(C-&i-l-d,) these results, the following model for active sites was
CH, -CH-CH,
(3-4)
D proposed to elucidate the role of the copper component
s, s, s, in alloy catalysts. The surface composition (70-80% Cu
( i i ) D i s s o c i a t i v e mechanism in all the alloys employed) indicates a surface where the
H,C= CH
Group VIII metals are isolated atomically from each
other and surrounded by copper atoms. In this sit-
uation, copper metal clusters or mixed clusters of Cu-
Group VIII metals become the active sites, which
implies the important role of electronic interaction
between surface copper and Group VIII metal in alloy
t t t I catalysts.
CHD-CH-CH, CH2-CD-CH3 CH,-CH-CH,D CH,-CH-CH,D The activity and selectivity of the catalytic reaction
( 1 -4) (Z-d,) (3-4) (3-d,l
( i i i ) I n t r a m o l e c u l a r hydrogen s h i f t
over supported metal catalysts greatly depend on the
particle size of the metal as well as on the nature of the
4
CHD-CH-CH,( 1 -d,] CHz-CD-CH,(2-d,)
t support materials. Morphological changes of the metal
with particle sizes and its electronic interaction with
the support may be the main factors governing these
I I I I phenomena,
1 1 Such effects for supported metal oxide catalysts have
CH,D-CH=CH,(3-d,) CH,D-CH-CH, ( 3 -d,l been investigated in the cases of C#L-D2 and C3H6-
Figure 5. Reaction pathway and reaction intermediates of pro- C3D6 reactions over the catalysts with various particle
pene-deuterium addition and exchange reaction. sizes of ZnO, TiO2, and ZrOl dispersed on Si02 [23-
251.
Over unsupported metal oxide catalysts, deuterium
kinetic investigations of C3H6-D2 and C3H6-C3D6 addition and exchange took place through different re-
reactions may be helpful to distinguish whether the action pathways. The addition process to form propane
exchange proceeds through associative or dissociative proceed via the associative mechanism of propyl inter-
mechanisms [191. Although some difficulties exist, this mediates, whose reverse reaction to form propene-dl
technique is powerful in studying the structural change was prohibited. Independently, hydrogen exchange of
of active sites, such as surface composition of alloy propene proceeded through a 71-ally1 intermediate over
catalysts or particle size effects of supported oxide ZnO and through carbenium ion intermediates over
catalysts. Ti02 and ZrO2. By dispersing the oxides on silica, the
In the case of alloy catalysts consisting of active rate of C3H6-D2 reaction increased considerably with
Group VIII metals and inactive Group IB metals, the decrease of activation energy. Accompanied with
alloying has been considered to reduce the number of the deuterium addition process to form propane, the
atoms in active metal ensemble that are necessary for hydrogen exchange process began to take place
a certain type of adsorption or product formation through common 1-propyl and 2-propyl intermediates.
(Section A.5.3.3). On the other hand, changes in the Lower loading catalysts of ZnO and Ti02 exhibited
electronic structure (ligand effect) due to alloying are much higher activities predominantly through 1-propyl
not very pronounced in these systems. The propene- intermediates with smaller activation energies. From
deuterium exchange reaction mentioned above was X-ray photoelectron (XPS) and X-ray absorption fine
applied with Ni, Pd, Pt, and their alloys with Cu, to structure (EXAFS) spectroscopies, it was suggested
investigate the role of copper in the modification of that small oxide particles were trapped between silica
active sites and reaction mechanisms of Group VIII support particles and particular active sites were pro-
metals [20-221. duced on them. In the case of ZrOz/SiOz, XPS analysis
Over Group VIII metals deuterium addition and ex- suggests the formation of a Zr02 monolayer over silica,
change proceeded via common reaction intermediates, which exhibits completely different catalytic behavior
namely 1-propyl and 2-propyl adsorbed species. Their as compared to larger unsupported ZrO2 oxide particles.
relative activities as well as activation energies were
considerably different on each metal catalyst, as sum- References see page 1012
1010 5 Elementary Steps and Mechanisms

Table 1. Isotope distribution in monodeuteriopropene formed during c3H6-D~ reaction over various catalysts (P(D2) = 4 kPa,
P(C3H6) = 2 kPa).

Catalyst Reaction ECX, Ehyd. Mean Da cis-1-dl tr~ns-1

-dl 2-dl 3-dl
temp. (K) (kJmoI-‘) (kJmol-’) content (%) (%I (“4 (“w
(4)
Ni 200 41 39 0.03 2 3 95 0
0.24 3 3 94 0
Pd 210 34 33 0.03 35 33 16 16
0.10 28 28 14 30
0.19 23 22 14 41
Pt 235 45 43 0.01 9 57 28 6
0.05 16 48 28 8
0.10 20 42 28 10
Ni-Cu 180 35 33 0.03 11 12 77 0
0.14 11 11 78 0
Pd-Cu 225 36 35 0.02 20 17 58 5
0.20 20 18 57 5
Pt-Cu 248 44 43 0.01 13 9 68 10
0.09 12 10 67 11
cu 263 - - 0.01 14 14 72 0
0.05 13 14 73 0
6
aQ = 1/600 C i x dl (mean deuterium content in propene molecule).
i= 1

5.2.5.3 Kinetic Isotope Effect

A theoretical evaluation of the kinetic isotope effect

requires precise knowledge of the potential energy sur-
face of the reaction, which is quite difficult to obtain in
ordinary chemical reactions. Accordingly, the ratios of
reaction rates of reactions involving different isotopes (2)
is used for the evaluation of the kinetic isotope effect. where M , I,, Iy,I, and vi represent the molecular
Bigeleisen and Wolfsberg [26] developed the following weight of reactant A, the moment of inertia of the ro-
theoretical derivations, utilizing the activated complex tation, and vibrational frequencies. The superscript T
formulation. represents the activated complex. If we assume that a
Consider two sets of reactions with different isotope- particular bond j , which contains an isotope, is broken
labeled reactants A, B, . . . , through activated com- by the reaction, the vibrational partition functions of
plexes X1 and X2 to form products L, M, . . . the A molecule and activated complex will cancel each
other out except for the vibrational mode vj. Con-
sequently, the activation energy may be expressed from
the zero point energy of this vibrational mode as
A2+B2+ . . . +X: +L2+M2+...

The ratio of the rate constants kl/k2 can be expressed

as in eq 1, using partition functions of the reactants In the case of molecules which contain C-H and C-D
QA,, Q B ~.,. . and of the activated complexes Q,’ and bonds, the zero point energy of a C-H vibration is
Q,’ 3 about 5 kJ mol-’ larger than that of a C-D vibration.
Since there is no difference in the electronic state of
- - xi Q: Q A ~Q B ~. . .
ki -
(1) isotopic isomers, the same potential energy curves can
k2 x2.Q: QA, QB, . .. be applied to them. Such potential energy curves in the
where ic1 and x2 represent the transmission coefficients. initial and activated states of the reaction are drawn in
When only the A molecule is substituted with isotope the same figure. Figure 6(a) shows the case when a
atoms, partition functions for the rest of the reactants C-H or C-D bond is broken completely in the acti-
can be canceled out, and eq 2 is derived by separating vated state, where the difference of the zero point en-
the partition function of A into translational, rota- ergies between C-H and C-D is zero. As a result, the
tional, and vibrational components activation energy as well as the reaction rate for the
 5.2 Microkinetics 101 1

Eg(bond broken)

EH ' ED EH ED EH ' ED
Figure 6 . Potential energy diagram of vibrational modes in the reaction of molecules having C-H or C-D bonds: (a) complete breaking
of C-H and C-D bonds in the activated state; (b) no change of the C-H and C-D bonds in the activated state; (c) strengthening of
C-H and C-D bonds in the activated state. & ( E D ) = activation energy of the reaction involving C-H(C-D) bond. Eo(C-H),
Eo(C-D) =zero point energy level of C-H and C-D bonds

molecule with C-H bond becomes larger than those NH3(a). The rate-determining step of these processes
for the molecule with C-D bond. On the other hand, depends on the kind of catalyst, partial pressures of
Fig. 6(b) shows the case that C-H or C-D bonds do H2 and N2, and the reaction temperatures. Isotope-
not change when the activated complex is formed. The labeling experiments with I5N and D were carried out
difference of the zero point energies between C-H and in various catalytic systems to determine the rate
C-D vibrations in the activated state is the same as determining step and reaction intermediates.
that in the initial state (5.0 kJ mol-I). Accordingly, Ozaki et al. [28] compared the ammonia formation
there is no difference in the activation energies and the rates in N2-H2 and N2-D2 reactions and found an in-
reaction rate between these two reactions. In some cases, verse isotope effect over a doubly promoted catalyst,
C-H and C-D bonds in activated complexes are stron- where deuterium reacted three or four times faster than
ger than those in the initial states, and the difference of hydrogen. This large inverse isotope effect has been
the zero point energies becomes larger than those of the explained by the difference in adsorption of ammonia
initial state. In such cases, the activation energy as well and deuteroammonia to form the imino radical as an
as the reaction rate for the molecule with a C-D bond adsorbed species which retards the reaction rate. Aika
is larger than that with a C-H bond, as shown in Fig. and Ozaki [29] have shown a similar inverse isotope
6(c). This is called an inverse isotope effect. effect in ammonia synthesis over an unpromoted iron
catalyst. This effect was also explained by the difference
A Ammonia Synthesis in the equilibrium concentration of adsorbed species
Ammonia synthesis (Section B.2.4) is one of the oldest that retards the rate of the nitrogen dissociation, i.e. the
and most important catalytic reactions ever inves- rate determining step. The main mechanistic difference
tigated. A number of substances show considerable ac- between promoted and unpromoted catalysts is the
tivity as ammonia synthesis catalysts. Fe, Ru, Os, and most abundant adsorbed species during the reaction.
Re and nitrides of Mo, W, and U are the best known. Over promoted catalysts, NH(a) is the main adsorbed
Among them, iron, doubly promoted by A1203 and species, whereas this is N(a) over unpromoted catalysts.
K20, is the most important catalyst in industrial use. It has been reported that the rate of ammonia for-
The role of these promoters has been investigated mation over transition metals is markedly enhanced by
extensively be Strogin et al. [27] using single-crystal addition of alkali metal cations. Since the most difficult
model catalysts. step for ammonia synthesis is accepted to be the dis-
It is generally accepted that ammonia synthesis from sociation of nitrogen molecules, this enhancement is
HZ and N2 proceeds through dissociative adsorption of also expected in the isotopic exchange of nitrogen which
hydrogen and nitrogen followed by the subsequent
stepwise hydrogenation of N(a) to NH(a), NHZ(a), and References see page 1012
1012 5 Elementary Steps and Mechanisms

References
1. M. Polanyi, A. L. Szabo, Trans. Faraday SOC. 1934,30, 508.
2. A. Ozaki, K. Akia, Isotopic Studies of Heterogeneous Cutal-
ysis, Academic Press, Kodansha, 1976.
3. M. Araki, V. Ponec, J. Catal. 1976, 44, 439.
4. P. Biloen, J. N. Helle, W. M. H. Sachtler, J. Catal. 1979, 58,
95.
5. Y. Kobori, H. Yamasaki, S. Naito, T. Onishi, K. Tamaru, J.
Chem. SOC., Faraday Trans. I , 1982, 78, 1473.
6. H. Yamasaki, Y. Kobori, S. Naito, T. Onishi, and K. Tam-
aru, J. Chem. Soc., Faraday Trans. I , 1981, 77, 2913.
7. A. Takeuchi, J. R. Katzer, J . Phys. Chem. 1981,85, 937.
8. A. Takeuchi and J. R. Katzer, J. Phys. Chem. 1982,86,2438.
9. H. Orita, S. Naito, and K. Tamaru, J. Catal. 1984, 90, 183.
2.1 2.2 2.3 2.4 10. 0. V. Isaev, L. Ya Margolis, I. S. Sozanova, Dokl. Akud.
I 1T (X lo3 K) Nauk. S S S R 1959,129, 141.
Figure 7. Temperature dependence of the rates of methane and 11. 0. A. Golovina, 0. V. Isaev, M. M. Sakharov, Dokl. Akad.
CZ hydrocarbon formation in the reactions of CO-H2 and CO-Dz Nauk. S S S R 1962, 142.
over Ru/SiO2: A methane and A CZ+hydrocarbons in CO-H2; 0 12. G. F. Berndt, Catalysis, Royal Society of Chemistry, 1983,
methane and 0 C24 hydrocarbons in CO-Dz (from Ref. 27). p. 144.
13. H. H. Voge, C. D. Wagner, D. P. Stevenson, J. Catal. 1964,
3, 549.
14. C. R. Adams, T. J. Jennings, J. Catal., 1963, 2, 58.
requires the dissociation. Morikawa and Ozaki [30] 15. G. W. Keulks, J Catal. 1970, 19, 232.
found that the isotopic exchange over an unpromoted 16. B. D. Wragg, P. G. Ashmore, J. A. Hockey, J. Catul. 1971,
22,49.
iron catalyst is much slower than the ammonia forma- 17. C. Kemball, Ado. Catal. 1967, 17, 223.
tion rate, which is not enhanced by the presence of H2. 18. T. Kondo, S. Saito, and K. Tamaru, J. Am. Chem. SOC. 1974,
On the other hand, over doubly promoted catalysts, 96, 6857.
the exchange rate became comparable to the ammo- 19. S. Naito, M. Tanimoto, J. Catal. 1986, 102, 377.
20. S. Naito, M. Tanimoto, J. Chem. SOC.,Chem. Cornm. 1987,
nia formation rate and was accelerated by the presence 363.
of H2. 21. S. Naito, M. Tanimoto, J. Catal. 1989, 119, 300.
22. S. Naito, M. Tanimoto, Chem. Letts. 1988, 411.
23. S. Naito, M. Tanimoto, Chem. Letts. 1990, 2145.
B Hydrogenation of Carbon Monoxide 24. S. Naito, M. Tanimoto, M. Soma, Y. Udagawa, Stud. Surf:
The effects of using D2 rather than H2 during CO hy- Sic. Cutal. 1993, 75, 2043.
drogenation were investigated using alumina-supported 25. S. Naito, M. Tanimoto, M. Soma, J. Chem. SOC.,Chem.
Comm. 1992, 1443.
Ru catalysts [3 11. For the alumina-supported catalysts, 26. J . Bigeleisen, M. Wolfsberg, Adu. in Chem. Phys. 1958, I , 15.
the rate of CD4 formation was 1.4-1.6 times faster 27. D. R. Strogin, S. R. Bare, G. A. Somorjai, J. Catal. 1987,
than the formation of CH4. Noticeable isotope effects 103, 289.
have also been observed during the synthesis of C2-Cll 28. A. Ozaki, S. H. Taylor, M. Boudart, Proc. Roya/ SOC.
alkenes and alkanes. For c 2 - C ~hydrocarbons, the syn- (London) 1960,258, 47.
29. K. Aika, A. Ozaki, J. Cutal. 1969, 13, 232.
thesis occurs more rapidly in the presence of D2 rather 30. Y. Morikawa, A. Ozaki, J. Catal. 1968, 12, 145.
than H2, but the magnitude of the inverse isotope 31. C. S. Kellner, A. T. Bell, J. Catal. 1981, 67, 175.
effect declines towards unity with increasing numbers 32. Y. Kobori, S. Naito, T. Onishi, K. Tamaru, J. Chem. SOC.,
of carbon atoms in the product. The observed inverse Chem. Comm. 1981, 92.
kinetic isotope effect can be rationalized by the results
of a combination of the kinetic and equilibrium isotope
effects associated with individual elementary steps.
The Hz and D2 kinetic isotope effect was measured 5.2.6 Transient Catalytic Studies
on silica-supported R u catalysts not only for the hy- K. TAMARU
drogenation of CO but also for the hydrogenation of
deposited carbon formed by the disproportionation
of CO [32]. Figure 7 shows the inverse kinetic isotope 5.2.6.1 Importance of In Situ Transient studies
effects in both cases (kH/kD = 0.57 for methane and
0.43 for higher hydrocarbons), which led to the con- In chemical reactions, generally speaking, if the rate
clusion that the rate-determining step was the hydro- (rate equation, rate constant, and activation energy) of
genation of carbon formed by dissociative adsorption each of the elementary steps which make up the overall
of CO. The inverse effect can be interpreted in terms of reaction is known, the kinetic behavior of the overall
a higher surface concentration of CD, than of CH, reaction may be understood. In the reaction between
because of the thermodynamic stability of CD,. hydrogen and bromine, for instance, the kinetic be-
 5.2 Microkinetics 1013

havior of the overall reaction is rather complicated as in the ambient phase, but also the heats of chem-
follows: isorption of those species and also reaction inter-
mediates and spectator species. Even more important is
that the catalytic reaction proceeds through a certain
However, if all the elementary reactions in the over- number of elementary steps or reaction intermediates,
all reaction are known, the kinetic behavior of the and the chemical potentials of these intermediates
overall reaction may be explained on the basis of the depend upon which of the steps is rate determining.
rate constants, activation energies of the forward and Consequently, by estimating the chemical potentials of
backward reactions of the following elementary steps: the intermediates during the reaction, the rate deter-
mining step may be identified. One of the best-known
Br2 = 2Br examples of this kind is the case of ammonia decom-
Br+H2=HBr+H positionon on an iron surface. Since the rate of de-
sorption of chemisorbed nitrogen is rate determining in
H+Br2=HBr+Br
this reaction, the chemical potential of chemisorbed
In the case of such gaseous reactions the rate constants nitrogen, or the virtual pressure of nitrogen which
and activation energies of each of the elementary steps would be in adsorption equilibrium with the chem-
are independent of the concentration of reactants, re- isorbed nitrogen in the working state, may become very
action products and reaction intermediates. This ap- high during the course of the reaction, and iron nitride
proximately also holds for reactions in solution. is easily formed in the catalyst surface by decomposing
In the case of heterogeneous catalytic reactions, the ammonia on iron surface. This is because the chem-
properties of the medium (catalyst surface) where those isorbed nitrogen during the course of reaction is not in
reactions take place depend upon the concentrations of equilibrium with the ambient nitrogen gas, but is equi-
reactants, reaction intermediates, and reaction prod- librated with the ambient ammonia and hydrogen:
ucts and, in some cases, spectator species that do not
participate in the reaction path but which are chem-
isorbed on the catalyst surface. This is because the Consequently, the iron catalyst surface during the re-
properties of metal surfaces, such as work function and action may be surface iron nitride, which is quite dif-
heat of chemisorption, are markedly susceptible to the ferent from a clean iron surface.
amounts and kinds of coadsorbed species. In many The properties of catalyst surface, consequently, are
cases surface restructuring may happen along with the determined not only by the concentration of the re-
adsorption, which results in marked changes in the re- actants and products in the ambient phase, but also by
activity of the surface. Consequently, even if the sur- the mechanism of the reaction, or by the location of the
face is well-defined at the beginning, being examined rate determining step of the overall reaction. It is, ac-
by various spectroscopic techniques, it can be markedly cordingly, concluded that the kinetic behavior of each
different under the reaction conditions. In the case of of the elementary steps in heterogeneous catalytic re-
oxide catalysts, for instance, the extent of oxidation of actions is influenced by the reaction itself through the
the catalyst surface during the redox reaction is also properties of the catalyst surfaces, which is again de-
influenced by the relative ratio of the rates of reduction termined by the concentration of the adsorbed species
and oxidation. This results in prominent changes in the during the course of the reaction.
properties of catalyst surfaces depending upon the rel- Under these circumstances the rate and activation
ative concentration of the reactants and reaction tem- energy of the elementary reaction in heterogeneous
perature. The fugacity of oxygen over an oxide is one of catalysis should be measured under the reaction con-
its inherent thermodynamic properties and its change ditions, since the surface which works as a catalyst is
definitely influences the properties of the oxide itself, or that under the reaction conditions. In many cases the
its catalytic activity. In the case of acid catalysts the rate of desorption of a chemisorbed gas is estimated by
acidity of the working catalyst surface, which should be temperature programmed desorption, using the gas and
associated with the catalytic activity, is that under the the adsorbent under vacuum. The reactivity of chem-
reaction conditions and not that under the conditions isorbed species is similarly estimated by temperature
far from those prevailing in the actual reaction. programmed reaction. The rate of desorption and the
In the case of heterogeneous catalysis the rate con- reaetivity of the chemisorbed species thus estimated are
stants, activation energies and, sometimes the kinetic not necessarily the same as those under the reaction
equation as well, of elementary (or simpler) steps which conditions-under the reaction conditions many other
consist of the overall reaction will change, depending chemisorbed species are present to various extents on
upon the concentrations of the chemisorbed species on the catalyst surface which modify the properties of the
the catalyst surfaces. The concentrations of the chem-
isorbed species on the catalyst surfaces, depend not
only upon the concentrations of reactants and products References see page 1023
1014 5 Elementarv Stem and Mechanisms

catalyst surfaces. In some cases, if all the simpler pro- action. In addition to observations of the chemisorbed
cesses which make up the overall reaction are studied species under the reaction conditions, in situ dynamic
separately, as functions of surface coverages of all the or transient approachs should be employed to identify
possible adsorbed species and partial pressures of re- the real reaction intermediates, for instance by isotopic
actants and reaction products, the kinetic structure of methods [3]. Since the isotope has the same chemical
the overall reaction can be elucidated. properties as the nonlabeled species, a change in the
Adsorption during the course of reaction may be es- concentration from the nonlabeled to the labeled spe-
timated by direct measurements in a closed circulating cies will not perturb the chemical environment or the
system with a comparatively large amount of catalyst. total surface concentration of adsorbed species during
Such volumetric measurements only provide the total the reaction. Such a replacement will propagate to the
amount of each of the compounds, and do not identify successive reaction intermediates, finally reaching the
the chemisorbed species [l]. Gas chromatography may reaction products. By following this behavior the re-
also be employed by using a microcatalytic reactor, or action path may be followed and the rate of each of the
by putting the catalyst in a separatory column, and by elementary steps may be estimated. This information
using the flowing reactants (or an inert gas) as the car- should be compared to the rate of the overall reaction
rier gas [2]. Direct studies of adsorbed species during measured separately. This approach was first proposed
the course of reaction by spectroscopic techniques, in 1964 [3], and these basic principles of studying cata-
such as IR and EXAFS gives more information on the lytic reactions under reaction conditions are described
adsorbed species [3]. in other publications [l, 41.
When a catalytic reaction is a zero-order reaction
with respect to the reactant, the active sites in the cat-
alyst surface are saturated with such species as re- 5.2.6.2 Experimental Method
actants or reaction intermediates, the adsorption being
independent of the ambient gas pressure. The kinetic As an example of the experimental techniques for the
behavior does not tell what species are occupying the in situ transient approach, the apparatus of Chuang
active sites, but adsorption measurements may yield and coworkers is shown in Fig. 1 [5]. The infrared cell
the amount of pressure-independent adsorption and employed in the apparatus is shown in Fig. 2 [6]. It has
its composition. This provides important information four stainless steel flanges, gas inlet and outlet, and two
on the number of active sites and the kind of the spe- step CaF2 windows. It is used at temperatures up to
cies which saturate them. Spectroscopic measurements 533K and under a pressure of 60atm. The step win-
of pressure-independent adsorbed species during the dows minimize the reactor volume and reduce the op-
course of reaction may provide additional information tical path length for the gaseous species in the reactor.
about the saturating species. The catalyst is pressed into a self-supporting disk and
In 1992 the book Catalysis Looks to the Future was then placed in the IR cell, and subsequently treated
published by the National Academy Press, Wash- prior to the reaction studies. By means of the inlet
ington, prepared by the panel on New Directions in system shown in Fig. 1 one of the reactants can be
Catalytic Science and Technology, Board on Chemical switched to its labeled species in the steady state of the
Sciences and Technology, National Research Council, reaction, total reactant flow being maintained constant
from which the following quote is taken: throughout the experiment. The change in the isotope
content in the chemisorbed species after the switch is
It is desirable to focus on areas in which the extensive
monitored by in situ IR spectrometry and the effluent
scientific and technological resources of academe and
composition is examined continuously by a mass spec-
industry may lead to the fastest practical results. In
trometer, including its isotope abundance. The com-
order of priority, these areas are: 1. in situ studies of
position of the reaction products is also determined
catalytic reactions; 2. characterization of catalytic sites
with time by a gas chromatograph. In this way the
at atomic resolution (metals, oxides). . .
structure of the adsorbed species, the reaction path,
It is certainly important to study catalyst surface and also the rate of each of the elementary steps on the
under the reaction conditions, especially by spectro- catalyst surface under the reaction conditions may be
scopic methods, but even if some chemisorbed species estimated.
are observed during the course of the reaction, it does Additional information which may be obtained from
not mean that it is a reaction intermediate through the in situ transient approach is to estimate the chem-
which the overall reaction proceeds. It may be just oc- ical potentials of the reaction intermediates during the
cupying the active sites as a spectator, even retarding course of the reaction. In the steady state of chemical
the rate of the overall reaction. It is, accordingly, not reactions the chemical potentials of the reaction inter-
sufficient to study the catalyst surface in the working mediates prior to the rate determining step may be
state to elucidate the mechanism of the overall re- approximately equal to that of the reactants, in many
 5.2 Microkinetics 1015

Valve for
Balancing
Pressure
*COIAr

l2 co

C 2H4

Figure 1. Combined in situ IR and mass spectrometry system.

CaF2 reactants or products was added and its retention time

Flange Fluid in O-ring window Nut measured to estimate the value of A x l A p on the work-
\
ing catalyst, where Ax is the increase of its adsorption,
when its pressure was increased by Ap. If the sample
gas is fully saturated on the catalyst surface during
the reaction, no additional adsorption takes place
( A x / A p = 0).
Various applications of this technique may be
readily proposed. In the simplest case, if the reacting
gas used as the carrier is switched to an inert gas in the
steady state, the adsorbed species on the working cata-
Fluid out lyst will be desorbed with time. In this case, instead of
inert gas, one of the reacting gases may be employed to
Side view Front view
study the reaction between the adsorbed species and
Figure 2. High-pressure cell for in situ IR studies. the reacting gas under the reaction conditions.
Gas chromatography is a convenient way of study-
ing both the amount and the kinetic behavior of each
cases, being in partial equilibrium. For instance, for of the adsorbed species on the working catalyst. Vari-
ammonia decomposition on iron catalyst, the chem- ous types of reactors may be used, such as fixed-bed
isorbed nitrogen is in partial equilibrium with the am- reactors, well-stirred or backmixed reactors, and single
bient ammonia and hydrogen. Consequently, by meas- pellet reactors. In this way transient response data may
uring adsorption during the course of the catalytic be obtained, which can contribute significantly to the
reaction, the chemical potentials of reaction inter- chemical engineering aspects of reactor design and
mediates may be estimated, which gives important in- catalyst development [2]. However, such overall ad-
formation with which to identify the rate determining sorption kinetic data will not necessarily elucidate the
step of the overall reaction. mechanism of the catalytic reaction at an atomic or
In some cases, transient response can be monitored. molecular level.
Under reaction conditions, the chemical potential (or
the pressure) of one of the reactants or the products
may be suddenly changed (or even reduced to zero) 5.2.6.3 Kinetics of Adsorption and Desorption
and the subsequent changes in the chemical potentials
(or concentrations) of the reaction intemediates may be In Langmuir adsorption isotherm theory, the adsorp-
followed. In this manner the rate of simpler steps in the tion isotherm may be derived by equating the rates of
overall reaction may be estimated [3, 71. adsorption and desorption. The rate of desorption, is
Gas chromatographic or pulse techniques can be assumed to be proportional to the amount of chem-
used to study kinetic behavior of adsorbed species isorbed species, and the rate constant is independent
under reaction conditions, as proposed by Tamaru in of coverage. The rate constant of desorption may be
1959 [2]. Using the reacting gas as a carrier gas and in
the steady state of the reaction, a pulse of one of the References see page 1023
1016 5 Elementary Steps and Mechanisms

adsorption of labeled species and desorption of non-

labeled species, as shown in Fig. 3 [9]. In this manner
the absolute rates of adsorption as well as desorption
can be estimated in the presence of the adsorbing gas.
In the case of desorption of hydrogen chemisorbed
on transition metals, the rate was independent of the
ambient gas pressures, as generally accepted. It is of
interest, however, that the rate of desorption of carbon
monoxide on various transition metals is a function

1
0 I
I not only of its coverage, but also of the pressure of the
I
I adsorbing gas-a feature known as adsorption-assisted
1.0 desorption. The rates of adsorption (Ta) and desorption
Total CO
0
(Yd) of carbon monoxide on transitiion metals can be
P expressed by the following equations and, accordingly,
the adsorption isotherm could be obtained:
0.5
ra = k a P / [ 1 + K d / ( 1 - O)]
Yd = kde( 1 + BP")
0 where K and n are constants which are approximately
0 60 120 180 0.2 and 0.8, respectively, and ka and kd are rate con-
Timelsec
stants [lo]. The rate of adsorption is expressed by the
Figure 3. CO, C 1 * 0and total CO coverage during adsorption well-known Kisliuk mechanism [ 1 11. Lombard0 and
and desorption measurements on Pd at 380 K. Bell reported that the rate of adsorption-assisted de-
sorption may be explained by taking repulsive inter-
action among adsorbing species into consideration [121.
dependent on its coverage in many cases and various Kawai and coworkers recently studied the process of
empirical rate equations have been proposed, such as dynamic equilibrium between the gaseous and adsorbed
Frumkin's equation [8]. However, in all cases the rate CO by means of time-resolved infrared reflection ab-
of desorption was considered to be only dependent on sorption spectroscopy using l2CI6O and 13C'80[13].
the coverage and independent of ambient gas pressure. Their results are given in Table 1. It was accordingly
This is why the rate of desorption is usually measured demonstrated that the potential well of the preadsorbed
by temperature programmed desorption under vacuum. CO sites became shallow due to local repulsive inter-
In this technique a gas is chemisorbed at lower tem- action between the preadsorbed CO and the incident
peratures and the temperature is raised under vacuum CO molecules from the gas phase, the rate of desorp-
to observe the desorption. tion consequently being enhanced, as shown in Fig. 4.
Very few experiments have been carried out to mea- It is generally accepted that the molecular beam of CO
sure the rate of desorption while adsorption is taking scatters isotropically, which suggests comparatively
place, or in the presence of adsorbing gas in the am- long residence times for CO molecules as precursors
bient phase. The rate of desorption can be measured by before they scatter. Those long lived precursor species
the transient method, by replacing the adsorbing gas may assist the desorption of preadsorbed CO molecules
by its labeled species and subsequently measuring the due to dynamic repulsive interaction.

Table 1. The rates of the desorption process under equilibrium with gas phase CO, the cross-section for the flux-induced desorption and
the desorption rates into vacuum. The desorption rates into vacuum are calculated from a preexponential factor 1.6 x lOI4 s-' and a de-
sorption energy of 127 kJmol-I.

Temperature (K) +
kl ($)Fa1 ki 01
Rate of the desorption Rate of the desorption Cross-section of the
under the equilibrium into vacuum (SKI) flux-induced desorption
with gas phase CO (Cm2)
(s-')
368 2.9 10-3 1.5 x 3.5 x 10-15
380 4.7 10-3 5.6 x 10-4 5.1 x 10-15
392 7.1 10-3 1.9 x 10-3 6.6 x
400 9.4 x 10-3 4.1 10-3 6.6 x
 5.2 Microkinetics 1017

--+0
15

Desorption
-i
t
v

C
.-
Surface parallel 3 lo
C !i
P
.
c

$ 5
W
Temporal and local shallowing
a
2
r
L

a
Ic
o Incident CO $!

Adsorbed CO / 0 1 2 3
Time (h)
4 5

Figure 5. Decomposition of surface formate prepared from

I3C0 and D2 reaction over Crz03 at 573 K for 1 h: ( 0 ) amount of
Potential energy surface
D13CO0 under evacuation at 533K; (c) amount of DI3COO
during circulation of "CD3OD at 533 K; ( i ) amount of D ' * C 0 0
during circulation of "CD30D at 533 K.
Figure 4. Interaction of incident CO and preadsorbed CO

is not a reaction intermediate (Fig. 5). However, in the

5.2.6.4 Catalysis presence of methanol in the ambient gas, the surface
formate becomes very reactive to form readily the re-
In the case of desorption, the bond between the chem- action products, as shown isotopically [15]. In the
isorbed molecules and the surface is broken, whereas presence of alcohol, the infrared absorption spectra of
in catalysis the bond within the chemisorbed species chemisorbed formate shifts to suggest weakening of
is broken or synthesized. Since adsorption-assisted de- C-H bond (Table 2).
sorption was observed, the reactivity of chemisorbed The decomposition of ethanol proceeds readily on
species may be influenced by the presence of ambient an N b monomer catalyst on SiOz with high selectivity
gas. to dehydrogenation [16]. This reaction was studied by
means of EXAFS and IR techniques. When ethanol
A Catalytic Decomposition of Alcohol was introduced onto the catalyst, dissociative adsorp-
In the case of methanol decomposition on chromia, as tion takes place to form an ethyl radical and a proton
in the case of zinc oxide [14], the reaction proceeds via on the catalyst. In the presence of ethanol in the gas
formation of methoxide and then formate ion on the phase, dehydrogenation takes place. If, during the
catalyst surface prior to the reaction products [15]. The course of the reaction, the ethanol is removed from the
formate ion thus formed is stable at reaction temper- gas phase, the reaction stops, although chemisorbed
atures under vacuum, which may suggest that formate species remained on the catalyst surface, unchanged

Table 2. IR absorption bands for formate ions on Cr203.

Assignment Wavenumber (cm-')

CD30D decompositions DCOOD adsorption

DCOO DCOO DCOO DCOO

only +CD30D only +CD30D
~~

C-D stretching 2184 2160 2182 21 50

0 - C - 0 antisymmetric stretching 1548 1573 1548 1573
0-C-0 symmetric stretching 1329 1337 1331 1337

References see page 1023

1018 5 Elementary Steps and Mechanisms

400 500 600 700 800

Temperature/K

Figure 7. Temperature programmed desorption spectra from

adsorbed ethanol on Nb/SiOl.
Reaction timelmin

Figure 6. Dehydrogenation of C2H50H on Nb/SiOz: (0)H2; (A) H

00 0,
CH3CHO.
Nb/.H, CHI
/ *, CH,
? ?
(Fig. 6). If the ethanol is then reintroduced the reaction
continues, at the same rate as before. In this manner
the presence of the reactant promotes the selective de-
hydrogenation reaction.
The ethanol thus chemisorbed was not reactive at
the reaction temperatures, but if it is treated at tem-
peratures considerably higher than the reaction tem- zm%n%% 52TamZm

peratures under vacuum, dehydration decomposition CH,CHO + H, H

takes place to produce C2H4 and (CtH5)2O, as shown O0,O\
0 Nb-H-CH
in Fig. 7. It is of interest that the dehydrogenation re- c,n5 0 ?o C H 3
action proceeds selectively in the presence of ethanol, zTm%mzz
whereas in the absence of ethanol molecules in the gas
Figure 8. Mechanism of the dehydrogenation of ethanol on
phase, the chemisorbed species decomposed to give Nb/SiO2.
dehydration at considerably higher temperatures. The
scheme of the overall reaction is depicted in Fig. 8.
The decomposition of the chemisorbed species is pro- techniques using one of the reactants, this may not give
moted not only by the reactant, but also by the presence its reactivity under the reaction conditions.
of various species in the gas bhase. It is of interest that The mechanism of water-gas shift reaction on MgO
the decomposition of the chemisorbed species is pro- and ZnO was studied by EXAFS and FTIR and the
moted by the presence of various molecules in the am- coadsorbates on the surface species, such as water
bient gas, in particular those with higher donor num- vapor, showed a marked effects on not only the re-
bers (Fig. 9). It is therefore important to note that the activity, but also the selectivity (to dehydrogenation) of
reactivity of chemisorbed species on the catalyst sur- the decomposition of surface formate [ 171.
faces is markedly influenced by the presence of not only
the reactants, but also other molecules. Consequently, B Decomposition of Formic Acid
even if the reactivity of the chemisorbed species on the The decomposition of formic acid on various metal
catalyst surface is studied by temperature programmed surfaces has been widely studied as a typical catalytic
 5.2 Microkinetics 1019

4.0

0.8

Lo
0.7 -._, 3.0

-8 E
+ -E
7

0.6 .
7'
z
9
E 2.0
.-
C
._
._
I0
2
E
I I I I I I I I I i
D
0 20 40 60 80 1.o
Donor number

Figure 9. Rate of initial dehydrogenation decomposition of

chemisorbed species and donor numbers of nucleophilic reagents.

350 1 PtOoIr
0 log v = -0.8
0 log v 10
0
0 05
Coverage OHCOO-
1.o

400
Figure 11. The decomposition rate of formic acid as a function
of its coverage and temperature over Ni/Si02: (-) under 11
torr formic acid vapor: (- -) under vacuum; ( 0 . 5 ) 293 K: (A, .>)
383 K; (m, 1) 373 K.
450

500
In connection with this reaction, Block and Kral re-
g ported that the rate of the reaction on a silver catalyst
t was different for four different isotopic compounds, i.e.
550 the rates of decompositions of HCOOH, HCOOD,
DCOOH and DCOOD are 3.02, 2.24, 1.78, and 0.61
( lop4ml min-'), respectively [19]. If the decomposition
of the surface formates is the rate determining step of
the overall reaction, these four different isotopic species
will give only two different rates.
The rate of the decomposition of surface formate in
the absence or presence of formic acid in the gas phase
was measured, which clearly showed a marked influ-
60 70 80 90 100 I10 ence of the presence of formic acid in the gas phase
AH,(kcal eq-') (Fig. 11) [20]. This appears to be an adsorption-assisted
process, where the decomposition of surface formate is
Figure 10. Catalytic activity of various metals given by the
temperatures to show the same rate and their heats of formation promoted by the presence of formic acid in the gas
of formate salts. phase. It has been demonstrated, as mentioned above,
that the reactivity as well as the selectivity of the de-
composition of chemisorbed formate ion are markedly
reaction. When the catalytic activity of the reaction on
influenced by the presence of water vapor, which plays
various metal surfaces was plotted against the heats of
an important role in not only formic acid decom-
formation of their formates, a volcano-shaped curve
position, but also the water-gas shift reaction, since
was obtained (Fig. 10) [18]. It is therefore concluded
both reactions proceed via formate ion.
that the stability of the surface formates, through
The catalytic decomposition of formic acid on
which the overall reaction proceeds, determines the
TiOz(il0) was also studied in detail and it was con-
catalytic activity: if it is too stable or too unstable, the
cluded that the catalytic dehydrogenation reaction
activity will be slow and, consequently, demonstrates a
maximum activity (or volcano curve) at an optimum
stability of the formate. References see page 1023
1020 5 Elementary Steps and Mechanisms

0 0.4 0.8 1.2 1.6 2.0

Time (min)

Figure 12. Fractional respones F(t ) of gaseous effluent species during isotopic switching from Ar/'2CO/H2/C2H4 to '3CO/H2/CzH4:
C? = steady-state concentration of the species before the switch; C" = steady-state concentration of the species after the switch; CO
chemisorption = 28.5 pmol CO per gram of catalyst.

proceeds in a bimolecular process, requiring surface for- C2H5CH0 to C2H:3CH0 took approximately 1.6min.
mate and a formic acid molecule from the gas phase [21]. The rate of appearance of 13C0 in the gas phase is in
good agreement with the appearance of adsorbed I3CO
C Hydroformylation and Methanation on the catalyst surface. The residence time for the
One recent example of a transient infrared study is intermediates involved in propionaldehyde formation
hydroformylation and methanation over Rh-Ce/SiOz was estimated to be 0.44min; that of linear CO, which
catalyst, [5, 6, 7, 221. In this study the experimental is the precursor for CO insertion, was 0.05 min.
apparatus mentioned above (see Figs 1 and 2 ) was The reaction mechanism for the methanation and
employed. hydroformylation, proposed by Chuang and co-workers
The Rh surface area was measured to be 2 8 . 5 ~ [22], taking the results obtained by Sachtler co-workers
mol g-' by pulse chemisorption at 305 K. The ratio of [23] into consideration, is summarized in Scheme 1
CO : H2 :C2H4 used for hydroformylation was 1 : 5 : 5 where (8) and (a) represent gaseous and adsorbed
(instead of 1 : 1 : 1) to enhance formation of the alde- states, respectively. In the methanation reaction the
hyde. The reaction products were C2H6 as the major adsorbed CO can dissociate and then hydrogenate to
species and C2H5CHO and CH4 as the minor species, produce methane. Propionaldehyde is formed by the
with a turnover frequency (TOF) for propionaldehyde insertion of linearly adsorbed CO into the adsorbed
production of 0.43 min-' at 453 K and 0.1 MPa. The C2HS(a) species which is formed by hydrogenation of
results, given in Fig. 12, were normalized to F(t), which ethylene. The results of this study indicate that the
is the fraction of the final response. The evolution of propionaldehyde may be formed via (i) the insertion of
the I3CO curve is faster than that for C2Ht3CH0. The CO into adsorbed ethyl species to form the acyl inter-
complete switch from "CO to I3CO was achieved at mediate, (ii) hydrogenation of the acyl intermediate to
approximately 0.85 min, whereas the switch from produce adsorbed propionaldehyde, and (iii) desorp-

Hfa) H(a)
CO(g)=CO(a)- CH,(a) -+ CH4(g)

C2H4(g)+ iH2 + CzHs(a) -

\
COW ClHSCO(a) -%C2HsCHO(a) - C2HsCHO(g)

\ H(a)

C2H6(g)
Scheme 1
 5.2 Microkinetics 1021

I I
0

"0 60 120 180

Reaction time (min)

Figure 13. Adsorption measurements during the hydrogenation of butene (1-butene fH2) + D2 over ZnO at 513 K: (): H2 (g); (0)
H(a); (I)D2(g); (m) D(a); (0)
HD(g); ( x ) 1-butene (a); (3) butane (g).

Table 3. Deuterium content in the main products produced by the reaction of C4H6 + H2 + DZ (1 : 1 : 1) over ZnO at 29 "C.

Reaction Conversion 1-Butene Hydrogen H2-D2 exchange"

time (min) ("A)
C4H6 C4Hz C4H7D C4H6D2 H2 HD D2 H2 HD D2

10 6.9 1.oo 0.46 0.08 0.46 0.45 0.07 0.48 0.29 0.40 0.31
20 10.4 1.oo 0.51 0.11 0.38 0.42 0.01 0.48 0.26 0.46 0.27
40 16.9 1.oo 0.48 0.17 0.35 0.31 0.18 0.51 0.25 0.49 0.26
80 27.0 1 .oo 0.46 0.20 0.34 0.33 0.19 0.48
160 45.0 1 .oo 0.44 0.26 0.30 0.34 0.26 0.40

"H2-Dl exchange reaction in the absence of 1,3-butadiene under similar conditions.

tion of adsorbed propionaldehyde, and that step (ii) is known that hydrogen is heterolytically dissociated to
the rate determining step. The steady-state rate mea- chemisorb on ZnO, but the behavior of such chem-
surements show that increasing reaction pressure de- isorbed hydrogen seems to suggest that such dis-
creased the overall activation energy and increased sociatively chemisorbed hydrogen does not participate
both rate and selectivity for propionaldehyde. The in the hydrogenation, the hydrogen to be added com-
coverage of C2H5CO was estimated from TOF and ing from the gas phase.
residence time to be 0.19 min. The hydrogenation of ethylene over ZrO2 was stud-
ied, which showed similar hydrogenation behavior [25].
D Hydrogenation of Alkenes on Oxides In this reaction system various adsorbed species may
Hydrogenation of butadiene and butene was studied be observed by IR techniques, such as OH, Zr-H, n-
over ZnO catalyst, adsorption during the course of the bonded ethylene, end-on ethane, and side-on ethane.
reaction being measured as given in Fig. 13 [24]. The Hydrogen was first chemisorbed on ZrO2 at room
adsorption of butadiene as well as hydrogen stayed temperature and cooled down to 220K and then eth-
unchanged under various pressures of reactants during ylene was introduced step by step as shown in Fig.
the reaction, but the order of the reaction was first 14. The ZrH absorption peak decreased steadily and n-
order with respect to hydrogen and zero order with re- bonded ethylene peak increased, whereas no absorp-
spect butadiene. The products of the reaction between tion spectra due to C2H5(a) and CzHs(a) were detected.
H2, Dz, and butadiene are given in Table 3. The H2- although n-bonded ethylene increased successively
D2 exchange reaction proceeds on the catalyst, but
is markedly retarded by the presence of unsaturated
hydrocarbons. The reaction products clearly indicate This behavior indicates that the dissociatively pre-
that the hydrogen, which is added, has just the same adsorbed hydrogen is not added to the ethylene in-
isotopic composition as that in the ambient gas, which
looks as if it is added in molecular form. It is well References see page 1023
1022 5 Elementarv Stem and Mechanisms

3.0 1

11* . u s

reaction timelmin 0 30 60 90 0 30 60 90 0 30 60 90
ethene pressure / Tom P=O.14 P=0.17 P=0.14

1st reaction 2nd reaction 3rd reaction

Figure 14. Interaction of ZrH(a) and ethene gas.

CH2 DCH2D (g)

techniques [27]. The reaction of adsorbed NO and CO
DZ r \ has been investigated by Chuang and co-workers,
combining in situ infrared and mass spectroscopy on
Rh/SiOz [28].

x-bonded ethene side-on ethane end-on ethane

5.2.6.5 Summary
Figure 15. Reaction mechanism of ethene hydrogenation over
ZrOz. The in situ transient approach is one of the most or-
thodox ways to elucidate the mechanism of heteroge-
neous catalysis. Since catalysis takes place on the active
troduced to form ethane, but is desorbed as molecular catalyst surface, which can differ considerably from the
hydrogen under such conditions. Further important clean catalyst surface, the properties of the surface
evidence for nonreactive Zr-H and OH species was under working conditions should be examined in order
provided by the results from volumetric measurements to understand the real nature of heterogeneous catal-
which showed that ethylene hydrogenation proceeds ysis. In addition, the behavior of each chemisorbed
even at temperatures below 223 K where heterolytic species on each reaction site on the working catalyst
dissociative adsorption of hydrogen does not take surface should be studied istopically under working re-
place. The overall reaction was first order as to hydro- action conditions. In this manner not only the reaction
gen and zero order with respect to ethylene, which path, but also the rate of each component step of the
is quite similar to the case on ZnO catalyst. Various overall reaction may be estimated, and the rate de-
evidence suggests the mechanism of ethylene hydro- termining step may be elucidated. The spectator species
genation reaction on ZrO2 to be as shown in Fig. 15. of the reaction which are chemisorbed on the catalyst
surface, but not participating in the reaction, may also
E Other Catalytic Reactions be identified.
The examples introduced above are some of the typical In many cases of heterogeneous catalysis small
catalytic reactions studied by in situ transient tech- amounts of poisons retard the rate of reaction, and
niques. Similar techniques have been also applied to promotors enhance the rate considerably. In some
various catalytic reactions, and many important results cases the life of the catalyst plays an important role.
have been obtained, demonstrating the effectiveness of especially in industrial catalysts. The nature of such
the approach. Some of the examples are as follows. poisons, promotors, and catalyst life can be inves-
The rate coefficients for elementary processes occurring tigated by the in situ transient approach using isotopes.
during Fischer-Tropsch synthesis over Ru/Ti02 were Any technique which is available for the study the
estimated by Komaya and Bell [26]. The oxidation of catalyst surface under the reaction conditions may be
carbon monoxide on molybdenum trioxide was also used in the in situ transient approach. Techniques such
studied by Iizuka et al. by in situ transient isotopic as IR spectroscopy can be used to follow the behavior
 5.2 Microkinetics 1023

of labeled species. In situ polarized total-reflection 17. T. Shido, K. Asakura, Y. Iwasawa, J. Chem. Soc., Faraday
fluorescence extended X-ray absorption fine structure Trans. I 1989, 85, 441; Y. Iwasawa, Elementary Reaction
spectroscopy can also give new information about the Steps in Heterogeneous Catalysis (Eds: R. W. Joyner, R. A.
van Santen) Kluwer, 1993, 287.
working catalyst surface [29]. Gas chromatographic 18. W. M. H. Sachtler, J. Fahrenfort, Actes du Deusieme Congres
techniques may be widely used to study the kinetic lnternationale de Catalyse, Paris, 1960, 1961, p. 831.
behavior of adsorbed species under the reaction con- 19. J. Block, H. Kral, Z. Elektrochem. 1959, 63, 182.
ditions. Transient methods also provide important 20. K. Takahashi, E. Miyamoto, K. Shoji, K. Tamaru, Catal.
Lett. 1988, 1, 213.
information on catalyst and reactor designs, to assist 21. H. Onishi, T. Aruga, Y. Iwasawa, J. Catal. 1994, 146, 557.
with chemical engineering aspects. 22. S. S. C. Chuang, R. Narayanan, Appl. Catal. 1990, 57, 241;
In many cases of heterogeneous catalysis the inter- G. Srinivas, S . S. C. Chuang, J. Phys. Chem. 1994, 98, 3024.
mediate species on the catalyst surface are too reactive, 23. P. Biloen, W. M. H. Sachtler, Adu. Catal. 1981, 30, 165; W.
and their concentrations become too small to be de- M. H. Sachtler, M. Ichikawa, J. Phys. Chem. 1986, 90, 4752.
24. S . Naito, Y. Shimizu, T. Onishi, K. Tamaru, Bull. Chem.
tected by spectroscopic techniques. It then becomes SOC.Jpn. 1970, 43, 2274; S. Naito, Y. Sakurai, H. Shimizu,
necessary to develop increasingly sensitive techniques T. Onishi, K. Tamaru, Trans. Faraday, SOC.1971,67, 1529.
with higher resolution to detect small amounts of 25. J. Kondo, K. Domen, K. Maruya, T. Onishi, J. Chem. Soc.,
chemisorbed species on different sites of the catalyst Faraday Trans., 1990, 86, 397; 3021; 3665.
26. T. Komaya, A. T. Bell, J. Catal. 1994, 146, 237; B. J. Savat-
surface. The nature of different surface sites, such as sky, A. T. Bell, ACS Symp. Ser. 1982, 178, 105.
steps, kinks and defects, should also be studied in con- 21. Y. Iizuka, Y. Onishi, T. Tamura, T. Hamamura, J. Catal.
nection with surface catalysis. The role of those partic- 1980, 64, 437.
ular sites in catalysis require to be studied in more de- 28. G. Srinivas, S. S. C. Chuang, S. Debnath, J. Catal. 1994, 148,
tail. It is also of fundamental importance to identify the 748.
29. M. Shirai, T. Inoue, H. Onishi, K. Asakura, Y. Iwasawa, J.
real nature of active sites in heterogeneous catalysis. Catal. 1994, 145, 159.
In this respect recent advances in studying the micro-
scopic structure of solid surfaces using scanning tun-
neling microscopy will undoubtably yield more infor-
mation on the nature of active catalytic sites. 5.2.7 Positron Emitters in Catalysis
Research
References G. JONKERS
1. K. Tamaru, Bull. Chem. SOC.Jpn. 1958, 31, 666.
2. K. Tamaru, Nature 1959, 183, 319; J. Happel, Catal. Rev. 5.2.7.1 Introduction
1972. 6,221; H, Kobayashi, M. Kobayashi, Catal. Rev. 1974,
10, 139; C. 0 . Bennett, Catal. Rev. 1976, 13, 121; P. L. Mills,
J. J. Lerou, Reo. Chem. Eng. 1993, 9, 1. Much quantitative information on reaction mecha-
3. K. Tamaru, Ado. Catal. 1964, 15, 65. nisms and kinetics is originating from (ultra) high vac-
4. K. Tamaru in Catalysis: Science and Technology (Eds: J. R. uum technique studies on catalytic (model) systems,
Anderson, M. Boudart), Springer Verlag, Berlin, 1991, Vol.
9, 38.
which may or may not have been pretreated. With re-
5. G. Srinivas, S. S. C. Chuang, M. W. Balakos, AIChE 1993, spect to the acquired data, the question often is raised
39, 530. is whether these are also valid for the actual conditions
6. S. S. C. Chuang, S. I. Pien, J. Catal. 1992, 135, 618. (e.g. high pressure, temperature and hostile environ-
7. M. W. Balakos, S. S. C. Chuang, J. Catal. in press. ment) under which catalysts may operate in commer-
8. A. Slygin, A. Frumkin, Acta Physicochim., U.R.S.S., 1940,
12, 321. cial units. Therefore, there has always been a strong
9. T. Yamada, T. Onishi, K. Tamaru, Surf: Sci. 1983, 133, incentive for analytical techniques, which may provide
533. the quantitative data on reaction mechanisms and
10. T. Yamada, K. Tamaru, Z . f : Physik. Chem., N.F. 1985, 144, kinetics from the catalysts under true operating
195; T. Yamada, Y. Iwasawa, K. Tamaru, Surf: Sci. 1989, conditions.
223, 527.
11. P. J. Kisliuk, J. Phys. Chem. Solids 1957, 3, 95; 1958, 5, 5. To carry out in situ kinetic studies on catalysts sev-
12. S. J. Lombardo, A. T. Bell, Surf: Sci. 1991, 245, 213. eral criteria must be satisfied. First, detection of re-
13. N. Takagi, J. Yoshinobu, M. Kawai, Phys. Reo. Lett. 1994, action and/or interacting molecular species should not
73, 292. perturb the process under investigation. Detection
14. A. Ueno, T. Onishi, K. Tamaru, Trans. Faraday SOC.1971,
67, 3585. should preferably allow both identification of any in-
15. K. Yamashita, S. Naito, K. Tamaru, J. Catal. 1985, 94, termediate reaction species and quantification of the
353. relevant reaction parameters. Second, the kinetic pro-
16. M. Nishimura, K. Asakura, Y. Iwasawa, Proceedings of the
9th International Congress on Catalysis, (Eds: M. J. Phillip,
M. Terna), 1988, 4, 1842. References see page 1032
1024 5 Elementary Steps and Mechanisms

cess being studied should characterize the entire inner techniques which exploit physical characteristics of
and outer surface of a real catalyst system. Finally, isotopes are mass spectroscopy (nuclear mass, sampling
the surface detection technique should be capable of required), FTIR and FTRS (nuclear mass effects),
resolving continuous changes in the surface process. Mossbauer Spectroscopy (nuclear state), NMR (nuclear
However, it should be realized that no single technique spin) and radiotracer techniques (decay of unstable
will be able to provide the ultimate answer to the nucleus). However, in special cases only the latter
questions raised and that the solution should be sought technique can provide quantitative data from in situ
in multidisciplinary studies, taking into account the studies of heterogeneous catalysts.
scope and limitations of detection techniques, and cat- Radiotracer techniques, exploiting radionuclides
alyst preparation and characterization techniques. such as 3H, 14C, 32P, and 35Sas tracers, may provide
quantitative information about reaction mechanisms
Several analytical techniques are potentially capable of and rate limiting steps in reaction kinetics, but no in
generating information about the state of a catalyst situ information from the catalyst surface can be ob-
surface under operating conditions: tained. However, due to the specific radiation charac-
teristics, radionuclides such as "C, 13N, I5O, and '*F
Fourier transform infrared and Raman spectroscopies can be applied to quantitative, in situ studies of heter-
(FTIR, F T R S ) : as the fundamental spectroscopic ogeneous catalysts. The latter radionuclides have had
parameters of adsorbed species are unknown and application in biological and biochemical experiments
many distinct components may be present, even as early as 1936 [3]. The first applications to heteroge-
qualitative evaluation of the recorded spectra will be neous catalysis are more recent [4].
difficult. To date, therefore, the extraction of quanti- This article will briefly describes the radiation prop-
tative information has turned out to be impossible. erties of /?-emitters, the production and synthesis of
Mossbauer (emission) spectroscopy: capable of prob- /?-labeled compounds and the (in situ) detection of
ing the molecular environment of catalytic centres. /?-labels. Four different applications of llC, 13N and/
However, due to the available isotopes this technique or, 150in heterogeneous catalysis are also summarized,
is limited to Fe or Co catalytic centers. as are some developments areas and potential future
Nuclear magnetic resonance ( N M R ) : although the applications.
existence of intermediate species at a catalyst surface
can be demonstrated [l], quantification of these spe-
cies in terms of concentration is not yet possible. 5.2.7.2 Characteristics of /I-Emitters
Positron annihilation spectroscopy ( P A S ): capable of
probing electronic properties of surfaces, of localized Any radioactive decay process, in which the mass
defects - pores, vacancies, shear planes, grain number A remains unchanged but the atomic number
boundaries - and of the solid bulk. Applications of 2 changes, is classified as /?-decay.Unstable nuclei with
this technique to catalysis are fairly new and have superabundant neutrons, such as 14C, emit a fast elec-
been reviewed in Ref. 2. A triad of detection tech- tron or /?--particle, thereby accomplishing a more
niques may provide qualitative information on prob- stable nuclear state, here 14N. Nuclei with insufficient
ing of inner catalytic sites, such as Brernsted acid neutrons, such as "C, may also be unstable and emit a
sites. In PAS the characteristics of positron anni- fast positron (the antimatter particle of an electron) or
hilation, such as positron life-time, momentum and /?+-particle, thereby achieving a more stable nuclear
energy distribution, are utilized for the study of cat- state, here B. The radiation characteristics of relevant
alytic materials. Here, the positrons are originating /?-emitters (2 < 18) which may be applied for hetero-
from a suitable external positron-emitting source. geneous catalysis studies are summarized in Table 1.
Consequently, this technique [2] is fundamentally The SI unit of radioactivity is the becquerel (Bq),
different from the application of positron emitters as which represents the number of nuclear disintegrations
described in this review. per second. Once the molecular mass of the compound,
in which the radionuclide is embedded, and the half-life
If data on reaction mechanisms and kinetics are re- of the radionuclide is known, the number of labeled
quired, isotopic labeling techniques may provide an molecules giving rise to one nuclear disintegration per
efficient means, as this is one of the few methods for second, i.e. the specific activity, can be computed. For
distinguishing two atomic species of the same element 'normal' manageable quantities of radioactivity up to
in the same compound, in a similar chemical form (see about 109Bq (or lGBq), this activity corresponds to
Section A.5.2.5). For hydrocarbon heterogeneous cat- about 1mmol 14C0 or 7 pmol "CO (Table l), empha-
alysis the main elements of interest are isotopes of hy- sizing the sensitivity of "C-labeling experiments. For
drogen, carbon, oxygen, and nitrogen and, to a lesser quantification of the health, safety, and environment
degree, fluorine, phosphorus, and sulfur. Analytical (HSE) effects, the SI unit sievert (Sv), for equivalent
 5.2 Microkinetics 1025

Table 1. Radiation characteristics of relevant p-- and p+-emitters.

Radionuclide Half-life Decay mode Max. Energy Max. linear Max. specific
and yield (MeV) range in A1 activity
("/.) (mm) (Bq mol-I)

1'C 20.4 min p+ >99 0.96 1.4 3.4 x 1020

I3N 9.96 min p+ 100 1.19 1.9 7.0 x lozo
150 2.07 min p+ 99.9 1.72 3.0 3.4 x 1021
';F 110 min p+ 97 0.635 0.9 6.3 x 1019
H 12.4 y p- 100 0.0186 0.002 1.1 x 10'5
'4c 5730 y p- 100 0.155 0.1 2.3 x 10l2
32P 14.3 d p- 100 1.71 3.0 3.4 1017
35s 87.4 d p- 100 0.167 0.1 5.5 x 10'6

and effective does is used. This takes into account the irradiation facility, often a nuclear reactor. The radio-
potential biological damage caused to the human body labeled precursor material from the target has to be
by irradiation or intake of radionuclides. By taking radiochemically purified, after which this precursor
appropriate shielding measures these doses can by kept material has to be converted into the required com-
as low as 1 pSv per pulse experiment (as compared to pound by chemical (micro)synthesis and, optionally,
the world-averaged natural background dose per indi- subsequent chemical purification. As the shortest-lived
vidual of about 2 mSv per annum). of these four radionuclides lives for more than 2 weeks,
The average number of 0-particles emitted per there will be ample time to carry out the synthesis and
nuclear disintegration is given by the P-yield which, to deliver the labeled compound for experiments at a
due to a competing decay process (electron capture), radionuclide laboratory. As the range of P--particles is
may be lower than 100% for P+-particles. P-Particles limited, protection against radiation hazards is easily
are emitted with a continuous energy distribution ex- achieved by shielding the radioactivity with layers of
tending from zero to a maximum value. Coulomb in- perspex.
teractions with the (atomic) electrons of the matter In general, "C, 13N, 150,and lSFare produced by
traversed will limit the maximum range of P-particles deuteron (8 MeV) or proton (16 MeV) bombardment
(Table 1). of suitable target materials, in which the labeled pre-
In cases where 3H, 14C, 32P,or 35S labeling studies cursor molecules will be formed instantaneously. The
are applied to obtain quantitative information, the labeled precursor compound [5] is utilized either for
limited range of p--particles requires sampling of the "direct" conversion into the required chemical com-
outlet gases or liquids from a catalytic bed and sub- pound, or for conversion into other labeled precursor
sequent (destructive) analysis. After a fast P+-particle compounds to be used as a starting compounds for
has been retarded by Coulomb interaction, it will chemical (micr0)synthesis (Table 2). With respect to
associate with a "slow" electron (generally valence the half-life time of the "C, I3N, 150,and 18Fradio-
electrons) thereby converting both the mass of the p+- nuclides, synthesis and purification steps should be fast,
particle and the (valence) electron into electromagnetic and experiments with labeled compounds have to be
radiation. This so-called annihilation process is gov- carried out in the near vicinity of the site where the
erned by the energy ( E = m x c2 where m is the mass of radionuclides were produced. Next to lead shielding
the electron or positron and c is the speed of light (hot cells and dedicated shielding) when handling Pt-
= 511 keV) and the momentum conservation law (two emitters, the synthesis and experimental procedures
y-photons emitted in the opposite direction). The re- should as far as possible be remotely controlled for
leased annihilation radiation is very penetrative and protection against radiation hazards.
can be detected external to catalytic beds and therefore Through the emergence of positron emission com-
makes both in situ and quantitative studies of catalysts puted tomography (PET) during the last decades as
feasible. a medical imaging tool [6] the general reputation of
I1C, 13N, 1 5 0 , and lSFhas become more wide spread.
For medical PET applications dedicated self-shielding
5.2.7.3 Production of Labeled Compounds cyclotrons have been developed to allow medical re-
search and diagnostic studies [7]; however, existing
Though 3H and 14C are continuously generated in the nuclear accelerator facilities at a university or nuclear
outer atmosphere by cosmic radiation, the commercial research institute generally may be used for "C, I3N,
production of 3H, 14C, 32P, or 35S is carried out by
irradiation of suitable target material in a neutron References see page I032
1026 5 Elementary Steps and Mechanisms

Table 2. Precursor molecules available immediately, or with limited synthesis (<t112), after bombardment [ 5] .

p+-emitters Target Precursor Limited synthesis (<tip)

N2/02 (trace) "coz, "co Hzl'CO, "CH31, "CH3Li, C1211C0

NdH2 HWN
H2O 1 3 ~ 03 - , 1 3 ~ 20 - 1 3 ~ 01,3 ~ 0 213
, "0, H I ~ N O ~
CHI 13NH3
various 1500 c I 5 0 , c i 5 0 0 ,~ ~~~~~0
~ ~ 0 ,
'ONe or l80O 1 8 ~H I ~~ F , CH3I8F, cIO3lsF, N0I8F, Xe18FF, (C2H&NS18F
H2I80 18F-

Table 3. Comparison between 14C- and C-labeling for heterogeneous catalyst studies.

Step Radionuclide

14C(tip = 5730 years) "C (tip = 20.4 minutes)

Production of radio- Relatively simple, cheap at nuclear irradiation Dedicated targets and target materials. Relatively
nuclide precursor facility, e.g. nuclear reactor. Large amounts simple and at moderate costs from nuclear
molecules can be produced, exceeding 10 GBq. accelerator facility, e.g. cyclotron, linear
accelerators; up to approximately 5 GBq.
Synthesis of labeled No time constraints. Complex compounds may Time constraints. Synthesis routes for industrially
molecules be synthesized by standard organic synthesis interesting small molecules available. For
routes, followed by purification. Costs vary larger molecules further exploration required.
considerably, dependent on the molecule to be Costs vary, dependent on molecule to be
labeled and available knowledge of synthesis labeled and available knowledge of synthesis
routes. routes.
HSE aspects (synthesis) Handling of large amounts can easily be shielded. Remotely controlled synthesis in lead-shielded
Generation of radioactive waste. fume cupboards ("hot cells"). No generation of
radioactive waste (decay).
Transport and storage of Particularly during long time storage, compounds Prolonged storage not possible. Transport/
labeled molecules with high specific activity may decompose delivery only possible to nearby institutes (time
due to self-irradiation (radiolysis). Transport/ window between end of synthesis and start of
delivery over large distances is feasible. experiments, preferably shorter than 1 h).
Measurement and Detection requires sampling. Sensitive techniques, Quantitative, external in situ detection of radio-
analysis particularly in combination with accelerator nuclide inside (transient, steady-state etc.)
mass spectroscopy (AMS). Quantitative reactor or body. Extremely sensitive. Quanti-
molecular information only from sampled tative molecular information only from sam-
(intermediate) reaction products. pled (intermediate) reaction products.
Potential application Studies into reaction mechanisms, kinetics, effectiveness, and yields in biology, medicine, various types of
area process chemistry (homogeneous/heterogeneous catalysis). Both these radionuclides can be substituted
for stable carbon ("C, I3C) in organic molecules without changing the chemical properties of these
molecules.
Radiotracer in oil/gas fields (mean residence Only processes completed over time-scales shorter
times > year). Natural I4C activity exploited than approximately 1 h.
for carbon dating (AMS).
HSE aspects (applica- Handling of large amounts relatively simple. Supply and temporary waste containers should
tion) Shielding can easily be achieved; potential for be lead-shielded; remote control of valves; no
contamination; generation of radioactive generation of radioactive waste.
waste.

150,and/or 18Fproduction. The successful application 5.2.7.4 Detection of p - and Annihilation Radiation
of llC, 13N and/or 150to, heterogeneous catalysis
requires close interdisciplinary cooperation between Before the emitted B--particles can be detected, the
radionuclide production experts, radiochemical syn- outlet gases or liquids from catalytic beds have to be
thesis experts, radioanalytical experts and experts on sampled (see Section A5.2.7.2),after which the samples
the discipline of application (Table 3). may be separated into the constituting compounds
 5.2 Microkinetics 1027

quantitatively analyzed in the presence of the radio-

label. Depending on the application, a variety of de-
tection techniques for b-tracers can be used [8], such
as ionization chambers, liquid scintillation counters,
pyrolysis combustion detection in combination with a
ionization chamber, and autoradiography (two-dimen-
sional b-tracer distributions).
The presence of p+-tracers can also be quantitatively
analyzed by external detection of the indirectly emitted
511 keV y-photons. This is achieved by, for example,
scintillation detectors consisting of relatively large vol-
ume, single crystals of Nal(T1) or small volume, single
crystals of Bi4(Ge04)3 (BGO). A detector is generally
contained in a lead collimator - comprising a slit which L l
defines the detector's field of view by stopping all 7 - A A
8
photons from unwanted directions - thereby also re- I I I I

ducing the signal due to natural background radiation. C2H2 0 0.2 0.4 0.6 0.8 I .o
In cases where only one of the emitted 51 1 keV y- C,H, 1.0 0.8 0.6 0.4 0.2 0
photons is used (single photon mode), the distance of M O L FRACTION A L K Y N E
the detector to the p+-source contained in a reactor, the Figure 1. CrV1catalyst: effect of carrier alkyne mole fraction on
dimensions of the detector and collimator slit, and the the "C-labeled xylene product distribution.
settings of the ?-energy analyzer (pulse height analysis
or PHA) are the main factors determining the total
signal received and the attainable positional resolution propyne, the labeled molecules were condensed in
(order of magnitude, centimeters). Depending on the vacuo on the catalyst surface. Single annihilation pho-
effectiveness of the collimation and the PHA settings, tons from adsorbed C-labeled molecules were moni-
the signal due to natural background radiation may tored by a lead-collimated (pinhole 8 x 35mm), large
vary from approximately 5 to 25 counts per second. volume (76.2 x 76.2 mm) NaI(Tl).The products (ben-
Two scintillation detectors on opposite sides of the zene, toluene, xylenes) desorbed from the catalyst sur-
contained p+-source are required for simultaneous de- face were analyzed using a (radio) gas chromatograph
tection of two 51 1 keV y-photons (coincidence mode). (RGC) with thermal conductivity response detector
Only limited absorptive collimation shielding is re- and a flow-through gas proportional counter.
quired, as the field of view of the pair of detectors is The molecular orientation on CrVrof the adsorbates
now mainly determined by electronic collimation, with respect to product selectivity and the competitive
thereby rejecting 5 11 keV y-photons, which are not '
sorption of HI CCH and propyne could qualitatively
registered within a preset time window (< 10 ns). An be described. The kinetics of HI'CCH displacement by
improved positional resolution, which is more or less propyne from CrV1 was analyzed to be first order in
determined by the range of the p+-particles in matter acetylene and second order in propyne concentration,
(Table l), may be achieved by the coincident mode. while the catalyst selectivity dependence modeled to the
The total coincident background signal (accidental co- relative HI 'CCH displacement rate could be quantified.
incident events) will be very low, generally less than With this technique lop8 of a monolayer surface
0.01 coincident events per second, making "C-labeling coverage could be detected. Therefore it could be es-
an extremely sensitive analytical technique for hetero- tablished that the selectivity was altered at monolayer
geneous catalysis research. alkyne coverage through variation of the acetylene-
propyne distributions. Calculation of modeled xylene
yields as a function of the acetylene displacement rate
5.2.7.5 Application to Heterogeneous Catalysis resulted in distribution curves which were nearly iden-
tical with experimental data (Fig. 1).
The mechanism and kinetics of acetylene-propyne ad- The mechanism and kinetics of CO oxidation on a
sorbate interactions on a Cr"' catalyst have been eval- platinum/ceria,$yalumina catalyst has been evaluated
uated using "C-labeled acetylene and diacetylene [4, using "C-labeled CO and C02, and 150-labeled CO,
91. These labeled molecules were directly produced C02, and 0 2 [lo-181 under the transient conditions
in the target during irradiation of appropriate hydro- that apply during the cold start of a car. Large quanti-
carbon gases. After chromatographic purification at ties of "C02 (up to 50 GBq) were extracted from a N2
the start of each experiment about 0.2MBq H'ICCH
and 5KBq H"CCCCH was available. Together with References see page 1032
1028 5 Elementary Steps and Mechanisms

target (Table 2) and subsequently trapped. "CO (up to

30 GBq) is obtained by reducing ' I COz and subsequent I T=130"C I
purification. The I50-labeled molecules were produced
on-line by a flow-through target, and appropriate traps
and convertors were applied to obtain C150, C i 5 0 0
or I5OO of required radiochemical purity. Synthetic
exhaust gas was passed through a catalyst bed, of
length approximately 15 cm, under the required con-
ditions for several hours to achieve steady state. Then,
approximately 1 MBq of the "C-labeled and 0.2 MBq
of the 150-labeled molecules were used to carry out 0 80 160 240 320 400
pulse experiments under steady state, transient con-
time. s
ditions. Gases from the catalyst bed were monitored
by a NaI(T1) scintillation detector (Fig. 2), then ana-
lyzed by mass spectrometry and a gas chromatograph
equipped with a conventional flame ionization detector
and an ionization chamber.
I II T= 140°C

Initially, the labeled molecules flowing through or

P
adsorbed on a catalyst bed [lo, 161 were monitored
both by one (single photon mode) and by two (co-
incident mode) large volume (76.2 x 76.2 mm) NaI(T1) -
d
E
3
detectors. Other than being shielded by lead rings, the 8
scintillation detectors were not collimated, resulting in
a sensitivity profile over the axis of the catalyst bed.
A computational model for the kinetics of CO oxi-
dation and C02-ceria interaction was set up. Using 0 80 160 240 320 400
literature data the measurements could be simulated time, s
reasonably well. A relatively high sticking probability
of 0 2 on the catalyst surface, caused by the promoting
effect of ceria, had to be used to simulate the mea-
surements. Additionally, the degree of occupation of I 1 T= 150°C
CO on a Pt surface and the CO oxidation rate under
different reaction conditions were determined. The P
adsorption-desorption equilibrium of C02 on ceria d
was quantified by establishing the equilibrium con- E
3
stant. However, accurate quantification of the kinetics 8
turned out to be complex using the experimental set-up
with two large volume Nal(T1) scintillation detectors,
because in a plug flow reactor steep gradients occur II . . .

while only the sum of the total reactor signal was reg- 0 80 160 240 320 400
istered. Also, the signal from the total catalyst bed was
time, s
subject to large inhomogeneous field-of-view effects.
More information on the presence of reactants and in- Figure 2. Pt/ceria/y-alumina catalyst: (single photon) annihila-
termediates at the catalyst surface would considerably tion signal as recorded by the Nal(T1) detector monitoring the
increase the accuracy of the kinetic reaction parameters. outlet gases of the catalyst bed during "CO pulse experiments at
130, 140 and 150 "C. "CO/"CO2 (product) distribution assessed
This need for more information required the devel- from RGC data points (indicated by open circles).
opment of a linear array of opposing detectors. How-
ever, such an array of detectors was already present in
the PET apparatus [19] formerly used to explore in- as a two-dimensional (x, t ) false-colour matrix, or so-
dustrial PET applications [20]. Now, the catalyst bed called reaction image, (Fig. 3) and subsequently ana-
could be monitored by two parallel arrays of 11 BGO lyzed. Although the banks of BGO detectors were an
detectors resulting in 21 independent points (separa- integral part of a PET setup, this method of data re-
tion about 11 mm, spatial resolution per point about cording can at most be classified as one-dimensional
lOmm), at which the "C- c.q. i50-concentration was PET.
measured simultaneously; this measurement could be Some further experiments were carried out to
repeated every 1.2 s. The recorded data were presented achieve an accuracy improvement with respect to the
 5.2 Microkinetics 1029

Figure 3. Ptlcerialy-alumina catalyst: reaction image (display of coincident data from 11 individual BGO detectors of two opposing
banks, simultaneously recorded approximately every second at 21 measuring points and subdivided over a total length of about 22cm) of a
I'CO pulse experiments, 75% conversion at 140°C. The vertical axis represents the time coordinate, the horizontal position and the grey
values are a measure of the I'C concentration. The I'C profile at 80 s, and the residence time distribution of the "C-label at -5 crn are
indicated. A computer simulation of the reaction image is shown in the top right comer.

kinetic data obtained with the NaI(T1). Although dissociative and irreversible adsorption of 0, at the
labeled 13N0was not available, the effects of blocking surface is the rate limiting step. Oxygen atoms of CO
a significant amount of the available Pt reaction sites remain much longer in the catalyst bed than the carbon
could effectively be demonstrated by adding some sta- atoms, which could be ascribed to carbonate formation
ble NO to the synthetic exhaust gas. This was quanti- at the ceria surface and exchange of the oxygen atoms
fied by the lower CO desorption rate and a somewhat of these carbonate groups with the ceria lattice oxygen
higher activation energy for desorption. Rather un- atoms (Fig. 4).
expectedly, the labeling of different atoms of the same The selective reduction of N O by NH3 over vanadial
reactant molecule (e.g. " C O and C150), provided titania catalysts at very low reactant concentrations has
much insight into the mechanism of the overall cata- been studied using 13N-labeled NO [21]. 13N-labeled
lyzed reaction. The rates of adsorption, desorption, and HNO3 (83%), NO (9"/0), and N2 (8%) were contin-
surface reaction were determined by simulating the uously produced in the oxygen gas target during irra-
quantitative experimental results by means of the diation. By exploiting the appropriate convertors and
computational model. During low temperature CO traps, either pure 13N0, about 50 Bq ml-' at an overall
oxidation by oxygen, the catalyst surface is predom-
inantly covered by adsorbed CO molecules, while the References see page 1032
1030 5 Elementary Steps and Mechanisms

Figure 4. Pt/ceria/y-alumina catalyst: a collection of reaction images of different positron emitter labeled species at 140°C (75% con-
version). (A) I3NN over inert carrier material (noninteractive flow); (B) "CO (reaction and product interaction with ceria); (C) I'COz
(interaction with ceria; label hold-up, chromatographic effect); ( D)I5OO (25% immediately to outlet, reaction and I5O in product ex-
changes with ceria); (E) CI5O (reaction and I5O in product exchanges with ceria); (F) C 1 5 0 0(I5O exchanges with ceria).

flow rate of 580 ml min-' , or pure 13N02 was obtained. raphy, adsorption enthalpy for 13N0 and 13N02, and
Coincident photons were monitored by lead-collimated, hence NO and NO2 on various oxides, have also been
high purity Ge semiconductor detectors. determined.
The selective catalytic reduction of NO by NH3 has, The heat of adsorption and surface coverage of n-
been monitored with 5 x lop9ppm of 13N0,more than hexane on H-mordenite has been studied using "C-
11 orders of magnitude lower than the usually used labeled n-hexane [22]. C02 was batch-wise converted
concentrations (Fig. 5 ) . These low concentrations re- into "CO using standard procedures (Table 2), after
sult in very low conversion rates, enabling investigation which H3 l1 CCsHll was produced via a newly developed
of the kinetics of the catalyst materials after pretreat- route [23]. This is a two-step homologation reaction
ment with various reactive gases without adding these in which "CO is pulsed at 350°C over a vanadium-
gases during the conversion experiment. Catalysts pre- promoted Ru/SiO2 catalyst, after which the temper-
treated with NH3 did reduce 13N0, whereas pretreat- ature is rapidly reduced to about 100 "C and 1-pentene
ment of H2 did not show any 13N0conversion. For the is pulsed over the catalyst. Desorptive hydrogenation
NH3-pretreated catalyst the first-order reaction rate leads to a mixture of alkanes in the c1-c6 range.
for NO conversion and its activation energy could be By optimizing the heat treatment protocol and the
determined quantitatively. Using thermochromatog- subsequent chromatographic purification procedures
 5.2 Microkinetics 1031

PEP images - similar to the reaction images de-

scribed above - of adsorption/desorption phenomena
1500 on H-mordenite have been recorded between 150°C
A

a
v1 and 230°C at 10°C intervals by injecting H3"CCsH11
0
v into a hydrogen feed stream (150mlmin-'). The
x
.->
4-
1000 PEP images showed an enormous reduction in the
._
e H3 l 1 CCsH" retention time, when about 10 pL min-'
2 n-hexane was added to the hydrogen feed stream
500
(Fig. 6). From these studies a heat of adsorption for
n-hexane on H-mordenite was determined to be
0 66.7 k 1.3 kJ mol-' . In addition, the H-mordenite
0 50 100 150 200
surface coverage of n-hexane at various temperatures
Temperature ( " C ) and n-hexane partial pressures could be analyzed
quantitatively.
Figure 5. Vanadia/titania catalyst: NO conversion measured
as positron-emitting activities of I3NO (open circles) and I3NN
(solid squares) as a function of temperature. Gas hourly space
velocity was about 72 000 per hour with a feed composition of
5x ppm I3NO and 15% 0, in He.
5.2.7.6 Conclusions

The scope for "C, 13N, and 1 5 0 positron emitters in

''
towards the production of C-labeled hexane, about heterogeneous catalysis research has effectively been
2 MBq H3 CCsHl1 was available for experimental use. demonstrated. These applications illustrate the benefits
A dedicated positron emission detector has been of "C, 13N, and 150labelling techniques, for the ac-
designed and constructed, specifically for studies in quisition of time- and position-dependent data. The
tubular reactors [24]. The detector, consisting of two high sensitivity of data acquisition and its quantitative
opposite arrays of nine independent (moveable) BGO interpretation, in terms of reaction mechanisms, re-
scintillation crystals, has been optimized to measure action rates, concentration of intermediate species and
the positron label concentration profile along the coverage of adsorption sites, activation energies and
longitudinal axis of the reactor (spatial resolution transport phenomena, have been demonstrated.
3 mm, temporal resolution 0.5 s). This method of one- Although the number of applications is as yet lim-
dimensional data recording is called positron emission ited, the potential of this technique to investigale other
profiling (PEP). heterogeneous catalysis systems is clear. The recent de-

Figure 6. Positron Emission Profiling (PEP) images obtained on H-mordenite at 150°C at 150mL/min: u ) . I ' C H ~ C S H Iinjected
I into a
hydrogen feed stream, b ) , C H ~ C ~1Hinjection
I following presaturation using n-hexane (10 pL/min)/hydrogen.

References see page 1032

1032 5 Elementary Steps and Mechanisms

velopment of a "C02 generator [25] makes feasible the 14. K. A. Vonkeman, G. Jonkers, S . W. A. van der Wal, R. A.
in situ, on-site application of "C02 or (in combination van Santen, Ber. Bunsenges. Phys. Chem. 1993,97, 333-339.
with an appropriate catalytic convertor) "CO in 15. G. Jonkers, K. A. Vonkeman, S. W. A. van der Wal, in Pre-
cision Process Technology, (Eds. M. P. C. Weijnen and
operational pilot plants. Storage of the "C-label in a A. A. H. Drinkenburg), Kluwer, Deventer, 1993.
carbonate solution both facilitates the transport of the 16. K. A. Vonkeman, G. Jonkers, S . W. A. van der Wal, J. de
C0:- supply vessel and the controlled release of Jong, H. Oosterbeek, R. A. van Santen, unpublished results.
"co*. 17. K. A. Vonkeman, G. Jonkers, J. de Jong, H. Oosterbeek,
R. A. van Santen, unpublished results.
However, there are some factors which may limit the 18. K. A. Vonkeman, G. Jonkers, P. Goethals and K. Strijck-
widespread application of this technique. These are mans, R. A. van Santen, unpublished results.
an awareness of the potential of this type of label, 19. E. J. Hoffman, M. E. Phelps, S.-C. Huang, J. Nucl. Med.
the required close interdisciplinary cooperation, and the 1983,24,245-257.
number of available synthesis routes for labeling the 20. E. A. van den Bergen, G. Jonkers, K. Strijckmans, P. Goe-
thals, Int. J. Radiat. Appl. E. 1989, 3, 407-418.
required molecular species. The first two factors may 21. U. Baltensperger, M. Ammann, U. K. Bochert, B. Eichier,
be easily overcome, but the third requires some pre- H. W. Gjggeler, D. T. Jost, J. A. Kovacs, A. Tijder, U. W.
planning [22-241. Sherer, A. Baiker, J. Phys. Chem. 1993,97, 12 325-12 330.
Although routes to some interesting molecules have 22. R. A. van Santen, B. G. Anderson, R. H. Cunningham, A. V.
G. Mangnus, J. van Grondelle, L. J. van IJzendoorn, paper
already been reported [5] or have recently been devel- submitted to the 11th Int. Congress on Catalysis, 1996.
oped [23, 261, greater variety will extend the areas of 23. R. H. Cunningham, R. A. van Santen, J. van Grondelle,
potential application of this very promising labeling A. V. G. Mangnus, L. J. van IJzendoorn, J. Chem. SOC.
technique. Comm., 1994, 1231.
24. A. V. G. Mangnus, L. J. van IJzendoorn, J. J. M. de Goeij,
R. H. Cunningham, R. A. van Santen, M. J. A. de Voigt,
Nuclear Instruments and Methods B 99, 1995, 649.
25. P. S. Kruijer, J. D. M. Herscheid, Appl. Radiat. Isot. 1995,
References 46, 337-338.
26. P. S. Kruijer, J. D. M. Herscheid 1995 personal communica-
1. G. J. Nesbitt, H. H. Mooiweer, A. K. Novak, T. H. L. tion ("C-labelled n-heptane synthesis).
Maessen, D. Schuize, A. Mizee, W. Kuhn, K. Mehr, P.
Dejon, S. Hafner, unpublished results.
2. R. Miranda, R. Ochoa, W.-F. Huang, J. Mol. Cat. 1993, 78,
67-90.
3. J. M. Buchanan, A. B. Hastings, Am. Physiol. Rev. 1946,26,
120-155, and references therein. 5.2.8 Nonlinear Dynamics: Oscillatory
4. R. A. Ferrieri, A. P. Wolf, J. Phys. Chem. 1984, 88, 2256-
2263.
Kinetics and Spatio-Temporal
5. J. S . Fowler and A. P. Wolf, Positron Emitter Labelled Pattern Formation
Compounds: Priorities and Problems, P. 391-450, in Positron
Emission Tomography and Autoradiography: Principles and
Applicationsfor the Brain and the Heart, eds. M. E. Phelps,
G. ERTL
J. C. Mazziotta and H. R. Schelbert, Raven Press, New
York, 1986.
6. S. Webb (ed.), The Physics of Medical Imaging, Adam Hiiger, 5.2.8.1 Introduction
Bristol, 1988.
7. M. E. Phelps, J. C. Mazziotta, H. R. Schelbert (eds), Positron
Emission Tomography and Autoradiography: Principles and The rate of a catalytic reaction is governed by the un-
Applicationsfor the Brain and the Heart, Raven Press, New derlying mechanism, i.e. the sequence of elementary
York, 1986. reaction steps, and depends on the external control pa-
8. G. F. Knoll, Radiation Detection and Measurement, Wiley rameters such as the concentrations (= partial pres-
and Sons, New York 1989.
9. R. A. Ferrieri, A. P. Wolf, J. Phys. Chem. 1984, 88, 5456-
sures) p, of educt and product species and temperature
5458. T , if transport processes are excluded in this context.
10. K. A. Vonkeman, PhD thesis, Technical University Eind- More specifically, usually the adsorbed species are
hoven, 1990. assumed to be randomly distributed over the surface
11. K. A. Vonkeman, G. Jonkers and R. A. van Santen, Studies and their concentrations (= coverages) Bi are described
to the functioning of Automotive Exhaust Catalysts using in-
situ Positron Emission Tomography, SAE technical paper within a mean-field approximation so that the reaction
#910843 SOC.Automobile Eng., New York, 1991. rate (=number of molecules r formed per unit time,
12. K. A. Vonkeman, G. Jonkers and R. A. van Santen, Studies dn,/dt) is given by
to the Functioning of Automotive Exhaust Catalysts using In-
situ Posftron Emission Tomography, p. 239-252 in Cataiy-
sis and Automotive Pollution Control II, (Ed.: A. Crucq),
Elsevier Science, Amsterdam, 1991.
13 G. Jonkers, K. A. Vonkeman, S . W. A. van der Wal, R. A. whereby the coverages 8i are in turn determined by a
van Santen, Nature 1992,355, 63-66. set of differential equations (modeling the individual
 5.2 Microkinetics 1033

steps of adsorption, desorption and surface reaction) of mensions of the reaction vessel which is operated
the type as a continuous flow reactor. Hence, concentration
gradients in the gas phase are practically instanta-
neously (I lop3s) transmitted. Analysis of such
experiments is thus appreciably simplified.
Proper treatment then requires that additional con- (iii) Experiments with polycrystalline, i.e. “real”, cata-
straints given by heat and mass balance are taken into lysts are usually conducted at elevated partial
consideration. pressures ( 21 mbar) under which the heat released
Under flow conditions with the external control pa- by the reaction may lead to noticeable temper-
rameters being kept fixed, usually the reaction proceeds ature variations. The resulting thermokinetic effects
at steady state with constant rate, i.e. dn,/dt =constant may become dominating, so that even the non-
and dOi/dt = 0. Due to the nonlinear character of the uniformity of the surface chemistry is masked, and
quoted differential equations, this has, however, not quite novel phenomena may arise. Ideally, the
necessarily to be the case; the kinetics may - for certain reaction is conducted in a way which may be
ranges of parameters - become oscillatory or even described by a continuously stirred tank reactor
irregular (chaotic). Such systems are typically far away (CSTR), i.e. perfect mixing ensures that the con-
from equilibrium and as a consequence “dissipative centrations are everywhere identical. However,
structures” [l] may emerge. The coverages Bi may frequently a concentration profile exists along the
vary both in time and space and may give rise to phe- reactor which is hence rather of the plug-flow
nomena of spatio-temporal self-organization as being type. It is thus evident that heat and mass transfer
treated in the general area of nonlinear dynamics [2]. limitations may play important roles with such
Experimental observations on oscillatory kinetics systems.
have been made with quite different systems, first with
electrochemical reactions [3] and later quite extensively Generally, an extended system such as a single crystal
in homogeneous solution with the famous Belousov- surface, or even more a supported catalyst, exhibiting
Zhabotinsky (BZ) reaction and related systems [4,51. temporal variations of the integral reaction rate has to
In heterogeneous catalysis, rate oscillations were first be subject to a coupling mechanism between various
reported about 25 years ago by Wicke and co-workers parts. Otherwise, superposition of the uncorrelated
for the oxidation of carbon monoxide on supported contributions from different regions would cause aver-
platinum catalysts [6, 71. Since then numerous catalytic aging so that constant steady-state behavior would re-
reaction systems have been investigated in more or less sult. As a consequence, the coverages Bi as introduced
detail, and this subject has also been reviewed quite in eqs 1 and 2 will in general not only depend on time
extensively [8-161. Oscillatory kinetics have so far been but also on spatial coordinates, and proper mathemat-
found with more than a dozen catalytic reactions, in ical modeling will be achieved in terms of partial dif-
particular with CO oxidation, but also with oxidation ferential equations (PDE) as will be outlined further
of H2, NH3, or hydrocarbons, with reduction of NO by below.
CO, H2, or NH3, as well as with hydrogenation re- The following coupling mechanisms may be operat-
actions and even with the endothermic decomposition ing:
of methyl amine. Further distinction is made with re-
spect to the type of catalyst (e.g. single crystal or poly- (i) Surface diffusion Local differences of the coverages
crystalline material) as well as the pressure range stud- will lead to surface diffusion of the adsorbates, and
ied. This classification is reasonable for the following inclusion of this effect into mathematical modeling
reasons: extends eq 2 to reaction-diffusion (RD) equations
of the type
(i) By far the most detailed insights into the under-
lying mechanisms and the general phenomenology (3)
of spatio-temporal self-organization were obtained
in studies with well-defined single crystal surfaces where Di is the diffusion coefficient of the respec-
by applying the arsenal of modern surface physical tive adsorbed species. Diffusion lengths of the sys-
methods. tems under consideration here are typically of
(ii) Single crystal studies are usually conducted with the order of about 1 pm. Concentration patterns
bulk samples under low pressure conditions will hence be formed on extended single crystal
(I lop4mbar) where the temperature changes as- surfaces, but also on monolithic polycrystalline
sociated with varying reaction rate are negligible. material where the individual grains have typically
In addition, the mean free path of gaseous mole-
cules is comparable or even larger than the di- References see page 1049
1034 5 Elementary Steps and Mechanisms

much larger diameters [17]. However, other types by two variables can only be stationary or harmonic
of RD phenomena will develop on the small oscillatory. These two situations are corresponding to
( I10 nm) crystal planes of supported catalyst fixed points or limit cycles, respectively, in a phase-
particles as modeled in experiments with field space representation of the mutual dependencies of
emission tips [18, 191. the two variables where time is eliminated. With three
(ii) Gas-phase coupling Varying reactivity will also af- or even more variables the situation becomes much
fect the partial pressures of the reactants, even in a more complex and may involve so-called mixed-mode
flow system. As outlined above, at low pressures oscillations or chaotic behavior, the latter being char-
these changes will propagate practically instanta- acterized by “strange attractors” in the phase-space
neously and may offer a rather effective “global” representation.
coupling mechanism which synchronizes different The specific nature of the differential equations de-
parts of a single crystal surface or even of sepa- scribing the kinetics depends, of course, on the mecha-
rated samples [20]. Experiments with external nism of the underlying elementary steps. However, it
periodic modulation of one of the partial pressures has been demonstrated that any exothermic reaction in
revealed that indeed amplitudes far below 1% may an open system can give rise to bistable, excitable or
suffice to cause such synchronization effects [21]. oscillatory behavior for which the principle features
At elevated pressures, however, this coupling may be obtained by using just a single unimolecular
mechanism will be of minor importance. step [24, 251. Various mathematical models have been
(iii) Heat conductance Local variations of reactivity proposed to describe oscillatory catalytic reactions,
will be accompanied by temperature differences either as general models or adapted to specific experi-
due to the finite reaction enthalpies. Coupling be- mental situations. The latter may quite often be traced
tween different regions may thus occur through back to one of the various types of general models
heat flux counterbalancing the temperature gra- which, e.g. may contain a slow buffer step [26], com-
dients. This mechanism generally prevails at higher prise coverage-dependent activation energies [27-3 11 or
pressures and also with supported catalysts where involve the creation of vacant sites [32, 331.
temperature changes of up to order of 100 K may The decision as to whether a proposed scheme yields
arise. The characteristic “diffusion” length is in oscillatory solutions can, of course, be reached by in-
this case of the order of about lmm, which is tegrating the differential equations or, even more ele-
much larger than the mean separation between gantly, by applying a more general method denoted as
catalyst particles or even the diameters of their in- stoichiometric network analysis (SNA) [24, 251.
dividual crystal planes. As a consequence, such a As outlined in the introductory section, with any ex-
system may again be regarded as being uniform tended system the effects of spatial coupling between
(on the relevant length scale), but the observed different parts play an important part. If coupling by
phenomena will be strongly affected by these heat diffusion is dominant, proper theoretical description
phenomena rather than by the details of the sur- has to be based on partial differential equations
face chemistry, and external constraints (such as (PDEs) of the type of eq 3. The general nature of pos-
a constant average temperature) may provide effi- sible resulting concentration patterns has been explored
cient global coupling. quite extensively in connection with the analysis of
chemical reactions in homogeneous solution [2, 5,
In the following, after a brief outline of the theoretical 34-36]. The basic feature is that of a propagating
background, rather than to attempt to present an ex- “chemical” wave, as recognized already in 1906
tended review of the field, the underlying principles will [37], which propagates with a velocity determined
be illustrated by selected examples with progressing in- by d m where D is the diffusion coefficient and k an
herent complexity. effective, first-order rate constant. Apart from prop-
agating waves, stationary so-called Turing patterns [38]
may be formed with which phenomenon, for example,
5.2.8.2 Overview of the Theoretical Background the periodic faceting of a Pt(ll0) surface in the course
of CO oxidation was identified [39, 401.
Sets of coupled nonlinear ordinary differential equa- The different types of chemical waves may be clas-
tions (ODES) of the type of eq 2 may be subject to sified with regard to whether the medium is bistable,
systematic analysis of possible solutions in the frame- excitable, or oscillatory [2]. In a bistable medium a
work of bifurcation theory [22, 231. Bifurcation simply transition from one state to another (differing in con-
means a qualitative change of the dynamic behavior of centration) may proceed via a propagating reaction
a system upon variation of one of its control parame- front. In excitable media an external perturbation of
ters, e.g. a transition from stationary to oscillatory be- sufficient strength may cause a transient excursion of
havior. The temporal behavior of a system described the system to another state from where it returns to the
 5.2 Microkinetics 1035

initial state. After some refractory time it may then be decomposition [46] which has already been successfully
excited again. Propagating pulses and spiral waves are applied to catalytic reactions in a few cases [47, 481.
the characteristic features of such a situation. In con-
trast, oscillatory media do not need external perturba-
tion but perform autonomous periodic changes, asso- 5.2.8.3 CO Oxidation on Pt(ll0): A Case Study of a
ciated, for example, with the formation of so-called Uniform Isothermal System
target patterns, unless global coupling mechanisms are
operating. Finally, irregular and rapidly changing pat- As mentioned above, kinetic oscillations associated
terns known as “chemical turbulence” may be formed with a catalytic reaction were first discovered with the
which represent the spatio-temporal counterpart of oxidation of CO on supported platinum catalysts [6, 71,
temporal chaotic behavior. and it was also this reaction which was first inves-
In a bistable system both states may coexist just tigated using the “surface science” approach, i.e. with
at one specific value of the varied control parameter, well-defined single-crystal surfaces under low pressure
while otherwise the less stable state is pushed away by a conditions [49]. It is still the system studied in most
moving interface. If the front is not flat but exhibits a detail, among which the Pt( 110) single-crystal surface
curvature with radius R,it propagates with a modified exhibits the richest variety of phenomena and is un-
velocity c = co D/R [2], where D is the diffusion co- derstood best.
efficient and co the velocity of the plane wave. Evi- The mechanism of this reaction is well established
dently a critical radius, Rc = D / C Oexists
, below which [50] and proceeds schematically along the following
c < 0, i.e. a front does not expand but shrinks. That steps:
means that Rc represents the critical radius for nucle-
ation of a concentration wave in a defect region which co + * * toad
is typically of the order of 1 pm, as determined for CO 0 2 + 2* + 20ad
oxidation on Pt [41].
Spiral waves are ubiquitous in reaction-diffusion oad + toad + c02 + 2*
systems and characteristic for excitable media, whereby Here, * denotes a free adsorption site; this has a dif-
the excitation not necessarily requires an external per- ferent meaning for the two adsorbates. Whereas dis-
turbation, but quite frequently may be identified with sociative oxygen adsorption is strongly inhibited by the
an inherent local variation of kinetic parameters such presence of preadsorbed CO, the chemisorbed 0 atoms
as found with a defect zone on a surface. The general form rather open adlayers which do not significantly
properties of spiral waves may be rationalized in the affect the additional uptake of CO (asymmetric in-
framework of the so-called kinematic approximation hibition). Under steady-state flow conditions the tem-
[2, 42, 431. The core of a spiral on a catalytic surface is perature has to be high enough ( 2400 K) to enable
often formed by a defect to which the spiral is ‘pinned’ continuous desorption of CO and creation of free ad-
and which determines its characteristic properties, such sorption sites, otherwise complete blocking of the sur-
as rotation period and wavelength [42]. face by adsorbed CO would inhibit oxygen adsorption
Global coupling is often decisive for the formation of and, consequently, the catalytic surface reaction. Fig-
patterns in oscillatory media. Depending on the kind ure 1 shows the steady-state rate of C02 formation on
of feedback, global coupling may either stabilize or a Pt(ll0) surface, which was either flat or periodically
destabilize the uniformly oscillating situation through stepped (faceted), as a function of CO partial pressure,
symmetry breaking [44]. Systematic analysis of the while the two other control parameters (PO, and T )
kinds of pattern formation in an oscillatory medium were kept fixed. At low pco, the surface is largely cov-
with global coupling was performed with a model sys- ered by adsorbed oxygen, and the reaction rate is gov-
tem, the modified Ginzburg-Landau equation whose erned by the supply of CO and therefore rises propor-
characteristic features are, however, of general validity tionally to pco. Eventually, the stationary CO coverage
[45]. It was shown that global coupling may, among becomes so high that it starts to inhibit oxygen ad-
others, modify or even suppress turbulent behavior. sorption noticeably, and further increase of pco causes
With realistic systems, such as nonuniform surfaces, a decrease of the reaction rate which becomes now
the observed spatio-temporal patterns may become limited by oxygen adsorption. Since the faceted surface
quite complex due to superposition and coupling of exhibits a higher oxygen sticking coefficient [51], for
differing contributions. Analysis may then become identical control parameters the rate also becomes
rather difficult. One is then interested in methods that larger. No such difference is observed at low pco where
allow extraction of the relevant features and sim- the rate is limited by CO adsorption whose sticking
plification of the dynamics. A suitable technique is the
Karhunen-Loeve decomposition into an optimal set
of eigenfunctions, also known as proper orthogonal References see page 1049
1036 5 Elementary Steps and Mechanisms

I I I I I I
Pl11101
Po2 = 2.0 x mbar 1 m - f a c e t t e d "LEED"
T :L 5 5 K ,,--,2 facetted "LEED"
-
6- / \
L /
' \ l d I 1x1
nv1 /'2
5 \\ I

-
/
\ '
\ ' -
\I\
10011
1x l -
-c
1x 2
\
\
mcil \ Figure 2. The two structural modifications of the Pt(ll0)
\ - surface.
\

I
I
2
I
3 L 5
'.
I..
6
PCO mbar

Figure 1. Rate of COz formation in catalytic CO oxidation at a

Pt(ll0) surface which is either flat (full line) or faceted (broken
line) as a function of CO partial pressure pco, with the oxygen
partial pressure PO,, and temperature T , kept fixed.

coefficient is not noticeably affected by the surface

structure.
The steady-state kinetics can readily be modeled by
solution of the corresponding differential equations for
the CO and 0 coverages, and the resulting data may
even be transferred to "real" catalyst systems [52]. The t [sl
decrease of the rate with increasing pco becomes Figure 3. Oscillatory behavior resulting from integration of the
steeper at lower temperature (due to the increasing three ordinary differential equations modeling the kinetics of
mean residence time of adsorbed CO on the surface), CO oxidation on a Pt(ll0) surface for a particular set of control
and the system eventually becomes bistable, exhibiting parameters: T = 540 K, PO, = 6.7 x lo-' mbar, pco = 3 . 0 ~
mbar. Temporal variation of the reaction rate, the 0-and CO-
branches of high and low reactivity, and a clockwise coverages as well as the fraction of the surface being in the 1 X 1
hysteresis upon variation of pco [53, 541 which can structure, respectively (ML = monolayer) [55].
readily be modeled with a two-variable system [55, 561.
While such a behavior is characteristic for the densely
packed Pt( 111) surface, novel effects-namely rate os- readily be rationalized. Starting with the 1 x 2 surface,
cillations-come into play with the more open crystal the po2:pco ratio will be such that sufficient CO is ad-
planes such as (100) [49, 571, (110) [58] or (210) [59, 601. sorbed to lift the reconstruction. On the 1 x 1 patches
Returning to Pt( 1lo), these oscillations occur within formed more oxygen will be adsorbed which then re-
a relatively narrow range of pco, marked by a bar in acts with adsorbed CO, so that the coverage of the
Fig. 1, and are associated with a periodic variation latter drops below the critical value for maintaining the
of the atomic structure of the surface. As indicated in 1 x 1 phase stable. The surface structure transforms
Fig. 2 the clean Pt(ll0) surface is reconstructed into a back to 1 x 2 where the 0 2 sticking coefficient is
1 x 2 "missing row" structure which is transformed smaller, so that the CO coverage may build up again,
into the normal 1 x 1 structure if the CO coverage and so on. In this way, the microscopic surface struc-
exceeds a critical value of about f3co = 0.2 [61, 621. ture acts as an atomic switch between states of high
This structural transformation is driven by the en- and low reactivity and is thus responsible for the oc-
ergetics of CO adsorption and is a rather local process currence of rate oscillations. Proper inclusion of the
which involves displacements of surface Pt atoms only surface state as a further variable leads to a set of three
over short distances as demonstrated by scanning tun- ODES whose solutions exhibit, apart from steady-state,
neling microscopy (STM) [63]. On the other hand, the bistable, or excitable behavior, oscillatory kinetics for
oxygen sticking coefficient is larger on the 1 x 1 phase certain ranges of control parameters such as those dis-
than on the 1 x 2 phase [64]. Since the kinetic oscil- played in Fig. 3 [55]. Note that the 0 and CO cover-
lations are observed under conditions for which oxygen ages are strictly anticorrelated, while the fraction of the
adsorption is rate-limiting, their occurrence may now surface being present as 1 x 1 phase oscillates with a
 5.2 Microkinetics 1037

1.60

1- 10 sec

Figure 4. Experimental time series of the rate of COz formation on a Pt(l10): T = 550 K, PO, = 4.0 x mbar, the CO pressure was
changed stepwise at the points marked.

phase shift and plays the role of a slow variable whose

time constant is determined by the kinetics of the
structural phase transition. The reaction rate strictly
parallels the 0 coverage, and since the latter is reflected
by the variation of the work function, Aq, this quantity
may serve as a convenient monitor for the rate oscil-
lations rather than direct recording of the C02 partial
pressure by means of a quadrupole mass spectrometer.
Figure 4 shows an experimental time series which
was recorded in this way, for which po2 and T were
kept strictly fixed, while pco was varied stepwise in
small increments. (The onset of oscillations at even
larger pco occurs via small amplitudes which con-
tinuously grow upon decreasing the CO pressure as
characteristic for a Hopf bifurcation [58].) The oscil-
lations in Fig. 4 are at first strictly periodic, until at a Figure 5. Phase portraits constructed by the delay method from
the experimental data of Fig. 4 for (a) p c o = 1.65 x mbar,
certain value of pco (1.64 x lop4mbar) a qualitative (b) p c o = 1.63 x mbar, (c) p c o = 1.60 x mbar, and (d)
change (i.e. bifurcation) occurs. Alternating small and pco = 1.59 x mbar.
large amplitudes are formed and the period is doubled.
Upon further decrease of pco the amplitude ratio con-
tinuously varies. until at 1.60 x lop4mbar another ponents became positive. This is the first example of
doubling of the period takes place. Further slight var- “hyperchaos” identified with a chemical reaction [66].
iation of pco to 1.59 x lop4mbar causes the appear- Although mathematical modeling, in terms of the
ance of irregular variations-a state known as deter- quoted system of ordinary differential equations for the
ministic chaos. The whole transition to chaos through laterally uniform surface concentrations, accurately re-
the sequence of period doublings follows the well- produces the stationary kinetics as well as the bifurca-
known Feigenbaum scenario and is demonstrated more tion to periodic (harmonic) oscillations, it fails to de-
clearly by the phase portraits in Fig. 5, which were scribe the period-doubling transition to temporal chaos
constructed from the corresponding time series [65]. [55]. This is because spatial coupling has been com-
Detailed analysis shows that for the chaotic state asso- pletely neglected; it was tacitly assumed that the whole
ciated with a “strange attractor” one of the Lyapounov macroscopic surface is always strongly synchronized,
exponents became positive so that initially nearby tra- so that the concentrations depend only on time. As
jectories in the phase space diverge. Analysis of an- outlined above, this will generally not be the case, and
other set of data recorded further inside the chaotic
window revealed that then even two Lyapounov ex- References see page 1049
1038 5 Elementary Steps and Mechanisms

Figure 6 . Spatio-temporal concentration patterns on a Pt( 1 10) surface during CO oxidation recorded by photoemission electron micro-
scopy (PEEM) for conditions of dynamic bistability: T = 443 K, PO, = 4 x mbar, pco = 3.6 x mbar [73].

as a consequence the formation of spatio-temporal typical length scale of the reaction-diffusion patterns
concentration patterns is to be expected. described.
If nonisothermal effects are neglected, coupling by The principle of PEEM is based on the differing di-
reaction-diffusion and global coupling through the pole moments of adsorbate complexes which give rise
gas phase have to be taken into consideration, and a to modification of the local work function. The yield of
proper theoretical description is achieved by inclusion photoelectrons emitted from a surface under the influ-
of surface diffusion, so that the equations are extended ence of ultraviolet irradiation is thus determined by the
into a set of partial differential equations (PDEs) of type and concentration of adsorbed species, and the
the type of eq 3 [41, 67, 681. The resulting theoretical lateral intensity distribution of these photoelectrons is
skeleton bifurcation diagram for the spatio-temporal imaged through a system of electrostatic lenses onto
pattern formation in the present system contains two a channel plate and a fluorescent screen. From there,
excitable and an oscillatory region, as well as two bi- the PEEM images are recorded by means of a CCD
stable regimes with one- or two-front solutions. (charge coupled device) camera and stored on video
Before discussing in some detail the characteristic tape. Typical resolutions are 0.2 pm and 20 ms, respec-
features of these patterns, their experimental verifica- tively, the latter being determined by the video fre-
tion will be briefly described. quency. Since 0 atoms chemisorbed on Pt(ll0) cause a
Imaging of lateral distributions of adsorbed species larger increase of the work function than adsorbed CO,
at low pressures was initially performed with scanning regions predominantly covered by oxygen will appear
techniques [57, 691 which, however, suffered from dark in the images, while those on which CO prevails
limited spatial and temporal resolution. These dis- are grey.
advantages are circumvented by photoemission electron Even for those conditions under which the integral
microscopy (PEEM) [70] which was used to record all reaction rate is constant, the composition of the surface
the images to be shown below. Related techniques such is not necessarily uniform, but may exhibit-frequently
as low-energy electron microscopy (LEEM) and mir- transient-propagating concentration patterns com-
ror electron microscopy (MEM) offer even higher lat- monly known as chemical waves [16].
eral resolution but, to date, have found few applica- The CO + Oz/Pt( 110) system exhibits, for example,
tions [71, 721. Field emission and, in particular, field parameter ranges in which both 0 and CO wave fronts
ion microscopy (FEM and FIM) [ 18, 191 enable almost are found to coexist and to propagate, as shown in Fig.
atomic resolution to be achieved, but these techniques 6 [73]. This situation is called “double metastability” or
are confined to very fine tips (<1 pm) where the ex- “dynamic bistability” and is also reproduced in model
tension of the individual crystal planes is far below the calculations [68]. The elliptical, rather than circular,
 5.2 Microkinetics 1039

Figure 7. PEEM images from a Pt(ll0) surface during CO oxi- Figure 8. Theoretical modeling of the temporal evolution of a
dation exhibiting the formation of spirals: interval between con- turbulent state from spiral patterns [75].
secutive images 30 s, T = 448 K, PO, = 4 x mbar, pc- =
4.3 x 10-5mbar [73].

shape of the growing islands is a consequence of the

anisotropy of the diffusion coefficient for adsorbed CO,
which is larger along the (110) direction than along the
perpendicular (001) direction [74]. As long as two con-
secutive fronts propagate with significantly different
velocities, the faster eventually overruns the slower
one. However, if the velocities become comparable,
pulses with stable width are formed, which in a two-
dimensional medium frequently develop into spirals.
Such a situation is shown in Fig. 7. Remarkably,
under identical external conditions, not all spirals exhibit
the same periods and wavelengths, but rather continuous
distributions. This has to be attributed to pinning of some
of the spiral cores to surface defects of varying size and
kinetic properties as reproduced by theoretical simu-
lations [68]. Extended ( 210 pm)defects may even form
the cores of multiarmed spirals [73].
Detailed theoretical modeling revealed that with the Figure 9. Experimental verification of chemical turbulence with
present system under certain conditions the spirals are the CO oxidation at a Pt(ll0) surface [76].
migrating (meandering). Eventually, the Doppler effect
becomes so pronounced that the spiral arms break up
and cause a transition to irregular patterns such as namely the formation of solitary pulses which prop-
shown in Fig. 8 [75] (chemical turbulence), quite sim- agate with constant velocity of about 3 pm/s along the
ilar to experimental observations (Fig. 9) [76]. Al- (001) direction as reproduced in Fig. 10 [77]. Upon
though not yet explored in detail, it is very likely that collision of two pulses these usually annihilate each
the situations of temporal chaos and hyperchaos de- other, as expected for reaction-diffusion systems, but
scribed above are to be attributed to interacting spatial sometimes one or even both pulses reemerged from the
and temporal instabilities. collision. The latter effect is denoted as soliton-like be-
The anisotropy of the surface diffusion with the
present system also gives rise to a novel phenomenon, References see page 1049
1040 5 Elementarv Stem and Mechanisms

all these phenomena could readily be reproduced by

theory, as for example shown in Fig. 11 for the effects
of soliton and wave splitting [78].
Parameter ranges for which oscillations of the in-
tegral reaction rate occur are characterized by global
coupling of different parts via the gas phase [79],
mainly by small variations of the CO pressure, since
oxygen is present in large excess under oscillatory con-
ditions. As a consequence of the asymmetric inhibition
of adsorption, a slight decrease ofpco (due to enhanced
reactivity) increases the probability for oxygen adsorp-
tion and hence causes a positive feedback loop and
favors synchronization. Frequently, the whole surface
oscillates uniformly in phase. At lower temperatures
(around 430 K) elliptical target patterns on an oscilla-
tory background are also observed (Fig. 12) [76], which
could be modeled theoretically by assuming defects act-
ing as pacemakers [80]. At high temperatures ( > 540 K),
standing waves are also formed which take the form of
Figure 10. PEEM images, recorded at an interval of 3s, from stripes of rhombic cells [76], which again could be mod-
a Pt(ll0) surface during CO oxidation at T = 485 K. PO, = eled by taking gas-phase coupling into account [8 11.
3.5 x 10-4mbar, pco = 1 x 10-4mbar. Dark pulses with in- In summary, the rich variety of phenomena asso-
creased oxygen coverage propagate as solitary waves along the
(001) direction as indicated by arrows [77].
ciated with catalytic CO oxidation on Pt( 110) single-
crystal surfaces under isothermal, low-pressure con-
ditions has been widely explored experimentally and
havior. Moreover, occasionally a pulse was observed largely understood theoretically.
to emit another one in the opposite direction (wave
splitting). Since the external parameters were identical
everywhere, these unexpected effects have again to be 5.2.8.4 Oxidation of Carbon Monoxide on Other
attributed to the local defect structure of the surface. Surfaces
Under the assumption that the local 1 x 1 + 1 x 2
reconstruction is not perfect everywhere (and conse- Carbon monoxide oxidation has also been extensively
quently the oxygen sticking coefficient also varies), studied with other catalysts. While the Langmuir-

Figure 11. Theoretical (one-dimensional) profiles of solitary waves propagating along the I direction with time where L> denotes the con-
centration of 0 atoms causing the dark pulses in the PEEM images of Fig. 10: (a) collision of two pulses propagating in opposite directions
in a defect region causes soliton-like behavior; (b) if a single pulse enters an appropriate defect zone, two pulses propagating in opposite
directions are created (wave splitting) [78].
 5.2 Microkinetics 1041

Figure 12. A sequence of PEEM images (200 x 300pm2) re-

corded at intervals of 4.1 s (30 s between the last two images) from
- 50 nm
Figure 13. Scanning tunneling microscopy (STM) from a
a Pt(l10) surface during CO oxidation showing the evolution of Pt(210) surface after prolonged CO oxidation at T = 480K,
so-called target patterns: T = 427 K, PO, = 3.2 x mbar, PO, = 2.0 x mbar, pco = 6.7 x mbar, demonstrating
pco = 3.0 x 10-5mbar [76]. the formation of facets preferentially oriented along the (001)
direction with average mutual spacings around 15 nm [95].

Hinshelwood reaction scheme formulated above is

generally valid, there exist quite some differences both the absence of a catalytic reaction, thermally activated
with respect to the observed phenomena as well as reordering takes place, and the initial situation is re-
with the microscopic mechanisms causing kinetic stored. The increase in reactivity has to be attributed
instabilities. to an enhancement of the oxygen sticking coefficient,
Prior to Pt(1 lo), the behavior of the Pt(100) single- as verified in experiments with a cylindrical Pt single-
crystal surface was investigated in quite some detail crystal sample exhibiting all surface orientations of the
[49, 57, 82-85]. Again, a reconstruction mechanism (001) zone. There the (210) plane was found to exhibit
similar to that of Pt(ll0) is in operation. The clean the highest value of the 0 2 sticking coefficient [94]. In-
Pt( 100) surface exhibits a quasihexagonal (hex) config- deed, the latter plane was also found to exhibit kinetic
uration of surface atoms which is transformed under oscillations [59, 941. Since the clean Pt(210) surface is
the influence of adsorbed CO into the normal 1 x 1 not reconstructed, the simple reconstruction model
configuration [86-901. However, in contrast to Pt(1 lo), at first seemed to fail to account for the oscillatory
there is now a much larger difference in the oxygen kinetics. However, it was found that this plane indeed
sticking coefficient, namely about 0.3 on the 1 x 1 facets under reaction conditions, preferably into (1 10)
phase and < l o p 3 on the hex surface [91, 921. As a and (310) orientations. On the (110) (and related) mi-
consequence, the parameter range for the occurrence of crofacets then, the same mechanism is operating as
kinetic oscillations is much wider than with Pt(ll0) with the respective extended single-crystal surfaces [60].
[79], and the global coupling mechanism through var- Figure 13 displays an STM image from a Pt(210) sur-
iations in the partial pressures is less efficient. This face after prolonged reaction where the facet formation
effect of imperfect lateral coupling causes the rate is directly discernible [95].
oscillations as well as the associated spatio-temporal Another, principally different mechanism comes
concentration patterns to become much less regular into play, however, with CO oxidation on palladium
than with Pt(1 lo). at low pressures, and even occurs with Pt catalysts at
Even on the latter surface, however, the situation higher pressures. Kinetic oscillations have been found
may become even more complicated. Under certain with Pd(ll0) and (1 11) single-crystal surfaces at total
conditions, the structure of the flat surface transforms pressures exceeding about mbar with a large ex-
into a sequence of steps and terraces (facets), which cess of oxygen in the gas phase [96-991. As outlined
process is associated with a continuous variation of the
reactivity of the type as displayed in Fig. 1 [93]. In References see page 1049
1042 5 Elementary Steps and Mechanisms

above, with Pt the normal Langmuir-Hinshelwood mation of platinum oxides [110]. Quite recently, the
mechanism causes the appearance of a clockwise (cw) application of in-situ X-ray diffraction with supported
hysteresis in the CO2 production rate if the CO pres- Pt catalysts revealed even more direct evidence for the
sure is continuously increased and decreased again. operation of the oxide mechanism. From analysis of
With Pd such a cw hysteresis loop is also observed at angular diffraction profiles it was concluded that the
low po2, but it changes into counter-clockwise (ccw) rate oscillations are associated with periodic oxidation
upon increasing the 0 2 pressure [97]. One therefore and reduction of PtO and Pt304, reaching a maximum
obtains a cross-shaped stability diagram by plotting the degree of oxidation of about 20-30% [lll]. It is felt
transition points of the cw/ccw hysteresis on a poZ/pco that the oxide mechanism is prevailing in CO oxidation
diagram [99], and the crossing point marks the lower on Pt catalysts, whenever the experiments are per-
limit of poZ for the occurrence of oscillations. This formed near atmospheric pressure, even if single-crystal
mechanism has to be attributed to the participation of samples are used [112].
another species, namely oxygen atoms which may be Still another mechanism, the carbon model, was
dissolved below the surface (i.e. subsurface oxygen) proposed in order to explain kinetic instabilities in CO
[97]. If the surface is largely covered with oxygen, 0 oxidation [113, 1141 in which it was assumed that de-
atoms will start to penetrate below the surface whereby activation of the surface by buildup of C atoms is fol-
the surface itself becomes less active, i.e. the oxygen lowed by their oxidative removal. So far, however, no
sticking coefficient is reduced. As a consequence, the convincing evidence for the operation of this mecha-
surface becomes predominantly covered by CO, and nism can be offered.
now subsurface 0 atoms are segregating back to the It should be mentioned in this context, that with CO
surface from their reservoir until the initial situation is oxidation on polycrystalline Pt catalysts near atmo-
reestablished and one oscillation cycle is completed. spheric pressure conditions, not only more or less
Inclusion of such a subsurface species into the reaction regular periodic rate oscillations were found, but that
model yielded satisfactory theoretical description of the chaotic temporal behavior was also identified in a
observed kinetic phenomena [loo, 1011. number of studies [115-1181.
The existence of subsurface oxygen at Pd surfaces
manifests itself mainly through the inverse dipole mo-
ment which leads to a lowering of the work function 5.2.8.5 Other Isothermal Systems with Oscillatory
Ap, instead of the increase usually caused by negatively Kinetics
charged 0 atoms on the surface [102, 1031.
A similar subsurface species may also be formed Apart from CO oxidation, quite a number of other
on Pt(100) and (110) surfaces under low pressure con- catalytic systems was found to exhibit rate oscillations
ditions where the work function may become even and other kinetic instabilities which have not primarily
lower (by up to l e v ) than that of the clean surface to be attributed to thermokinetic effects but to the un-
which effect causes the appearance of very bright spots derlying surface chemistry. Among these, reactions of
in the PEEM images [104, 1051. However, it does not NO with either CO, H2, or NH3 on a Pt(100) single-
play a major role with the kinetic instabilities at low crystal surface have been explored in most detail and
pressures and does, hence, not affect the validity of the will hence be described here to some extent. These re-
reconstruction model outlined above. actions have a basic feature in common, namely an
For platinum, the situation may also become quite autocatalytic step associated with the dissociation of
different at higher oxygen pressures. It is known that adsorbed NO.
for poZ 2 1 mbar Pt may form oxides, and the time- +
With the reaction NO CO --f 4N2 + CO, kinetic
scale on which such oxides are reduced by CO were oscillations were observed with a polycrystalline Pt
found to be similar to the period of rate oscillations ribbon in the low4mbar pressure range [119], following
[106]. Therefore, an oxide model was proposed [lo71 a short report on such effects with Pt(100) at extremely
which assumes that part of the active surface covered low pressures ( x mbar) [120]. Subsequently, this
by chemisorbed oxygen atoms is transformed into an reaction became subject of extended investigations with
inactive oxide state. This oxide may then be slowly re- Pt(100) in the lop7 to lop5mbar pressure regime [121-
duced by CO whereby the initial active state of metallic 1271. No oscillations were observed on Pt(ll1) and
Pt surface is restored. Experimental verification of this Pt(llO), which planes were found to be much less re-
mechanism was sought in Fourier transform infrared active in dissociating NO, in accordance with findings
spectroscopy (FTIR) experiments which were, how- made with the cylindrical Pt single-crystal sample [ 1251.
ever, not very conclusive [108, 1091. Indirect proof was With Pt(100) kinetic oscillations occur over a wide
obtained by solid-state potentiometry which experi- range of the p ~ 0 : p c oratio within two temperature
ments demonstrated that the conditions under which windows. In the low temperature (1430 K) range the
rate oscillations occur coincide with those for the for- oscillations occur on a pure 1 x 1 substrate. They are
 5.2 Microkinetics 1043

retical modeling [123, 1301. It therefore accounts for

the experimental observations in the low-temperature
window.
The oscillations in the high-temperature range are
associated with the adsorbate-driven hex .e 1 x 1
transformation of the surface structure. A qualitative
3.0 theoretical description could be achieved by including
I , I this step in the model [123], which was recently ex-
tended further by incorporating more accurately the
growth kinetics of the 1 x 1 phase triggered by lifting
the hex reconstruction [ 1311. Even then, however, the
T [KI
agreement between theory and experiment is not com-
Figure 14. Bifurcation diagram for the NO + CO reaction on pletely satisfactory, most probably due to the presence
Pt(100) for fixed pco NO = 4 x mbar as a function of of surface defects which play a significant role in the
temperature T in the upper temperature window. Open squares dissociation of NO [123] and may be modified by the
denote the amplitudes in the oscillatory regime, while full squares
represent stationary rates. The inset shows the Feigenbaum sce- reaction [132].
nario with the sequence of period doublings ( P I to p ~ and
) tran- Reduction of NO by either H2 or NH3 does not
sition to chaos (c) [126]. proceed along single pathways but through branching
channels whereby the aspect of selectivity also comes
+
into play. In the NO H2 reaction on Pt(100) both N2
not sustained, but may be initiated by a small temper- and NH3 are formed (apart from a minor yield of
ature jump after which they decay within a few cycles N20) [133, 1341 whereby chaotic kinetics were also
[123]. This effect is due to insufficient lateral coupling identified [135]. In the NO + NH3 reaction the main
as was verified by imaging spatio-temporal concen- products are N2 and N20, and oscillatory kinetics were
tration patterns by PEEM [127]. Periodic modulation found both with polycrystalline platinum at higher
of the temperature with small amplitude ( x 1-3 K) pressures [136, 1371 as well as in the lo-’ to lO-’mbar
suffices to create sustained oscillations [124]. In the pressure range with Pt(100) [138, 1391. The dynamic
upper temperature range ( 2450 K) the oscillations are behavior of both systems is nearly identical, and the
not damped and occur on a laterally uniform surface mechanism is obviously rather similar to that in the
whose structure switches periodically between 1 x 1 NO + CO reaction. Consequently, successful mathe-
and hex, similar to the CO oxidation reaction. The matical modeling could be achieved on the basis of
transitions to steady-state rates at both limits of the an analogous reaction scheme [140], and the participa-
high temperature range are illustrated by the bifurca- tion of the hex + 1 x 1 structural transformation was
tion diagram reproduced in Fig. 14. At the upper limit, demonstrated experimentally [138, 1411.
oscillations develop via a Feigenbaum scenario from NO is much more readily dissociated on Rh than on
small amplitude chaotic oscillations, while at the lower Pt, and oscillatory kinetics with this catalyst material
limit the transition to stationary kinetics is discontin- +
were again found with the NO H2 and NO NH3 +
uous and associated with the onset of spatio-temporal reactions with field electron microscopy [18, 1421 as
pattern formation [126, 1271. well as with a Rh(l10) single-crystal surface [143]. In
+
The mechanism of the NO CO reaction (with for- the latter study, by applying PEEM, quite unusual
mation of N20 in a side reaction being neglected) in- spatio-temporal patterns of the type shown in Fig. 15
volves dissociation of adsorbed NO as rate-limiting were detected, namely rectangularly shaped target pat-
Step [123]. This process, NOad + * + N,d Oad, re- + terns and spiral waves. This effect has been attributed
quires (formally) an additional vacant adsorption site to an anisotropy of the surface diffusion which, in ad-
(*). In the subsequent steps of product formation, dition, is influenced by adsorbate-induced reconstruc-
+
namely 2N,d + N2 2* and toad o a d + C02 23, + + tion effects [144].
more free sites are created than are consumed by the The H2 + O2 reaction on Pt deserves brief mention-
initiating process of NO dissociation. Hence, autoca- ing in this connection, since kinetic oscillations at high
talysis with respect to the formation of free sites is the pressures had been reported quite early for this system
consequence which explains the occurrence of a surface [9] and were later investigated again in quite some de-
explosion, i.e. of extremely narrow peaks, in thermal tail [145]. Quite recently, the heat generated with this
desorption spectroscopy experiments with NO CO + reaction at a pressure of 10-2mbar was directly de-
coadsorbed on Pt(100) [128, 1291. This autocatalytic termined experimentally [146]. Obviously, the quoted
process is also responsible for the occurrence of kinetic studies were not conducted under isothermal condi-
oscillations without involving a structural transfor-
mation of the surface as demonstrated by proper theo- References see page 1049
1044 5 Elementary Steps and Mechanisms

Figure 15. Concentration patterns associated with the NO + H2 reaction on a Rh(l10) surface: (a) elliptical target patterns, T = 427 K,
PNO = 1.6 x 10-6mbar, PH> = 1.8 x mbar; (b) nucleation of square-shaped target patterns, t = 595 K, PNO = 1.6 x 10-6mbar,
pH2= 5 x mbar; (c) same conditions as (b) but 60 s later [143].

tions so that heat transfer comes into play which effect

does, however, not account for the observed time scales
of oscillations. However, the experimental findings
could be satisfactorily modeled on the basis of an oxi-
dation-reduction mechanism similar to that proposed
for CO oxidation [147].
No kinetic oscillations could be observed with this
reaction on an extended Pt( 100) single-crystal surface
at low pressures, but merely simple bistable behavior.
Interestingly, if a field emitter tip was used instead on
which the (100) plane of only about 50nm diameter
was adjacent to other crystal planes, oscillatory phe-
nomena occurred [148]. It is felt that this effect is of
more general relevance for the catalytic properties
of small particles and it is therefore discussed further
below.
Figure 16. Space-time diagram of the temperature profile of a
5.2.8.6 Thermokinetic Phenomena 1 cm long segment of a Pt ribbon during oxidation of propylene.
While the average temperature is kept constant, a local temper-
ature front moves back and forth [162].
Due to the pronounced temperature dependence of
chemical rate processes, even small deviations from
isothermal conditios are expected to be of strong influ-
ence on the dynamic behavior. Such effects are very which was solely heated by the enthalpy released by the
likely to occur in any studies with “real” (either mon- reaction. It turned out that the oscillatory behavior
olithic or supported) catalysts conducted near atmo- changed substantially if the wire loop was cut into
spheric pressure, where frequently temperature changes two parts, again demonstrating the importance of heat
of several tens of degrees or even more are found. transport in such systems [157].
Local variations of temperature can most con- Systematic studies on wave propagation in electri-
veniently be recorded by infraed thermography [ 1491, cally heated wires have been reported for various re-
and numerous reports on such phenomena associated actions, including oxidation of ammonia and hydro
with catalytic CO oxidation on supported catalysts can carbons [149, 158-1641 as well as the endothermic de-
be found in the literature [150-155]. Among others, composition of CH3NH2 on a Pt wire [165]. Stationary
these experiments demonstrated the importance of (Turing) patterns as well as moving fronts were ob-
thermal coupling between different catalyst pellets served, the latter being associated with macroscopic
whose variation affects the degree of synchronization rate oscillations. As an example, Fig. 16 shows the
of the rate oscillations [154, 1551. By using a thin irregular motion of fronts associated with oxidation of
evaporated Pt film, the propagation of reaction waves propylene on a Pt ribbon which was heated electrically
during CO oxidation could be studied [156]. In another and maintained at constant total resistance whereby
experiment with the same reaction, a Pt wire was used the integral kinetics became chaotic (Fig. 17) [162].
 5.2 Microkinetics 1045

above [165]. The basic mechanism of the kinetic oscil-

lations in this latter system (exhibiting temperature
amplitudes of up to 500K) is in fact rather simple. In
the reactive state the temperature drops due to the
endothermicity, and at low enough temperature the
surface is then blocked by an inhibiting species. As a
consequence, the continuing electrical heating causes
the temperature to rise again until the inhibiting species
desorbs and the high reactivity is restored.
Although with the systems discussed in this section
the details of the reaction mechanism and of the ki-
.22 1 -I netics of the elementary steps is much less understood
than for the well-defined single-crystal systems de-
1 I I , I , I I

0 500 1000 1500 2000 2500 scribed in the preceding sections, in these cases the
t [secl basic features of spatio-temporal pattern formation
Figure 17. Chaotic oscillations of the total heat generated by could also be modeled successfully. This is because the
propylene oxidation on an electrically heated platinum ribbon decisive effects are thermokinetic in nature and can be
while the electrical resistance is kept constant [162]. approximated by a heat-balance equation in which the
chemistry of the reaction is reduced to a single variable
and the surface diffusion of the adsorbates is neglected
Instead of keeping the resistance (= average temper- [ 179-1 841. Coupling through the gas phase may also be
ature) constant, similar experiments were performed mostly neglected, although its inclusion may give rise
under different constraints, in which either the voltage to quantitative changes [ 1791. The basic equations take
or the heating current [161] was kept constant, and the general (dimensionless) form
the resulting dynamic properties were found to differ
significantly. Quite generally, such conditions represent
global constraints and may lead to spatio-temporal
pattern formation as a consequence of symmetry
breaking [ 166, 1671. (5)
However, similar types of patterns may also be
formed without external constraints, such as those ob- The termf( T ,8, I ) denotes the heat balance, QR is the
served with the oxidation of hydrogen on a Ni ring heat generated by the reaction, Q E ~is the heat ex-
without additional electrical heating [ 168, 1691. Under change with the surroundings, and QH(I) is the energy
certain conditions, a pulse rotating around the Ni ring input by electric current I , if applied. The term g(8. T )
with a period of about 10min was observed. The in- represents the surface chemistry of the catalytic re-
tegral behavior exhibited oscillations with three max- action, with 8 being a characteristic concentration
ima and minima per rotation period. This effect dem- variable. Typically, a species with concentration 8 is
onstrates that the rotating pulse changes its shape consumed by the decisive reaction step and is produced
periodically which is most likely due to nonuniformities in another process.
of the catalyst. Various types of solutions were extensively discussed
If two-dimensional (e.g. foils) rather than one- in the quoted literature to which the interested reader is
dimensional (rings or wires) catalysts are used, the re- referred to. It is just mentioned that for certain param-
sulting spatio-temporal patterns are usually still more eter ranges many stable solutions were found to coex-
complex, as demonstrated with the HZ 0 2 reaction + ist, depending on the initial conditions. That means
that even for identical steady-state control parameters
on Pt [170, 1711 and Ni [160, 1721.
Various approaches can be found in the literature to the dynamic behavior may differ considerably, which
implement nonisothermal effects in the theoretical renders this field rather complex.
modeling of the (integral) kinetics. For example, a
simple mechanism for thermokinetic oscillations is
possible in which catalytic sites are blocked at low 5.2.8.7 Some Consequences and Future Prospects
temperature and reactivated at higher temperature.
Such schemes have been analyzed in general form [ 173, The phenomena associated with the nonlinear dynam-
1741 and applied to various oscillatory reactions such ics of catalytic reactions demonstrated that the true
as NO + CO on Pd [175], H2 + 0 2 on Pt [53] and, in situation may be far more complex than expected on
particular, CO + 0 2 on Pt [176-1781 as well as with
the endothermic decomposition of CH3NH2 mentioned References see page 1049
1046 5 Elementary Steps and Mechanisms

the basis of conventional kinetic considerations. This

may also have implications for other areas of catalysis,
a few of which will be outlined by means of recent
experimental developments.

A Periodic Forcing
Instead of adjusting the control parameters in a way
that sustained rate oscillations develop, a system may
also be subject to periodic modulation of one of these
external parameters. The goal of increasing the yield 1

and (what would be even more important) the selec- 100 200
t Is1
tivity in this way has been achieved in several reports
on “real” catalytic systems [13, 185-1891. The response
of a system exhibiting autonomous oscillations with
period TOto external forcing with period T,, and am-
plitude A may be classified in the following way [190- - 50
>
1921. If the response of the system with period T, oc- LE 40
curs with fixed phase relation to the modulation, the 2 30
system is entrained, and the ratio between T, and T,, 20
may be expressed as that between two small integer
10
numbers, T,/Tex= k / l . With k / l = 1, the entrainment
is harmonic, for k / l > 1 it is superharmonic, with
k / l < 1 it is subharmonic. If the phase difference be- tlsl
tween response and modulation is continuously vary-
4.05
ing, the oscillations are denoted as quasiperiodic. The N

a
0

behavior of such a system may be rationalized by a 3.95

“dynamic phase diagram” in which the regions of
entrainment and quasiperiodicity are marked as a
function of TeX/Toand A . The structure of this dia-
gram does not depend on the specific features of the
reaction system, but only on its type of bifurcation
around which the perturbation occurs [ 191, 1921.
Single-crystal experiments on periodic forcing have
been performed with the CO oxidation on Pt( 100) [ 1931 50 100 150 200
and Pt(ll0) [21]. As an example, Fig. 18 shows a se- t 151
quence of time series for entrained and quasiperiodic
oscillations recorded with the latter system. The result-
ing experimental phase diagram (Fig. 19(a)) is in good
agreement with the results of a theoretical treatment
of the system on the basis of the mechanism outlined
above [194] (Fig. 19(b)).

B Uniform Modification of the Surface Composition

It is common practice to alter the properties of a cata-
lyst by uniform modification of its chemical com-
position, e.g. by alloying. The resulting effects on the
catalytic properties are usually discussed in terms of
local (i.e. atomistic) concepts, such as the “ligand” or 1
100 200 300 400 500
“ensemble” effects [195] (see this Handbook Part A, t Is1
Chapter 5.3.3) by which the modification of the elec-
Figure 18. Time series for periodically forced oscillations in the
tronic properties of a surface atom by its neighbors or CO oxidation on a Pt(ll0) surface exhibiting sustained oscil-
the specific configuration of surface atoms forming the lations with frequency vo. Modulation of PO, with frequency vp
active site are characterized. Quite different phenom- and amplitude A (as percentage of the basic value): (a) 1 : 2 sub-
ena on mesoscopic length scales may come into play harmonic entrainment, YO = 0.09s-l, vp = 0.18s-’, A = 1.2%; (b)
with systems exhibiting characteristics of nonlinear dy- 2: 1 superharmonic entrainment, vo = 0.25 s-’ , vp = 0.1 1 s-’ ,
A = 1.2%; (c) 7 : 2 superharmonic entrainment, vo = 0.185 S K I ,
namics such as spatio-temporal pattern formation. vp = 0.047s-’, A = 1.2%; (d) quasiperiodic behavior, vo =
These features are governed by kinetic parameters 0 . 2 5 ~ - ’ vp
, = 0.016~-’,A = 1.2% [21].
 5.2 Microkinetics 1047

,? b
ns , I
At% -..-pd ,
I
I
I
,
/

0
112 2/3 1 L / 3 3/2 513 2
Figure 20. PEEM image from a Pt(l10) surface on which the left
Figure 19. Dynamic phase diagram for periodically forced os- part was covered by 5% of a monolayer of Au during CO oxida-
cillations in the CO oxidation on a Pt(ll0) surface. Existence tion: T = 460 K, po2 = 4 x mbar, pco = 4.6 x mbar
range for entrained and quasiperiodic oscillations as a function of [196].
the period ratio of modulation and autonomous oscillations,
i“, : To, and of the amplitude (as percentage of the base pressure)
of the modulated 0 2 partial pressure. (a) Experimental results,
where shaded areas indicate conditions for quasiperiodic behavior the next step consists of prefabricating heterogeneous
between the sub- and superharmonic entrainment bands [21]. (b) structures with appropriate dimensions. It is generally
Theoretical result, obtained with the quoted system of differential known that formation and propagation of nonlinear
equations modeling the kinetics. Types of bifurcation: ns = Nei- waves may be markedly affected by the spatial bound-
mark-Sacker, pd = period doubling, snp = saddle node [194].
ary conditions in that, for example, certain modes are
selected, or the propagation through narrow channels
is suppressed etc. [197-1991. Photolithographic tech-
(such as rate constants, diffusion coefficients etc.) uuer- niques, as developed for microelectronics, offer a con-
aged over length scales typical for the resulting con- venient way to prepare surfaces with such micro-
centration patterns, i.e. of the order of about 1 pm, and structures. The first experiments of this type were
may already be substantially altered by rather small performed with a Pt(ll0) surface, onto which a tita-
amounts of foreign atoms. As an example, Fig. 20 nium mask was deposited. The latter oxidizes and is
reproduces a PEEM image reflecting spatio-temporal then completely inert in the CO oxidation reaction
pattern formation on a Pt(ll0) sample subject to which is hence restricted to the bare Pt areas [200]. A
steady-state CO oxidation where a part of the surface PEEM image from such a surface exhibiting formation
was uniformly covered by about 5% of a monolayer of concentration patterns is displayed in Fig. 21.
of Au atoms, while the other part was pure platinum Clearly in this way novel dynamic effects develop
[196]. Both the phenomenology as well as the dynamics which would not exist with uniform surfaces.
(velocity of wave propagation) are obviously signif-
icantly affected. The resulting effects on the overall D Phenomena on the Atomic Scale
kinetic properties have still to be explored, but it will The small particles of a “real” supported catalyst usu-
certainly not be possible to describe them properly in ally have dimensions of only a few nm, much smaller
terms of the quoted atomistic concepts. than the typical patterns found with isothermal re-
action-diffusion systems on extended uniform surfaces.
C Surfaces with Preformed Mesoscopic Structures Typical nonlinear effects with such systems are, how-
Instead of modifying a catalytic surface homogene-
ously, e.g. by uniform deposition of another material, References see page 1049
1048 5 Elementary Steps and Mechanisms

velopment of kinetic lattice-gas models, applicable also

to conditions far from equilibrium, is to be expected in
the near future.
The experimental situation has been significantly
affected by the possibility of observing nonlinear phe-
nomena with near-atomic resolution by the application
of field emission and field ion microscopic techniques
(FEM and FIM) [18, 19, 205, 2061 (see this Handbook
Part A, Chapter 5.3.5). Even if well-developed patterns
such as spirals may not develop for geometric reasons
on the small tips used in these experiments, propagat-
ing reaction-diffusion waves may become clearly dis-
cernible. Usually, their interfaces are much sharper
than expected for reaction-diffusion systems of non-
Figure 21. Pattern formation on a microstructured Pt(ll0) sur- interacting particles, and this effect is most likely at-
face during CO oxidation. Two of the patches are in uniform states tributed to , the operation of attractive interactions
while on the H spirals and propagating pulses develop [200]. by which mean-field descriptions become invalid, and
which may indeed lead to the formation of very sharp
interfaces and even to “uphill” diffusion opposite to an
ever, of thermokinetic origin, for which only the prop- existing concentration gradient [207].
erties averaged over macroscopic (= 1 mm) length scale A quite interesting effect was observed with the
are of significance, as outlined above. H2 + 0 2 reaction on Pt [148]. As outlined in Section
Quite different problems come into play, however, if 5.2.8.4, on an extended Pt(100) surface only bistable
processes occurring near the atomic scale become sub- behavior is found, whereas if the same plane is exposed
ject of closer inspection. On the theoretical side, for- as small area on a field emitter tip under certain con-
mulation of kinetics in the framework of a mean-field ditions oscillatory behavior is observed. This is illus-
description in terms of differential equations becomes trated by the sequence of images reproduced in Fig. 22.
questionable. Such an approximation is per se only The central Pt( 100) region becomes periodically acti-
justified if the mobility of the adparticles is sufficiently vated by reaction-diffusion waves triggered from ad-
high and if interactions between them may be ne- jacent higher index planes, and as a consequence also
glected. An alternative approach consists of performing the time-averaged reactivity of this plane is much
lattice-gas-type computer simulations [201], among higher than if existing isolated. It is important to dis-
which models for CO oxidation have attracted par- tinguish this effect from the phenomenon of “spill-
ticular attention [202-2041. Further progress in the de- over”, well-known in catalysis (see this Handbook Part

Figure 22. Series of field ion microscopy (FIM) images from a Pt tip during the Hz + 02 reaction at 3 0 0 K : p ~ ,= 6 x 10-4mbar,
po2 = 5 x mbar. Imaging gases are 0 2 and H20 formed by the reaction [148].
 5.2 Microkinetics 1049

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