1834 C. P.

FENIMORE
AND G. W. JONES VOl. 66

CONSUMPTION OF OXYGEN MOLECULES IN HYDROCARBON FLAMES

CHIEFLY BY REACTION WITH HYDROGEN ATOMS
BY C. P. FENIMORE
AND G. W. JONES
General Electric Research Laboratory, Schenectady, N . Y.
Received March 91, 1969
The rate of consumption of 0 2 is measured by probe sampling through low pressure, flat, premixed flames of CHI, 02,
A or through flames with C ~ Hor
P CaHa fuels, all burnt on cooled porous burners with flame temperatures of 1300 to 1950'K.
[HI is also measured in the same flames by the rate of formation of H D from added DP or DzO, and turns out to be the
concentration required, within 30y0 to account for the observed -d[Oz]/dt accordin to the known rate of the reaction,
H + Oz + OH + 8
0. It is concluded that 02 is consumed chiefly by reaction with atoms in either lean or rich hydro-
carbon flames.

Introduction TABLE I

+
The rate constant for the reaction H
0 is fairly well known,l-a so by measuring [HI,
+
0 2 --t OH RATE CONSTANTS IN L. MOLE-^ S E C . - ~AT FLAME TEMPERA-
TURES
IO,] and -d[02]/dt in hydrocarbon flames, one
(a) H + H ~ O=
kfanard kbaokwsrd
can tell whether this reaction is of major impor- I x I O ~ ~ ~ - ~ ~ 2~. 6OxO1 0~ 1 ~1 ~T- 1~0 ~ ~*0 ' ~ ~
tance for the observed decay of 0 2 . In the flames Hz + OH
(b) H + cop= 3 101ze-aa,aooi~~g 2 . 3 x 101Oe-lo,mo/m
reported in this paper, with CH4, C2H2 or C3Hs CO + OH
fuels, O2is consumed much more by reaction with H H + oz = 1 . 5 x 10s at IIOOOK.:
atoms than in any other way. OH + 0 E: = 18 3 kcal.
(d) H + NzO 4 X 1011"'6sa'O/RTa
Experimental Ns + OH
Water-cooled, flat-flame burners4 were used at reduced (e) + Nzo lolls-az'ooo~Rrlo
pressures to obtain moderately thick, flat flames. Any rich 2N0 or
flames used were free from soot. Temperature traverses approximate 0.9 x 1011e-*7,soo/nT
were made with quartz-coated thermocouples corrected for values only
radiation,' s a m p h g was through h e quartz Probes, and k. in Table I is the unchecked constant used to determine
analyses were carried out on a mass spectrometer. 101. The first value is the approximate estimate from our
The composition traverses were recast as reaction rates own work; the second is obtained from the assumption that
through the flame already described.* Briefly, the mole NO decays a t moderate temperatures via the reverse process,
fraction of each species was plotted US. distance from the and from Kaufman and Kelso's accurate determination of
surface of the burner, Xi v;. Z . Using approximate binary this decay rate.7 For the rough estimates of [O] made in
diffusion coefficients,s the diffusion velocity of the ith species this paper, it does notmatterwhich expression is used.
was calculated through the flame, VI = -(Di/Xd dXd&' It should be pointed out that a ercentage comparison of
and then the fraction of mass flow due to the 1th species [HI measured via reaction (a), + ~~0 = HD + OD,
with [HI re uired to destroy 02 ma reaction (c) depends on
u* = -
M the ratio rather than on the absolute value of either
constant. This is all to the good, for kb, IC, and kd of Table
lnthese formulas, D, = diffusion coefficient, M average I were determined relative to k, and while these constants
molecular weight, M~ = molecular weight of the jth species, are only claimed to be correct to within a factor of two, their
= gas velocity as calculated from the known mass flow pv ratios are correct to perhaps 30%. This estimate is sugges-
and the density Finally, the rate of appearance of the ith ted because we find a 3O% discrepancy between Our data and
species due to chemical reaction was obtained, it is equal to a conclusion which we believe to be consistent with them.
( p v / M i ) dGi/dz. It would be very difficult to estimate separately the errors
The concentrations of radicals were estimated by 'in& 8 resulting from approximate diffusion corrections, sampling
cator*#reactions as aheady described. The estimates of [HI errors, etc.; but an earlier comparison of reaction rate ratios,
are accurate to d t h i n a factor of two at least, because in&- k a h b with the reverse constants, gave about the same dis-
pendent estimates by other methods have been found to agree crepancy'a
at least this we11.8 A few estimates of [O] must be viewed Results from a Typical Run.-Some analyses and
more skeptically because the method used for this radical
has not been checked against other methods. derived ratesof reaction in CH( flames are plotted
The rate constants used to interpret the data are listed in in Figs. 1 to 3, and numerical data are listed in
Table I. The reverse constants for reactions (a) and (b) Table 11. The flame described by Fig. 1 is dis-
were calculated from the forward constants and from a tabu- cussed in detail as an example. This had the
lation of equilibria over the temperature range of interest.' reactant composition CH( + 1.87 o2+ 8~ + H ~ ,
IC. is known from measurements of the rate of consumption
of Oz in the early parts of three Hz, 01 flames, with simul- and was burnt with a mass flow of 8.65 x
taneous measurements of [HI via the formation of HD from g./Cm.', Sec. a t a pressure of 7 cm. Small con-
added heavy water.* The value of Table I lies between an centrations of C2 hydrocarbons and perhaps HzCO
estimate by Semenov'; 6.7 X lo6 a t 793' which would be- were formed in the strongly luminous zone, but did
come 1.8 X 108at 1100'K. if one accepts his activation en-
ergx of 18.5 kcal;. and Baldwin's%estimate of 2.7 X 108 at not persist into the post flame gas.
793 , which would become 0.7 x lOBat 1100'K. on the same The concentration of H atoms was estimated by
basis. two different methods. First, heavy water was
(1) N. N. Semenov. Acta Physicochim., 20, 290 (1945). added to the reactants and the rate of formation
(2) R.R.Baldwin, Trans. Faraday SOC.,62,1344 (1956). of HD measured just beyond the main reaction
(3) c. P. Fenimore and G. W. Jones, THIS JOURNAL, 63, 1154 zone.* At 0.4to 0.55 cm. from the burner surface,
(1959).
(4) W. E. Kaskan. "6th Symposium on Combustion," Reinhold (7) F. Kaufman and J. Kelso, J . Chem. Phys., 2 3 , 1709 (1956).
Publ. Corp., New York, N. Y.,1957, p. 134. (8) C. P. Fenimore and G . W. Jones, THISJOURNAL, 62, 693
(5) A. A. Westenberg, Combustion & Flame, 1, 346 (1957). (1958).
(6) B. Lewis and G. von Elbe, "Combustion. Flames and Explosions (9) C. P. Fenimore and G . W. Jones, ibid., 62, 1678 (1958).
of Gases," Academic Press, New York, N. Y.,1951. (IO) C. P.Fenimore and G. W. Jones, ibid., 62, 178 (1958).
Nov., 1959 CONSUMPTION OF OXYGEN MOLECULES FLAMES
IN HYDROCARBON BY HYDROGEN 1835

this method gave [HI = 50 X mole/l. in

the post flame gas at 1780°K. Second, part of
the Hz in the fuel was replaced by Dz and the rate
of formation of H D measured early in the flame.3
-
-- TEMPERATURt

500'K.
I n this second method, one must correct for the Y
fact that the gross rate of formation of HD is larger H2A 3

than [HD] observed because H D undergoes

simultaneous oxidation a t a rate which is approxi- --
'
COIA
z!
E
I
c
W

mated by CO2IA
300'
iHD1
hml x (rate of formation of water from H ~ )

The quantity (rate of formation of water from Hz)

is about 8 [COz][Hz]/[CO], see below, and then the
gross rate of formation of H D a t 1100°K. turned
out to be 4 times the [HD] observed. Equating
this to k'[H][Dz] where k' is the rate constant
for H + +
Dz+ H D D,3J1[HI = 80 X lo-' at
l l O O o , z = 0.137 em. Thus [HI by the two meth-
ods agreed to &25%.
The [HI found above is of the right order to
account for the observed rate of consumption of
02.If O2 is consumed only via reaction (c), - [O,]
= k , [ 0 2 ][HI. Introducing the measured [OZ]
and [OZ]a t 110O0K., and taking k, from Table I,
we get [HI = 60 X mole/l. This agrees
very well with [HI as measured directly. It can 0.3 c i CMS
be shown that reaction (c) accounts for - [ 0 2 ] DISTANCE FROM BURNER SURFACE.

not only a t 1100" but up to 1600"; for a plot of Fig. 1.-Analyses and derived reaction rates through a
log - [ 0 2 ] / [ O z us. ] 1/T is linear and possesses a moderately rich C&, Hz, 0 2 , A flame.
slope corresponding to 17 kcal. which is about the
activation energy of reaction (c). At temperatures STRONGLY
-2000°K
much above 16OO0K., toward the end of the re- REGION

action zone, - [OZJ/[OZJ decreases because the

reverse of reaction (c) increases rapidly.l2
Some additional information can be obtained W'

from Fig. 1. Until CHh has fallen below 10%. of - 150O0:

3

its initial value, [CO] is 70 to 85% of -[CHI]. w

s
w
0

This agrees with the common belief that CO is the

only carbon oxide formed directly from CHI, and
that COz is formed only from the intermediate CO.
Now if the last sentence is accepted, it can be -1000'
shown that H20 is not formed directly from CHI
either, but only from the Hz present a t any time.
We have found previously that in the early parts m'0
of flames of mixed H2 and CO fuel, a situation in
I I
which COz is surely formed only from CO, [H;O]. e- 120-
[CO]/[COZ][Hzl = 8; and this was considered VI

2 0
fair agreement with the ratio ka/k-b = 12 which L

would be expected if HzO were formed from Hz 5u' 60-

only via the reverse of reaction (a), and C02 from 5c
CO only via the reverse of reaction (b).a There- 2
fore, if HzO were formed from CH, in the present
flame as well as from Hz, but C02 still formed only DISTANCE FROM BURNER SURFACE.
from CO, one must have [Hi0I [COI/ [COzJ [Hzj > Fig. 2.-Results through a very rich CHI, 02,A flame.
8. But over the region z = 0.125 to 0.3 cm., we
find this ratio only 5 I 1; that is, the observed
rate of H2O formation relative to COz formation
(11) G. Boato, G. Cared, A. Cimino, E. Molinari and G. G. Volpi,
J . C h e n . Phgs., 24, 783 (1956).
is surely no greater and probably even less than we
(12) The inhibition of (0) toward the end of the reaction zone can- expect only from the Hzpresent. I n other flames,
not be a temperature effect because the reverse of (c) has practically [Hi01[CO]/[C02][H2] is sometimes larger, but
zero activation energy. Rather, the build u p of radicals by reaction never significantly greater than 8, and this rules
(c) ultimately limits their own formation. The inhibition sets in
rather sharply; possibly because (c) is a branching reaction, possibly out CH, + OH + CHa + H20 as an important
in part because H atoms can diffuse upstream more readily than 0 reaction in CHI flames; or at least admits it only
or OH. if H 2 0 is consumed in some other step so that the
1836 AND G. W. JONES
C. P. FENIMORE Vol. 63

shows some results for a very rich flame in which

more than 10% of the carbon fed as CH4 appears
as CZhydrocarbons, mostly as C2H2. [HJ is smaller
in this than in the preceding flame and near the
- 1500°K value appropriate to the equilibrium H2 = 2H,
Y for in the burnt gas the equilibrium [HI = 6 X
3
c lo-' mole/l. Small as it is, however, [HI is just
z
0 about that required to destroy O2 via reaction
B (c) a t the observed rate.
- 1000' Figure 3 gives results of a lean flame. I n such
flames, [HI cannot be determined easily in the burnt
gas by adding DzO, but can be estimated roughly
a t least by the residual [H,]. Because the re-
actions H + + +
O2 = OH + +
0, 0 H2 OH H, +
H + H2O = H2 OH are generally equilibrated
in the post flame gas,la the equilibrium 3H2 +
rn.
0
0 2 = 2H20 +2H is also generally satisfied. This
100- consideration, with equilibrium constants, from
ref. 6, gives the approximate [HI titled "other"
Y
.
In in Table 11. Once again [HI is just sufficient
& 50-
-I to react early in the flame with O2 at the measured
W-
rate of - [O,].
Ez 0- Finally, we replaced 10% of the O2 in the re-
0
u
actants by an equivalent amount of N20 in two
=
W flames, those described by Figs. 1 and 3, in order.
-50- to get an estimate of [O] by means of the reaction,
0 0.3 0.6 CMS
DISTANCE FROM BURNER SURFACE I
0 + N 2 0 + 2NO. The effect of this partial re-
Fig. 3.-Results through a lean CH4, 0 2 , A flame. placement was to raise the final temperature by
about 160°K. The general appearance of the
iI500'K curves for reaction rate vs. z was not greatly
changed however. [HI was reduced, see Table 11,
but remained the [HI required by reaction (c) to
W
give the - [02] observed early in the flame. Fur-
thermore, over the temperature range 1000 to
- 1000' c';
.a 1600"K., - [ 0 2 ] / [ 0 2 ] was within 30% the same
W as - [N10]/[N20]; and since N 2 0 reacts with H
atoms with a rate constant, k d of Table I, about
the same as k,, it is evident that N 2 0 also is de-
stroyed chiefly by attack of H atoms. The small
- 500'
amount of NO formed suggests that in the region
of maximum rate of reaction, [O] = 3[H] ap-
proximately in the fuel lean flame, and [O] = [HI
approximately in the rich flame. In both flames,
[0]decays rapidly as one moves downstream into
the post flame gas. Thus [O] behaves differently
from [HI which is about the same in the reaction
zone and in the post flame gas. The result that
[O] is comparable t o [HI in these flames means
that 0 atoms might be important in the decay
of CH4. Our finding that -[02] is accounted
for by reaction (c), however, is not affected by [O]
or [OH] because these species cannot destroy O2
molecules.
Since five times out of five tries we found re-
DISTANCE FROM BURNER SURFACE,
action (e) proceeding a t about the measured rate
Fig. $.-Results through a lean C2H2, 0 2 , A flame. of -[02],we took the chief mechanism of 0 2
destruction in either rich or lean CHI flames as
net H 2 0 formation from decomposing CH, is known a t this point.
zero or less than zero. Flames with Other Fuels.-The remainder of
We sum up the discussion of Fig. 1. It has been Table I1 shows that O2 is destroyed chiefly by
shown that O2 is destroyed chiefly via H atom at- attack of H atoms in rich or lean flames of other
tack just as in the Hz, O2 flame, and that no con- hydrocarbon fuels also. Figures 4 and 5 will be
siderable net formation of COZ or of HzO occurs discussed briefly.
directly in the decay of CH4. (13) (a) E. M . Bulewioz, C. G . James and T. M. Sugden, Proc.
Other CH4Flames.-Four other CH4 flames were Roy. SOC.( L o n d o n ) ,A236,89 (1950); (b) W.E. Kaskan, Combustion d
examined and are discussed briefly. Figure 2 Flame, 2, 229 (1958).
Nov., 1959 CONSUMPTION
O F OXYGEN MOLECULES FLAMES
IN HYDROCARBON BY HYDROGEN 1837

I1~
TABL
Is JUSTSUFFICIENT
THAT[HI I N FLAMES
DATASHOWINQ 0 2 AT THE RATEOBSERVED
TO CONSTJME
Figure
Reactants
0 2
c
1

1.87 1.12
2 3
CHI+
2.56
...
2.310
-
...
1.6V
...
vCzHn+--
1.88
4

4.84
-
c
...
8.33 3.13
5
CaHs+--
...
4.50
A 8 0.4 10 10 8 7.5 17.2 11.33 4.54 5.56
Ha 1 0 0 0 1 0 0 0 0 0
Massflow X 103,g./cm.a 8.65 1.93 8.81 7.96 8.4 5.05 7.26 3.0 3.2 4.23
X sec.
Flame T,O K . 1780 1860 1700 1860 1950 1818 1310 1500 1920 1940
Pressure, cm. 7 14 6 8 7 6 4 3 8 3
107 [HI found via
added D2O 50 5 ... ... 25 15 ... *.. 10 22
added Dz 80 4 60 30 20 10 44 6 6 33
Other *.. ... 30 30 ... ... 50 10 ... ...
107 [HI required by - [OZ] 60 3 40 30 14 10 35 4 7 23
[&O 1 [CO 1 5 5 9 8 8 7 9 8 5 7
tCOzI[Hzl
(1 Also had 0.51 N20per mole CHI in reactants. Also had 0.40 N2O per mole CHI in reactants.
It may be interesting to compare our lean CzHz
flame, Fig. 4, with a very lean C2H2, O2 flame
probed by Fristrom and co-workers.14 Their
+
flat flame was C2H2 3102 burnt at 7.5 cm. Hg
P with burning velocity 71 cm./sec. and calcu-
lated final flame temperature of 1451°K. Ours is
+ +
C2H2 4.8 O2 18 A a t 4 cm. Hg P, 90 cm./sec.
burning velocity, measured final flame temperature
1300°K. At our lower pressure, the strongly
luminous zone is a little thicker (-0.22 em. US. their
-0.16 cm.). We agree in finding that the maxi-
mum CO occurs just about when CzHz has fallen
to zero, and in placing this point within but
I I
I
toward the downstream edge of the luminous zone. 3CH4/A ‘O2lA
Also we agree in finding that the maximum H2
occurs earlier in the luminous zone, about 0.1 cm.
before the maximum CO, and when about 1/2 of the
total fall of O2 has occurred. In both flames,
H 2 0 is near its final value a t the downstream end
of the luminous zone. The principal differences
are: we find more residual Hz in the post flame
region than they do, and we find a much slower
formation of C02. These differences are probably
reasonable since their flame was much leaner.
Figure 4 also shows the course of HD formation
and decay when a little Dz is added to the reactants.
Since HD goes through a maximum, it is easy to
estimate [HI when d [HD]/dt = 0 on the assump-
DISTANCE FROM BURNER SURFACE.
tion3 that
Fig. 5.-A very rich C3Hs, Os, A flame.
-
k’[H] [Dz] = [HDI X (rate of formation of water from Ht)
[Hal that COZ appears to be formed only from the inter-
mediate CO. If this is really so, then the ob-
where IC’ is the rate constant for H + Dz --t HD + served value for the ratio [Hi01[COI/[CO2][Hz]
D. requires the conclusion that little direct net for-
Figure 5 gives some results for a very rich C3H8 mation of HzO occurs from these fuels either, but
flame which resembles the flame described by Fig. 2 that H20is formed chiefly from the Hz present a t
in that [HI is near the calculated concentration in any time.
the burnt gas appropriate to the equilibrium H2 =
2H; [ H I e q u i = 7 x lo-’. The flames described Conclusion
by Fig. 2 and 5 are the only ones in which the post Ignoring the rough estimates of [HI entitled
flame gas contains hydrocarbons, and are also the “other” in Table 11, we find that [HI determined
only ones which contain just the equilibrium [HI via added D2 or D2O is the same within an average
in the post flame gas. deviation of 30% as the [HI required if 0 2 de-
CzHz or C3Hs flames resemble CHI flames in cays solely by reaction (c), and this is true over a
(14) R. M. Fristrom, W. H. Avery and C . Grunfelder, “7th Sym-
20-fold change in [HI.
posium (International) on Contbuation,” Butterwortha, London, There is little doubt that 0 2 is destroyed more
1959. p. 304, by reaction (c) than in any other way. A de-
1838 R. W. KILB Vol. 63

struction of O2 entirely via (c), that is, no con- equilibrium H2 = 2H. It would also agree with
siderable reaction between 0 2 and any hydrocar- experiments on the slow CH,, O2 reaction in static
bon or hydrocarbon radical at all, would be con- systems at 900°K. or higher, where CH, inhibits
sistent with our results and with other observa- its own oxidation presumably by the destruction of
tions on hydrocarbon flames. For it O2 reacts radi~a1s.l~A destruction of O2 only via reaction
only with H atoms, the large amount of CO (c) would require that reactions between 0 2 and
formed in CH2 flames would have to arise by reac- hydrocarbon or hydrocarbon radicals, such as are
tions of 0, OH, H2O with species such as CHI, CH2, presumed to occur in low temperature oxidations
etc. But then all plausible reactions which form CO and in cool flames, be irrelevant to the main course
would also destroy free valences and the formation of the reaction in hot flames; but many persons
of CO and H2 from the hydrocarbon fuel should have believed the low temperature mechanisms to
have to be considered a chain terminating process be irrelevant to hot steady flames.
which was fed by free radicals generated in reaction It must be pointed out, however, that our data
(c). This view would account for the fact that are not sufficiently precise to exclude some reaction
flames rich enough to contain hydrocarbon in the of O2 in other ways than via reaction (c). All we
products possess only about the equilibrium [HI can claim is that (c) is more important than any
in the post flame gas, while fuel lean hydrocar- other way.
bon flames or either rich or lean H2 flames contain (15) M. Vanpee and F. Grard, “5th Symposium on Combustion,”
so many free radicals that [HI in the post flame gas Reinhold Publ. Corp., New York, N. Y., 1955, p. 484; D. E. Hoare
is many times the concentration appropriate to the and A. D. Welsh, ibid., p. 474; and references cited by these authors

THE EFFECT OF SIMULTANEOUS CROSSLINKING AND DEGRADATION

ON THE INTRINSIC VISCOSITY OF A POLYMER
BYR. W. KILB
General Electric Research Laboratory, Schenectady, New York
Received March 86, 1060

The change in intrinsic viscosity [q]is studied for a process during which a polymer is simultaneous1 degraded and cross-
linked. An example of such a process is irradiation of polymers. It is possible to determine the rerative amount of deg-
radation and crosslinking by following the change of [ q ] during the process. Qualitative agreement of theory with ex-
periment is good. Quantitatively the method is limited to the range unity to ten for the ratio of degradations to crosslinks.
outside these limits the shape of the [ q ]curve is insensitive to this ratio. It is found that the best sensitivity is obtained
when [ q ]is determined in e solvents. By followin the change in osmotic and li ht scattering molecular weight for silicone
irradiated by an electron source, the ratio of degrafations to crosslinks was f o u n t t o be less than 0.5.

During certain processes, polymer molecules are The problem of determining the relative amount
simultaneously crosslinked and degraded. Typical of crosslinking and degradation has also been
examples are irradiation and oxidation. This treated by C h a r l e ~ b y . ~His method involves fol-
leads to a polymer with long chain branching and lowing the amount of gel produced during the proc-
either increased or decreased molecular weight, ess.
depending on the degree of degradation. We are It has perhaps not been sufficiently forcibly
interested here in determining the relative amount pointed out in previous studies that the quantitative
of crosslinking and degradation from a study of the calculations are rather sensitive to the assumed ini-
change in intrinsic viscosity of the polymer. This tial molecular weight distribution. Consequently,
problem has been treated in an approximate manner in the application of the calculations, i t is neces-
by Shultz, Roth and Rathmann.’ Although most sary to determine if the experimental polymer ac-
of their results are qualitatively correct, their tually has the assumed distribution. If this is not
quantitative calculations are inexact because of the case, the results must be viewed with some scep-
their use of the Stockmayer and Fixman2 approxi- ticism.
mation for the effect of branching on the intrinsic I n this paper we shall make the assumptions: (1)
viscosity of a polymer. Recently Zimm and Kilb* the scissions are directly proportional to the cross-
have shown that previous theories seriously over- links throughout the process and their distribution
estimate the effect of branching on intrinsic vis- is “random”; (2) the crosslinks are tetrafunc-
cosity, and proposed a new theory which is in good tional, i.e., four branches radiate out from the
agreement with the available data. We propose crosslinked site; (3) the initial molecular weight
to use this theory in the present study. The quan- distribution is assumed to be the “most probable”
titative results of Shultz, et aE., also suffer to some distribution (see below),
extent from the lack of use of a definite molecular
weight distribution. On the basis of these assumptions, we may com-
bine the results of Zimm and Kilb with the dis-
(1) A. R. Shultz, P. I. Roth and G. B. Rathmann, J. Polymer Sci., tribution function given by Stockmayer5 to cal-
22, 495 (1956).
(2) W. H. Stookmayer and M. Fixrnan, Ann. N . Y . Acad. Sci., 61, (4) A. Charlesby, Proc. Roy. Soc. (London), A224, 120 (1954).
334 (1953). (5) W. H. Stookrnayer, J. Chem. Phys., 11, 45 (1943); 12, 125
(3) B. H. Zimm and R. W. Kilb, J. Polymer Sci., 87, 19 (1959). (1944).