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HI. ION-SOLVENT INTERACTION

STRUCTURAL ASPECTS OF ION-SOLVENT INTERACTION
IN AQUEOUS SOLUTIONS: A SUGGESTED PICTURE OF
WATER STRUCTURE
Published on 01 January 1957 on http://pubs.rsc.org | doi:10.1039/DF9572400133

BY HENRYs. FRANK AND WEN-YANG W E N

Dept. of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania, U.S.A.
Received 24th .Time, 1957
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In addition to the direct action of the ionic charge on water as a dielectric medium,
ions may exert an influence on the equilibrium between the ice-like and non-ice-like
forms which are present in room-temperature water. This provides a way of accounting
for experimental results in a variety of areas, including entropy, heat capacity, temperature
of maximum density, tracer self-difhsion, thermal conductivity, and dielectric relaxation,
as well as viscosity and ionic mobility and their temperature coefficients. The tetra-
butyl ammonium cation acts as a structure-promoter in the same way as do non-polar
soIutes, amino acids and fatty acid anions. These various effects seem explicable in a
straightforward manner in terms of a new picture of water as consisting of flickering
clusters of hydrogen-bonded molecules, in which the co-operative nature of cluster forma-
tion and relaxation is related to the partially covalent character which is postulated for
the hydrogen bond.

Liquid water has long been known to possess distinctive structural features
which are roughly describable by the statement that it retains a certain degree of
similarity or analogy to ice. The amount of this " ice-like-ness " may be altered
by changes in temperature and pressure and, as has also been known for a long
time,l alterations which are presumably comparable (e.g., shifts in the temperature
of maximum density) may also be evoked by the presence of ionic solutes. There
is therefore nothing very new in inquiring into the ways in which such structural
changes may influence, or may, in their turn, be studied by inferences from,
observable thermodynamic and kinetic properties of ionic solutions. There have,
however, been a number of advances in this field in recent times, and the subject
is currently of some interest. In discussing it we must remember that we are trying
to get at effects over and above those which the ions are expected to produce as
charged spheres in a dielectric medium, even those connected with the discrete
molecular nature of the medium, such as dipole saturation in the strong field
near an ion.
THE SIMPLE MODEL FOR SMALL IONS

Among the last-mentioned effects, which have no apparent necessary con-

nection with the special character of water, is the immobilization of the dipolar
solvent molecules which are nearest neighbours to the ions themselves.2 About
a spherical ion of radius 2-3 8, in a medium of uniform dielectric constant 80, the
field strength is of the order of 106 volts/cm and, except by Gurney,3 as noted
below, it seems to be generally agreed that in aqueous solutions of ions not larger
than Cs+ and I- the nearest-neighbour water molecules are always essentially
immobilized by direct ion-dipole interaction. This idea and the related one of
electrostriction have been invoked 4 to explain the small or negative values which
salt solutions display of the solute partial molal volumes, heat capacities, com-
pressibilities, etc. It also leads to a simple explanation of the influence of LiCl,
133
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134 STR U C T URAL ASPECTS OF I O N - S O L V E N T INTERACTION

say, in increasing the viscosity of water in which it is dissolved, and of the large
effective radius of Li+ (aq.) inferred from activity coefficient and mobility data.
Early discussions 5 of the numerical values of entropy of hydration of alkali and
halide ions seemed also to confirm that the principal, if not the only, thing that
an ion in solution does, over and above simple dielectric polarization, is to bind
near-neighbour water molecules.
An early disproof of this simple assumption was the fact that a 0.1 M solution
of CsCl, for example, is more fluid than pure water at the same temperature. This
phenomenon was interpreted by Bernal and Fowler,6 and by Cox and Wolfenden 7
Published on 01 January 1957 on http://pubs.rsc.org | doi:10.1039/DF9572400133

as meaning that the ions were somehow breaking water structure. A similar
conclusion was reached independently by Frank and Evans,s from a re-analysis of
entropy of hydration, a quantity for which numerical values are easily obtained
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FIG. 1.-A simple model for the structure modifications produced by a small ion. A,
region of immobilization of water molecules ; B, region of structure breaking ; C ,
structurally " normal " water.
by subtraction between the partial molal entropy of a salt (an experimental quan-
tity which may be re-calculated to a suitably chosen standard state) and the statis-
tically calculated molal entropies of the ions as perfect gases (also in some suitably
chosen standard state). The numerical results so obtained are compared with
the estimated entropy losses arising from (i) restriction of the ions in " free volume "
cells in the condensed phase, (ii) immobilization of first-layer water, and (iii) di-
electric polarization of more distant water. When this is done, it turns out that
all of the alkali metal catiors except Li+ and Na+, and all of the halide anions
except F-, lose " too little " entropy when dissolved from the gas state to infinite
dilution, the discrepancy amounting to as much as 33.6 cal/mole deg. for CsI
(where the use of the sum for Cs+ and I- eliminates whatever arbitrariness there
may be in the separate assignment of molar entropy excesses of 15.7 cal/mole deg.
to Cs+ and of 17.9 cal/mole deg. to I-). The model suggested by these results is
sketched in fig. 1 , which shows an ion surrounded by three concentric regions.
The innermost (region A) is one of immobilization, the second (region B) one in
which the water is less ice-like, i.e. more random in organization, than " normal ",
and the third (region C ) contains normal water polarized in the ordinary way by
the ionic field which, this far out, has become relatively weak. The cause of the
structure-breaking (cf. Gurney 3) is presumably the approximate balance in region
B between two competing orienting influences which act on any given water molec-
ule. One of these is the " normal " structural orienting influence of neighbouring
water molecules. The other is the orienting influence upon the dipole of the
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H . S . F R A N K A N D W E N - Y A N G WEN 135
spherically symmetrical ionic field. The latter influence predominates in region A,
and the former in region C, and it is not implausible that between A and C there
should be a region of finite width in which significantly more orientational disorder
should exist than in either A or C, or in unperturbed water.
Frank and Evans imagined that region A always existed, composed of nearest-
neighbour waters, and that an ion which was small, or multiply-charged, or both
(e.g. Li+, F-, Mg2+) might induce additional structure (entropy loss) of some sort
beyond the first water layer. Such encroachment on region B might almost
extinguish the latter, but would in any case tend toward the net structure-making
Published on 01 January 1957 on http://pubs.rsc.org | doi:10.1039/DF9572400133

influence observed for the ions named. They remarked that the outward orienta-
tion of like poles in all of region A should always produce at least some disorder
in a region B, but that large singly-charged ions (I-, Cs+) seem also to have a large
enough net structure-breaking effect to require the assumption of a good bit more
disorder than that simple cause would account for. Gurney 3 went farther and
assumed that in these cases region B encroaches on region A, perhaps to me extent
of extinguishing it altogether. (It is not clear whether or not he assumed the
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existence of region B for net structure-makers.) At any rate, it is possible to make

entropy data the basis for assigning an orderly gradation of net structure-altering
influence to a considerable number of ions. According to this, cations smaller
or more highly charged than K+ are net structure-formers, and become more
strongly so the smaller and the more highly charged. Kf is slightly structure-
breaking on balance, and this tendency increases through Rb+ and Cs+. F- is a
structure-former, and the other halide anions are structure-breakers, increasing
in this tendency with size. NOT and ClO, are strongly structure-breaking, and
SO$- less so. OH- seems to be a structure-former.

CORROBORATIVE EVIDENCE
Several additional sets of data, from independent fields of experimental re-
search, provide support for the essential correctness of this picture. These areas
include heat capacity,9 dielectric relaxation,lo diffusion of Hi*O in salt solutions,ll
thermal conductivity as interpreted by Eigen,l2 temperature of maximum density,l3
ionic mobility and its temperature coeEcient,l4 entropy of dilution,ls and temper-
ature coefficientof relative viscosity.16 In all of these fields there are experimental
findings which have been discussed in structural terms, with generally successful
results. Of special relevance to our present purpose are conclusions to be drawn
from heat capacity and dielectric relaxation measurements. These will therefore
be taken up separately, heat capacity immediately and dielectric relaxation later.

HEAT CAPACITY
It is assumed that since, when pure water is warmed, its degree of " ice-like-
ness " is reduced, the heat absorbed by this " melting " makes an important
contribution to the anomalously large heat capacity of this substance. In that
case, the presence of an ionic solute should be able to lower the heat capacity in
two ways : (i) by freezing-out degrees of freedom in region A and (ii) by destroying
" ice-like-ness " in region B, thus removing the possibility of some of the " thermal

melting " just referred to. The values of z$ listed in table 1 show that salts do
TABLE
l.-PARTIAL MOLAL HEAT CAPACITIES AT I"lTE DILUTION

electrolyte ci2(CalJdeg.mole) electrolyte

-0

5 2
LiCl - 15.6 NaI - 25.0
LiBr - 16.7 KCl - 29.0
Liz - 17.4 KBr - 29.5
NaCl - 23.8 KI - 30.2
NaBr - 24.3
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136 STRUCTURAL ASPECTS OF ION-SOLVENT INTERACTION

decrease heat capacity. Contrary to earlier assumptions 4 based on mechanism (i)

the effect is smallest where the ionic field is expected to be greatest. By contrast,
the order is in agreement with inferences 8 from mechanism (ii)-the more structure-
breaking the ion the more negative its contribution to c$.
TETRA-ALKYL AMMONIUM SALTS
The experiments and ideas considered above have not required any very clear-cut
picture of what " ice-like-ness " in water is. The fixation of water molecules in
region A and the breaking of structure in region B seem to be about equally
Published on 01 January 1957 on http://pubs.rsc.org | doi:10.1039/DF9572400133

visualizable in any of various contexts, including those postulated by Bernal and

Fowler,6 by Eucken,17 and by Lennard-Jones and Pople.18 There exists, however,
an additional type of solute-water interaction which seems not to be so tractable.
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rn(mol~/lOOOqH,O)

FIG. 2.-Apparen t molal heat capacity of (n-C4H9)4NBr in aqueous solution.

This is the structure-making influence of non-polar solutes, or of non-polar groups

in solute molecules, inferred by Frank and Evans 8 from entropies of hydration,
and confirmed by various later workers ; 16,199 2 0 ~ 2 1 by various experimental
means. That this structure-promotion can be evoked by otherwise simple ionic
solutes seems now to be demonstrated by the results of measurements we have
made of the specific heats of dilute solutions of tetra-n-butyl ammonium bromide
(n-CdH&NBr. The details of this work will be published elsewhere, but we
wish here to make use of the information contained in fig. 2, where $Cp, the
apparent molal heat capacity of the solute, is given as a function of concentration.
The point to be noted is that the observed values of &,, about 270 cal/deg.
mole, are very large, even for this salt. Estimates based on additivity rules found
valid for hydrocarbons and other types of compounds make clear that in the absence
of ion-water interaction $CP must lie somewhere between 120 and 150 caI/deg. mole,
depending on the assumptions. This requires that something in excess of 120
calldeg. mole must be regarded as " extra " heat capacity. The straightforward
explanation is the same as that offered above for the defect of heat capacity in
alkali halide solutions, but here in reverse, namely, that this cation causes the
water near it to be more ice-like than normal, and that this extra " ice-like-ness "
" melts " as the temperature is raised, causing extra heat to be absorbed.
If one reconsiders fig. 1 and imagines the radius R of the cation gradually to
increase, it is, of course, natural that region A will disappear when X gets big
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H . S . FRANK A N D WEN-YANG WEN 137

enough to reduce E to some appropriate figure. Gurney 3 thinks this has already
happened for I- (R w 2-16 A). Next to go will be region B, when E becomes
too small for its influence to compete with the " natural " structure of the water.
But now, apparently, the new effect comes in, which is also observed when krypton,s
or ethane,B or the hydrocarbon tail of amyl alcoho1,s or of octanoate i0n,l9 or of
a-amino butyric acid,21 is introduced into water. This is that the water adjacent
to the non-polar groups becomes more ice-like than normal, and in an amount
apparently more or less smoothly proportional to the size of the non-polar region.
This rather smooth proportionality is one of our reasons for rejecting the hypothe-
Published on 01 January 1957 on http://pubs.rsc.org | doi:10.1039/DF9572400133

sis of Claussen et uZ.20 that this extra " ice-like-ness " consists in the formation
of cages about solute molecules, similar to those known to exist in the solid clath-
rate hydrates.22 Such cages should have some specificity in size or shape of solutes
they could accommodate, and no such specificity seems to exist in the solution
phenomena.23 We are therefore led to an alternative interpretation in terms of a
somewhat novel picture of the water-structure equilibrium itself.
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A SUGGESTED PICTURE OF WATER STRUCTURE

We start out by postulating that the " true" hydrogen bond in water has a
covalent character which precludes the kind of " bending " assumed in the model
of Lennard-Jones and Pople 18 (LJP)-that is, a rotating, in continuously variable
amount, of the hydrogen, or the lone pair, or both, out of the 0-0 line of centres.
We do not, however, reject the LJP model, but use it instead with some necessary
modifications of detail, to describe non-bonded water. In this dipole-dipole
forces are still very strong, and still produce both a considerable degree of
orientational restriction and powerful binding of an individual molecule to the
whole liquid.
The picture usually used 24 to describe the covalency of the hydrogen bond
is suitable for our purpose. This considers resonance among the three bond
structures shown in fig. 3. Here the +
and - signs represent formal charges,
and the ordinary partial polarity of the 0-H bond is represented by the resonance
(with suitable weighting coefficients) of molecule b between structures I and IT.
The mixing-in of a contribution from structure 111is what constitutes the formation
of a hydrogen bond.
H H H H H H H H
I I ..I + I -a. ..I *.
I
+ ..I - ..1
H-:O: H-:O: H-:O:.. H : O..: H-:O: ..
H-:O:-H:O: H-:O:
a b a b c a b d
I TI I11
FIG.3.-Proposed resonance scheme for the hydrogen bond in water.

This gives formal recognition, as any realistic representation must do, to the
fact that, chemically, hydrogen bond formation is an acid-base interaction, and
that when the bond is formed molecule a becomes more acidic and b more basic
than an unbonded water molecule. This, in turn, has the consequence that the
a-b bond will be strengthened if a can also bond (acidically) with another
molecule c andfor b (basically) with d, and that the existence of the u-b bond will
promote the tendency of c-a and 6-d bonds to form. This will tend to introduce
a co-operative element into hydrogen bond formation. This element will, more-
over, not be limited to linear proliferation, for when b, for instance, is an interior
member of a bonded chain its remaining lone pair should, in any representation,
be more " eligible " for bonding than when b was not bonded at all, for the hybrid-
ization of the oxygen orbitals will now approximate more nearly to the tetrahedral
sp; mixing, thus increasing the localization of the unbonded electrons.
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138 STR U C TU RAL ASPECTS OF ION-SOLVENT INTERACTION

We therefore postulate that the formation of hydrogen bonds in water is pre-

dominantly a co-operative phenomenon, so that, in most cases, when one bond
forms several (perhaps “many”) will form, and when one bond breaks, then,
typically, a whole cluster will “ dissolve ”. This gives a picture of flickering
clusters, of various sizes and shapes, jumping to attention, so to speak, and then
relaxing “ at ease ”. The half-life of such a structure may well be 10-10 or 10-11
sec-short enough to correspond to the dielectric 25 and (presumably also) bulk 26
relaxation time of water, but long enough (102 to 103 times a molecular vibration
period) to constitute a meaningful existence of the cluster. It will be noted that
Published on 01 January 1957 on http://pubs.rsc.org | doi:10.1039/DF9572400133

since unbonded water is assumed 18 to have a potential energy some 9 kcal/mole

lower than in the vapour state, the extra lowering on bonding need not be more
than about 1 kcal/mole bond. Correspondingly, the entropy loss on bonding need
not be too great, as the unbonded molecule is by no means rotationally “ free ”.I8
Ascribing this character to the bonding process accounts simply for two other
facts : the change in the H-0-H angle from 104” 35’ in water vapour 27 to very
nearly 109”28’ in ice,2* and the high mobility of protons both in water and in ice
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as found by Eigen.29 The latter inference may be drawn from (i) the lowering
which the potential barrier between proton positions should suffer as a result of
the hybridizing-in of structure 111, and (ii) the co-operative nature of the bond-
forrning process. If any proton can jump then, typically, a group of concerted
jumps can take place.
Ascribing this character to the bonding process seems also to provide a new
polarization mechanism, which could contribute to the dielectric constant of water.
That is, in addition to what comes from rotation of individual m01ecules,30 and
from proton motions,31 it appears that a spontaneous fluctuation of local polar-
ization should also arise from the partial charge separations which would be pro-
duced in the formation of such a cluster as we have described and would disappear
as the cluster relaxed. Such an effect seems to be implicit in Sutton’s finding 24b
that the dipole moment of a hydrogen-bonded addition compound is greater
than the vector sum of the moments of its constituents, and should produce an
essentially electronic contribution to the low-frequency dielectric susceptibility
of the liquid.

MECHANISM OF STRUCTURE PROMOTION BY NON-POLAR SOLUTES

In this picture the statistical degree of “ ice-like-ness ” of the sample is

proportional to the average size and to the average half-life of the clusters. A
cluster will come into existence when a volume element of suitable size and
shape suffers a negative energy fluctuation of such magnitude as to outweigh
the disruptive influences at the boundaries of the patch, and will dissolve
when these disruptive influences-torques and displacements-succeed in trans-
mitting into the cluster the necessary energy of melting. Now a non-polar
solute particle or group should be relatively incapable of producing or of
transmitting such disruptive influences, on account of the relative feebleness of
the electrostatic interactions into which it can enter. An ice-like patch should
therefore be able to form more readily in a volume element bounded by a
non-polar solute particle and, once formed, should have a longer half-life than
“ normal ” by reason of having a part of its boundary protected from attack.

This would, on average, produce extra “ice-like-ness” in the solution. If this

extra “ ice-like-ness ” is assumed to melt (i.e., to become less in amount) with
rising temperature, at a proportional rate not smaller than that which character-
izes normal “ice-like-ness ”, then the excess apparent molal heat capacity of
(n-C4H&N+ is qualitatively accounted for.

DIELECTRIC RELAXATION
From the suggested mechanism a further inference may be drawn. If cluster-
polarity-fluctuation does indeed contribute to the dielectric constant of water. and
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H . S . FRANK A N D W E N - Y A N G W E N 1 39
structure-promotion by non-polar groups is related to cluster half-lives, then non-
polar solutes in water should give solutions with longer dielectric relaxation times
than that of pure water. Exactly this is what Haggis, Hasted and Buchanan 32
have observed, as shown in table 2. The quantity listed is 100& where 8As is
the molar lengthening of relaxation wave-length in cm, and is proportional to the
molar lengthening of the statistical half-period of the relaxation process. The
positive values for solutes containing non-polar groups are thus in accord with the
predictions of the model.
TABLE
Published on 01 January 1957 on http://pubs.rsc.org | doi:10.1039/DF9572400133

2.-MOLAR LENGTHENING OF THE RELAXATION WAVE LENGTH

&As x 100(&4), cm solute ”,x 100(f4) cm

- 10 n-propyl alcohol + 35
- 5 isoptopyl alcohol + 30
- 20 t.-butyl alcohol + 40
- 20 ethylamine + 20
+ 15
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- 25 ethylamine hydrochloride
- 10 n-propylamine hydrochloride + 15
- 20 triethylamine hydrochloride + 20
f 5
+ 10
+ 30
Negative values for salts had been observed earlier by Hasted, Ritson and
Collie,1*a and are confirmed by Harris and O’Konski.’Ob Both groups offer
explanations in terms of structure-breaking, essentially as represented in fig. 1.
As mentioned above, this seems compatible with almost any formulation of the
water-structure equilibrium. In terms of the flickering cluster picture one recog-
nizes that an ion with its first-layer water should be a disturbing centre, which would
both interfere with the initiation of clusters and hasten their disruption. This
would decrease net “ ice-like-ness ” and shorten half-lives and relaxation times as
observed. The structure-making influence of some ions-F-, Lif, Mg2f-would
correspond to a high enough degree of ‘‘ incipient hydrolysis ” of the first water
layer to produce hydrogen charge centres which would provide “ edge nuclei ”
for cluster formation, and edge stabilization for clusters once formed. This
corresponds to the “ incipient dissociation ” characteristic of covalent hydrogen-
bond formation (fig. 3) and provides an interpretation of the influence of these ions
in increasing net “ ice-like-ness ”. Interpretation of fig. 1 in these terms, then,
requires only the recognition of the essentially statistical meanings of regions
A and B.
POLAR AND “ M I X E D ” SOLUTES
Frank and Evans 8 found that NH3 in aqueous solution has a “ normal ”
entropy of vaporization, and that CH3OH is the least abnormal of the alcohols
in this regard, One infers that the hydrogen-bonding solutes, or groups like
-NH2 or -OH, do not alter water structure much, if at all. This is reasonable,
since such solutes or groups should be able to enter clusters with only slight dis-
tortion, and to transmit both cluster-forming and cluster-disrupting tendencies.
In addition, results obtained with alcohols,s amino acids,21 and fatty acid anions 19
suggest that, to the first order, the separate structural effects of disparate groups
in the same solute molecule are additive. This does not mean, however, that
structural group interactions may not, for some purposes, become important.

We are grateful to the Office of Ordnance Research and to the National Science
Foundation for grants under which the work of one of us (W. Y . W.) has been
carried out.
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140 S T R U C T U R A L ASPECTS OF ION-SOLVENT INTERACTION

1 Tamann, Uber die Benziehungen zwischen den innern Kraften uiid EigenscJzaften der
Liisugnen (Voss, Leipzig, 1907).
2 Debye, Polar Molecules (Reinhold, New York, 1929), chap. VI.
3 Gurney, Ionic Processes in Solution (McGraw-Hill, New York, 1953), chap. 16.
4 (a) Zwicky, Physik. Z., 1926, 27, 271. (b) Webb, J. Amer. Chem. SOC.,1926, 48,
2589.
5 Latimer, CJzem. Rev.,1936, 18, 349.
6 Bernal and Fowler, J. Chem. Physics, 1933, 1, 515.
7 Cox and Wolfenden, Proc. Roy. Sue. A , 1934, 145,475.
8 Frank and Evans, J. Chem. Physics, 1945, 13, 507.
9 Rossini, Bur. Stand. J. Res., 1931, 7, 47.
Published on 01 January 1957 on http://pubs.rsc.org | doi:10.1039/DF9572400133

10 (a) Hasted, Ritson and Collie, J. Chem. Physics, 1948,16,1. (b) Harris and O'Konski,
J . Physic. CJiem., 1957, 61, 310.
11 Wang, J. Physic. Chem., 1954, 58, 686.
12 Eigen, 2. Elektrochem., 1952, 56, 836.
13 see, for example, Frank and Robinson, ref. (15).
14 Gurney, ref. (3), p. 70.
15 Frank and Robinson, J. Chem. Physics, 1940, 8,933.
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16 Mason, Kampmeyer, and Robinson, J . Amer. Chem. SOC., 1952,74, 1287.

17 Eucken, 2. Elektrochem., 1948, 52, 6.
18 Lennard-Jones and Pople, Proc. Roy. SOC.A , 1951,205, 155, 163.
19 Goddard, Hoeve and Benson, J. Physic. Chem., 1957, 61, 593.
20 Claussen and Polglase, J . Amer. Chem. SOC.,1952, 74, 4817.
21 Robinson, J. Chem. Physics, 1946, 14, 588.
22 v. Stackelberg and Muller, Naturwiss., 1951, 38,456 ; 1952, 39, 20.
23 Powell and Latimer, J. Chem. Physics, 1951, 19, 1139
24 see, for example, (a) Coulson, Valence (Clarendon, Oxford, I952), chap. 12 ;
(b) Sutton, 2. Elektrochem., 1956,60, 1122.
25 Collie, Hasted and Ritson, Proc. Physic. SOC., 1948, 73.
26 Hall, Physic. Rev., 1948,73, 775. It seems that Hall's failure to account realistically
for entropy of mixing of his states 1 and 2 of water may have caused his inferred
bulk relaxation time to come out too short.
27 Darling and Dennison, Physic. Rev., 1940, 57, 128.
28 Peterson and Levy, Acta Cryst., 1957, 10, 70.
29 Eigen, 2. Elektrochern., 1956,60, 1037.
30 Debye, ref. (2), chap. 11.
31 Latimer, Chem. Rev., 1949, 44, 59.
32 Haggis, Hasted and Buchanan. J. Chem. Physics, 1952, 20, 1452.