Arguments are presented indicating that the large‐size limiting behavior of the ion‐pair size distribution is qualitatively the same both with, and without, Coulomb interactions between ions. This in turn implies that the static dielectric response function ε0 / ε(k) derived in the preceding paper is nonanalytic at k = 0. The specific singular behavior of this response requires a branch cut along the imaginary k axis. It furthermore induces an r−8 tail in the ion atmosphere charge distribution at finite electrolyte concentration.

1.
F. H.
Stillinger
and
R. J.
White
,
J. Chem. Phys.
54
,
3395
(
1971
), Preceding paper, Paper III.
2.
P.
Debye
and
E.
Hückel
,
Physik. Z.
24
,
185
,
305
(
1923
).
3.
J. C. Poirier, in Chemical Physics of Ionic Solutions, edited by B. E. Conway and R. G. Barradas, (Wiley, New York, 1966), p. 9.
See also
D. N.
Card
and
J. P.
Valleau
,
J. Chem. Phys.
52
,
6232
(
1970
).
4.
The exceptional ambiguous cases with equal pair distances have zero probability, and may be disregarded.
5.
F. H.
Stillinger
and
R.
Lovett
,
J. Chem. Phys.
48
,
3858
(
1968
).
6.
R.
Lovett
and
F. H.
Stillinger
,
J. Chem. Phys.
48
,
3869
(
1968
).
7.
J. G.
Kirkwood
,
J. Chem. Phys.
7
,
911
(
1939
).
8.
The constant C(s0) is required to maintain normalization of p(1)(s), and s0 is arbitrary.
9.
Use of the lower integration limit 0 (rather than 2a) causes no error in our leading‐order estimate.
10.
M. J. Lighthill, An Introduction to Fourier Analysis and Generalized Functions (Cambridge U.P., Cambridge, England, 1962), Chap. 4.
11.
H. L. Friedman, Ionic Solution Theory (Interscience, New York, 1962).
12.
J. E.
Mayer
,
J. Chem. Phys.
18
,
1426
(
1950
).
13.
P. M. V. Résibois, Electrolyte Theory (Harper and Row, New York, 1968), pp. 123–128.
14.
E.
Meeron
,
J. Chem. Phys.
28
,
630
(
1958
).
15.
D. D.
Carley
,
J. Chem. Phys.
46
,
3783
(
1967
).
16.
J. C.
Rasaiah
and
H. L.
Friedman
,
J. Chem. Phys.
48
,
2742
(
1968
);
J. C.
Rasaiah
and
H. L.
Friedman
,
J. Chem. Phys.
50
,
3965
(
1969
).,
J. Chem. Phys.
17.
J. G.
Kirkwood
and
J. C.
Poirier
,
J. Phys. Chem.
58
,
591
(
1954
).
18.
C. W.
Outhwaite
,
J. Chem. Phys.
50
,
2277
(
1969
).
19.
T. L. Hill, Statistical Mechanics (McGraw‐Hill, New York, 1956), Chap. 6.
This content is only available via PDF.
You do not currently have access to this content.