We study the molecular correlations in a lattice model of a solution of a low-solubility solute, with emphasis on how the thermodynamics is reflected in the correlation functions. The model is treated in the Bethe–Guggenheim approximation, which is exact on a Bethe lattice (Cayley tree). The solution properties are obtained in the limit of infinite dilution of the solute. With h11(r), h12(r), and h22(r) the three pair correlation functions as functions of the separation r (subscripts 1 and 2 referring to solvent and solute, respectively), we find for r2 lattice steps that h22(r)/h12(r)h12(r)/h11(r). This illustrates a general theorem that holds in the asymptotic limit of infinite r. The three correlation functions share a common exponential decay length (correlation length), but when the solubility of the solute is low the amplitude of the decay of h22(r) is much greater than that of h12(r), which in turn is much greater than that of h11(r). As a consequence the amplitude of the decay of h22(r) is enormously greater than that of h11(r). The effective solute-solute attraction then remains discernible at distances at which the solvent molecules are essentially no longer correlated, as found in similar circumstances in an earlier model. The second osmotic virial coefficient is large and negative, as expected. We find that the solvent-mediated part W(r) of the potential of mean force between solutes, evaluated at contact, r=1, is related in this model to the Gibbs free energy of solvation at fixed pressure, ΔGp, by (Z/2)W(1)+ΔGppv0, where Z is the coordination number of the lattice, p is the pressure, and v0 is the volume of the cell associated with each lattice site. A large, positive ΔGp associated with the low solubility is thus reflected in a strong attraction (large negative W at contact), which is the major contributor to the second osmotic virial coefficient. In this model, the low solubility (large positive ΔGp) is due partly to an unfavorable enthalpy of solvation and partly to an unfavorable solvation entropy, unlike in the hydrophobic effect, where the enthalpy of solvation itself favors high solubility, but is overweighed by the unfavorable solvation entropy.

1.
G. S.
Rushbrooke
,
Introduction to Statistical Mechanics
(
Oxford University Press
,
Oxford
,
1949
), pp.
300
304
.
2.
T. L.
Hill
,
Statistical Mechanics
(
McGraw-Hill
,
New York
,
1956
), pp.
348
353
.
3.
G. M.
Bell
and
D. A.
Lavis
,
J. Phys. A
3
,
427
(
1970
).
4.
G. M.
Bell
and
D. A.
Lavis
,
J. Phys. A
3
,
568
(
1970
).
5.
N. A. M.
Besseling
and
J.
Lyklema
,
J. Phys. Chem. B
101
,
7604
(
1997
).
6.
C. D.
Eads
,
J. Phys. Chem. B
106
,
12282
(
2002
).
7.
B.
Widom
,
P.
Bhimalapuram
, and
K.
Koga
,
Phys. Chem. Chem. Phys.
5
,
3085
(
2003
).
8.
N.
Guisoni
and
V. B.
Henriques
,
J. Phys. Chem. B
110
,
17188
(
2006
).
9.
T. L.
Beck
,
M. E.
Paulaitis
, and
L. R.
Pratt
,
The Potential Distribution Theorem and Models of Molecular Solutions
(
Cambridge University Press
,
New York
,
2006
), Chap. 7.
10.
D. M.
Rogers
and
T. L.
Beck
,
J. Chem. Phys.
129
,
134505
(
2008
).
11.
M. A. A.
Barbosa
and
V. B.
Henriques
,
Phys. Rev. E
77
,
051204
(
2008
).
12.
C.
Buzano
and
M.
Pretti
,
J. Chem. Phys.
119
,
3791
(
2003
).
13.
J. C.
Wheeler
and
B.
Widom
,
J. Chem. Phys.
52
,
5334
(
1970
).
14.
J. G.
Kirkwood
and
F. P.
Buff
,
J. Chem. Phys.
19
,
774
(
1951
).
15.
B. H.
Zimm
,
J. Chem. Phys.
21
,
934
(
1953
).
16.
A.
Ben-Naim
,
Water and Aqueous Solutions: Introduction to a Molecular Theory
(
Plenum
,
New York
,
1974
), p.
142
.
17.
A.
Ben-Naim
,
J. Chem. Phys.
67
,
4884
(
1977
).
18.
P.
De Gregorio
and
B.
Widom
,
J. Phys. Chem. C
111
,
16060
(
2007
).
19.
R.
Evans
,
R. J. F.
Leote de Carvalho
,
J. R.
Henderson
, and
D. C.
Hoyle
,
J. Chem. Phys.
100
,
591
(
1994
).
20.
P.
De Gregorio
,
J. C.
Toledo
, and
B.
Widom
,
Mol. Phys.
106
,
419
(
2008
).
21.
E. E.
Tucker
and
S. D.
Christian
,
J. Phys. Chem.
83
,
426
(
1979
).
22.
P. J.
Rossky
and
H. L.
Friedman
,
J. Phys. Chem.
84
,
587
(
1980
).
23.
C.
Chipot
,
P. A.
Kollman
, and
D. A.
Pearlman
,
J. Comput. Chem.
17
,
1112
(
1996
).
24.
H.
Liu
and
E.
Ruckenstein
,
J. Phys. Chem. B
102
,
1005
(
1998
).
25.
O.
Coskuner
and
U. K.
Deiters
,
Z. Phys. Chem.
220
,
349
(
2006
).
26.
O.
Coskuner
and
U. K.
Deiters
,
Z. Phys. Chem.
221
,
785
(
2007
).
27.
D.
Paschek
,
J. Chem. Phys.
120
,
6674
(
2004
).
28.
S. R. A.
Salinas
,
Introduction to Statistical Physics
(
Springer-Verlag
,
New York
,
2001
), Chap. 13.
29.
C. -K.
Hu
and
N. S.
Izmailian
,
Phys. Rev. E
58
,
1644
(
1998
).
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