Chemistry Reference
In-Depth Information
A only, excluding B molecules. Therefore, values of δ
x
AB
cannot exceed
x
B
. Similar
considerations are valid for δ
x
AA
that they may not exceed
x
A
.
Another way to represent preferential solvation is by means of the solvation ratio,
(
)
(
)
(
) (
)
L
B
L
L
B
L
Kx
=
x
x
x
=
x
x
x
x
(3.1)
AB
AB
BA AB
A
B
Preferential solvation takes place if
K
AB
≠ 1; however, this presentation loses the
details of the δ
x
AB
(
x
B
) and δ
x
AA
(
x
B
) curves and is less desirable.
Ternary mixtures, in which the third component, for example, S in the A + B
mixtures (Ben-Naim 1990b), is a solute present at vanishing concentrations do not
pertain to the subject of this chapter and are described elsewhere. However, proper
mixtures of three solvents, A + B + C, are briefly dealt with in this chapter.
3.2
CALCULATIONS
The three Kirkwood-Buff integrals (KBIs) for binary mixtures of solvents A
and B:
G
AA
,
G
AB
, and
G
BB
, are obtained from proper thermodynamic data for the
pure components and the mixtures as described elsewhere (see Section 1.3.2 in
Chapter 1). The preferential solvation parameters are related to the KBIs as follows
(Ben- Naim 1990b),
[
]
L
δ
x
=−=
x
xxxG
(
−
Gx Gx GV
)
+
+
(3.2)
BB
BB
BBA B B
B BB ABA
cor,B
[
]
L
δ
x
=−=
x
xxxG
(
−
Gx Gx GV
)
+
+
(3.3)
BA
BA
BBABAAB BA AAA
cor,A
as also illustrated in Section 1.3.4 in Chapter 1. The quantities
V
cor,B
and
V
cor,A
repre-
sent the correlation volumes around the central molecules B and A in which the pref-
erential solvation occurs. These volumes could correspond to only the first solvation
sphere (Figure 3.1), but may also include a second or further solvation sphere. It is
the determination of the correlation volumes as functions of the bulk composition of
the solvent mixtures that leads to definite values of the preferential solvation param-
eters according to Equations 3.2 and 3.3. The calculation of the correlation volumes
requires the determination of the correlation radii,
R
cor
of sequential solvation shells
around a given molecule, to which the correlation volumes,
V
cor
= (4π
N
A
/3)
R
cor
3
,
are related. Such radii of solvation shells are obviously sensitive to the composi-
tion of these shells (for molecules of different sizes); hence, an iterative calculation
is required (Marcus 1990). The hard sphere diameter 2
r
i
of a solvent molecule was
related to its pure molar volume
V
i
o
as (Kim 1978; Marcus 1990)
(
)
13
/
(
)
o
3
-
1
2
r
i
/
nm
=
0 1363
.
V
/
cm mol
-
0 085
.
(3.4)
i
The correlation volume,
V
cor
/ cm
3
mol
−1
, can be calculated for
m
consecutive spherical
solvation shells, taking into account partial penetration of molecules from farther
