Chemistry Reference
In-Depth Information
1.3.4 P
reFerenTial
s
olvaTion
in
B
inary
and
T
ernary
s
ysTems
As mentioned previously, one of the major advantages of FST is that it provides
information on local density fluctuations. An alternative approach to this problem
involves the concepts of local composition and preferential solvation (Ben-Naim
2006). To do this we first note that the average number of
j
particles in a region of
spherical volume
V
cor
surrounding a central particle
i
is
NN V
j
=+ρ
cor
(1.81)
ij
j
as long as the volume is large enough that all
g
ij
= 1. Using the above expression one
can define a local mole fraction of
j
particles in this volume as
N
NV
NV
+
ρ
j
L
ij
j
cor
x
=
=
(1.82)
∑∑
j
N
(
+
ρ
)
k
ik
k
cor
k
k
and then define the preferential solvation of
i
by
j
as
∑
x
x
(
GG
−
)
j
k
ij
ik
L
δ
xxx
=−=
k
(1.83)
∑
ji
j
j
V
+
x G
cor
kik
k
which applies for a solution containing any number of molecules. This is the approach
used in Chapter 3. Alternative definitions of preferential solvation can also be used
and are provided in Chapters 3 and 4. In addition, it has become usual to correct the
KBIs by subtraction of the ideal solution values (see Section 1.3.7) in an effort to help
interpret the experimental data. A full discussion is provided in Chapter 4.
The above expressions depend explicitly on the spherical volume of interest.
This volume must be large enough to ensure all RDFs are unity and therefore that
Equation 1.81 is valid. Unfortunately, the distance beyond which the RDFs are unity
is generally unknown. It will certainly depend on the species and specific composi-
tion, as well as the values of
T
and
p
. There are two solutions to this problem. First,
one can attempt to estimate the volume and thereby provide quantitative values for
the preferential solvation. This is described in Chapters 3 and 4. Alternatively, one
can take the approach of Ben-Naim and expand the above expression in powers of
V
cor
-1
to give (Ben-Naim 2006)
∑
(
)
+
x
x
GG
−
j
k
ij
ik
0
=−=
L
δ
ji
xx
k
(1.84)
j
j
V
cor
The numerator then provides the sign of the preferential solvation as we decrease
the value of
V
cor
from that of an infinite region in a closed system to that of an open
local region of the solution. The magnitude of the effect is therefore unimportant, but
