Chemistry Reference
In-Depth Information
ε = -1
1.8
0
ε = -0.001
ε = -3.5
1.7
-2
ε = -6
ε = -0.25
1.6
-4
ε = -0.5
ε = -8.5
1.5
ε = -0.75
-6
1.4
ε = -11
ε = -1.0
-8
1.3
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
x
A
x
A
The solvation Gibbs energy
Δ
G
B
in the same system as in Figure 2.8.
FIGURE 2.20
|ε| = 1. Δ
G
A
*
measures the average value of the quantity exp[-β
B
A
], where
B
A
is the
total interaction energy of a single A with the rest of the system. This quantity is
often referred to as the
free energy of interaction
of the species A. As |ε| ≤ 1 becomes
smaller, we see that the values of Δ
G
A
*
become larger. On the other hand, for |ε| ≥ 1, the
reverse trend is true. Also note that in all cases, Δ
G
A
*
converge to the value of Δ
G
A
*
for
the solvation of A in pure A (i.e., at
x
A
→ 1). We note also that the behavior of Δ
G
A
*
as a function of
x
A
for |ε| ≥ 1 is similar to the case of argon in mixtures of argon and
xenon (Ben-Naim 1989). The interpretation of this phenomenon is simple. Starting
from
x
A
= 0, we have the solvation of A surrounded by pure B. As
x
A
increases from
x
A
= 0 to
x
A
= 1, the surroundings of A changes from all B to all A particles; hence,
the free energy of interaction decreases strongly toward the value of Δ
G
A
*
for pure A.
A different behavior is exhibited by Δ
G
B
*
shown in Figure 2.20. Here again, we
find that Δ
G
B
*
is composition independent for |ε| = 1. However, in contrast to the case
of Δ
G
A
*
(Figure 2.19), the values of Δ
G
B
*
do not converge to a single value for pure B
(
x
A
= 0). The reason is simple. In the case of Δ
G
A
*
, “pure” A (i.e.,
x
A
= 1) means a
unique system of A particles with fixed molecular parameters σ
AA
= 1 and ε
AA
= −1.
On the other hand, when we say pure B (i.e.,
x
A
= 0), there are different “pure” sys-
tems with σ
BB
= 1, but varying values of ε
BB
.
2.7.3 l
local
P
roPerTies
c
alculaTed
d
irecTly
From
The
P
air
c
orrelaTion
F
uncTions
In this section we present the results of a recent paper (Ben-Naim and Santos 2009)
where we directly recalculated the KBIs for two component mixtures of particles
interacting via square-well potential. The theoretical background is lengthy and
will not be presented here. Instead, we show a sample of results for mixtures of
square-well particles. It is shown that the results are in quantitative agreement with
those obtained from the inversion of the Kirkwood-Buff theory of solution. We also
