Chemistry Reference
In-Depth Information
is defined symmetrically with respect to α and β, that is,
G
αβ
=
G
βα
, the suggestion
was made of referring to
G
αβ
as a measure of the extent of
affinity
between the α
and β species (Ben-Naim 2006).
It should be noted that the existence of a correlation radius (i.e., a
R
cor
distance
such that for
r
>
R
cor
,
g
αβ
(
r
) is practically unity), is based on what is known both
experimentally and theoretically concerning the pair correlation functions. There is
no proof of the existence of such a correlation distance (Ben-Naim 2006).
The second local quantity is the PS. In a two-component system, we focus on a
small
V
cor
region. We ask how the
composition
in this region changes by placing, say,
an A molecule in its center. The PS of the A particles with respect to composition,
measured as the mole fraction of A in
V
cor
, is defined as the difference,
L
δ
AA
,
(
Vx
)
=
()
Ax
−
(2.5)
cor
A
A
L
where
x
A
is the bulk mole fraction of A, and
x
A
is the
local
mole fraction of A around
an A particle in the volume
V
cor
. From the definition of the KBIs, it follows (Ben-Naim
2006)
xx GG
xG
(
−
)
AB
AA
AB
δ
A,A or
(
V
)
=
(2.6)
+
xG
+
V
AAABAB
cor
Note that this definition is valid for
V
cor
larger
than the correlation volume, since
G
αβ
was taken as defined in Equation 2.2. Application of Equation 2.6 for
any V
cor
,
requires the use of
G
αβ
(
R
cor
) as defined in Equation 2.4. Similarly, the PS of B with
respect to composition (in terms of the mole fraction of A) is defined as
xx GG
xG
(
−
)
L
AB
AB
BB
δ
A,B or
(
Vx
)
=
()
Bx
−
=
(2.7)
A
A
+
xG
+
V
AABB
BB
cor
Clearly, these quantities depends on the choice of the correlation volume
V
cor
; if
V
cor
is very large, then the local composition should approach the bulk composition;
hence, the PS should approach zero. Therefore, in order to eliminate the dependence
on
V
cor
and obtain an
intrinsic
PS measure of A and B, the suggestion has been
made (Ben-Naim 1988, 1990b, 1992, 2006) of introducing the irst-order term in the
expansion of δ
A,B
(
V
cor
) in power series around
V
cor
−1
. The coefficient of the irst-order
term in the expansion is (Ben-Naim 2006)
0
δ
A,AABAA
=
xx GG
(
−
)
(2.8)
B
0
δ
A,BAB
=
xx GG
(
−
)
(2.9)
B
BB
It should be noted that in expanding the quantities δ
A,A
and δ
A,B
, the
G
αβ
are not
viewed as functions of
V
cor
, since use of the definition in Equation 2.2 implies
