Chemistry Reference
In-Depth Information
1
100
0.8
0.6
0.4
0.2
50
0
0
0.5
1
0
-50
0
0.2
0.4
0.6
0.8
1
x
FIGURE 7.10
KBIs for the mixture model λ = 4/5 as a function of the weak-water mole
fraction. Full line is for
G
WW
, dotted for
G
ww
, and dashed for
G
Ww
(“W” stands for SPC/E
water and “w” for weak water). Dots are for data obtained from integrating of the RDFs and
the lines from the KB theory. The inset shows the concentration fluctuation function
D
(
x
) for
a simple model (dotted) and correct version (full line).
these values are unphysically high, they can be considered as the final values for the
G
ij
. The principal reason for the ambiguity is the fact that the RDFs do not seem to
reach a stable flat asymptote at the end of the simulation box. Clearly, larger system
sizes seem required. The principal question is the nature of the relation between the
large values obtained for the KBIs, as evaluated within the present system sizes, and
the way these high RKBIs could settle down to smaller and more realistic values.
This is where the idea of domain modulation seems the perfect solution to the prob-
lem. Indeed, if the RDFs are modulated by the domain size, they would oscillate
at large distances, thus reducing the RKBI to smaller and more acceptable values.
Figure 7.11 illustrates the problem of the KBIs in highly microheterogeneous sys-
tems. The dots are the KBIs evaluated by direct integration of the RDFs, by taking
the last value of the RKBI even when the asymptotes are not stabilized. It is seen that
for weak-water mole fraction above
x
= 0.5, the water-water and water-solute KBIs
seem excessively large. If we use these KBIs to compute the
D
(
x
) term, we find an
unphysical behavior near
x
= 1, as illustrated in the inset of Figure 7.11. By enforc-
ing these values to have the “proper” behavior illustrated by the continuous line, one
can calculate the KBIs that would produce such correct behavior, which are found
to be smaller. Examining the large distance behavior of the systems corresponding to
x
> 0.5, we find that the RDFs can be extrapolated by using a continuity solute that
satisfies the TS requirements. This is illustrated in Figure 7.12 for
x
= 0.8. It is seen
that the long-range extrapolation of the water-water RDF is very smooth and plausi-
ble, and leads to a smaller value of the KBI in excellent agreement with the expected
value, as seen in Figure 7.11 where the new KBIs are shown. This calculation reveals
