Chemistry Reference
In-Depth Information
2
1.5
1
0.5
0
0
2
4
6
8
10
12
k
σ
FIGURE 7. 6
Structure factors for the two Yukawa interaction models of Figure 7.5.
as can be seen by the corresponding structure factor. In all these three cases, the
main peak of the structure has remained unchanged and positioned at
k
m
= 2π/σ,
corresponding to the size of the constituent particles. The prepeak witnesses the
appearance of a new entity in the system, with size corresponding to
d
= 2π/
k
P
,
where
k
P
is the wave vector associated with the prepeak. We claim that the microhet-
erogeneity in aqueous mixtures is very similar to the physical phenomena we have
just described, and corresponds to a situation close to the Lifshitz state or the large
soft cluster case.
What is remarkable is that such a simple model is able to predict a prepeak in
the structure factor in agreement with the physical requirement governed by the two
parameters κ
i
. The reason for the prepeak is, in fact, very simple. A single Yukawa
potential provides a DCF that is essentially parabolic at small
k
, but two opposing
Yukawa interactions can give a nonnegligible
k
4
contribution because of the compe-
tition from the repulsive Yukawa. It is this contribution that gives a deviation from
the standard OZ behavior we described in Equation 7.17 and favors the appearance
of the higher-order
k
-vectors in the denominator. This
k
4
term produces the prepeak
and introduces an additional length scale, in addition to the OZ correlation length
that we would have if we were restricted to the
k
2
term only. This example shows how
a simple one-component system can develop a non-OZ behavior. Hence, it indicates
that fluctuations and domain size can appear for competing interaction.
In fact, the repulsive interaction is an artifact that we have introduced in order
to mimic the screening effect of the salt or the polymer. In a full description, the
k
4
term would appear naturally without the need to introduce a repulsive interaction.
Is it possible to introduce such a term with only spherical interactions—through,
for example, a binary mixture? It turns out that what is really required for morphol-
ogy is an interaction with two distances. So, it is always possible to create such an
interaction in model systems. The Jagla model for water-like systems is such a model
(Jagla 1999). However, in real systems, the appearance of a second distance in the
