Chemistry Reference
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In other words, all the correlations decay in the usual OZ fashion, but with modula-
tion associated with the domain size. The domain size is a unique parameter, just
like the correlation length. It is the same for all species, regardless of their respective
concentrations in the mixture.
In the above manipulation of the MOZ form at small-
k
vectors, we have followed
the approach used by Teubner and Strey for explaining the existence of prepeaks in
microemulsions (Teubner and Strey 1987). In the initial approach of these authors,
they started from considerations on the form of a Landau-Ginzburg free energy
Hamiltonian, containing gradients of the local density, considered as the order
parameter. This is a phenomenological approach, suitable when analyzing univer-
sal behavior (Chaikin and Lubensky 2000). The present derivation of the Teubner-
Strey form of the structure factor in
k
-space, as well as the decay in
r
-space, is more
microscopic in nature since it starts from the STL formulation of the correlation
functions. The derivation of Teubner and Strey is specifically adapted to microemul-
sions, which are about three orders of magnitude larger in scale than simple aqueous
mixtures. Indeed, the size of micelles or lamellas is on the micron scale (Tanford
1974) when the segregated domains in simple aqueous mixtures have sizes around a
few nanometers. The fact that the STL is able to describe both types of phenomena
in a unified manner is not a surprise, since both are aqueous mixtures, differing
only by the number of components and the size of the solute molecules. However,
the phenomenological Teubner-Strey formalism explains the existence of domain
modulations in microemulsions, as witnessed by a prepeak of the water-water struc-
ture factor.
It is not
a priori
obvious that, despite mathematical similarities, the expressions in
Equation 7.57 and Equation 7.59 might also describe domain formations and appear-
ance of prepeaks in simple aqueous mixtures. Recent small angle scattering experi-
ments in binary aqueous mixtures of monools, diols, and triols (D'Arrigo, Giordano,
and Teixeira 2009), show that only the latter two show clear non-OZ type decays. But
the problem is deeper than this simple remark. It is well known, particularly since
the work of Matteoli and Lepori, that some aqueous mixtures exhibit large KBIs
(Matteoli and Lepori 1984). If KBIs represent solely concentration fluctuations,
then domain formation can be considered as a variant of a concentration fluctuation.
Following this line of thinking, a micelle, or a lamella, would just be a manifestation
of concentration fluctuations, which is not very reasonable to assume. The MOZ for-
malism shows the way out of this dilemma. It indicates that large peaks that appear
in the structure factors are not necessarily due to increasing fluctuations, but to the
appearance of domains. These domains can be considered as
intrinsic concentra-
tion fluctuations,
, but they are truly new objects, just like micelles or lamellas. The
appearance of such new objects is witnessed by a new peak in the structure factor,
just like the main peaks associated with the presence of each constituent molecule.
When the concentration or other parameters are varied, the increase of the peak
at
k
= 0 ceases and a prepeak emerges instead. The crossover point is called the
Lifshitz point
in the microemulsion jargon (Ciach and Gozdz 2001), but this name
is also encountered in highbrow physics, such as high-energy physics and string
theories (Wen 2004). Indeed, in such theories, particles are seen to emerge from the
