Handbook of Solvents - George Wypych - ChemTech - Ventech!

190 Christian Wohlfarth
Furthermore, there is another effect which causes serious problems with LLE-data of
polymer solutions. This is the strong influence of distribution functions on LLE, because
fractionation occurs during demixing - see, for example, Koningsveld. 44,183 Figure 4.4.19 illustrates
the differences between the LLE-behavior of a strictly binary polymer solution of a
monodisperse polymer and a quasi-binary polymer solution of a polydisperse polymer
which is characterized by a distribution function.
One can see the very complicated behavior of quasi-binary solutions where the phase
boundary is given by a cloud-point curve and where an infinite number of coexistence
curves exists (one pair for each starting concentration, i.e., each cloud-point). The
cloud-point is a point in the T-w 2- or the P-w 2-diagram where a homogeneous solution of
concentration w 02 begins to demix (where the “first” droplet of the second phase occurs,
T(2) in Figure 4.4.19). If w 02 is smaller than the critical concentration, the cloud-point belongs
to the sol-phase, otherwise to the gel-phase.
As this subchapter is devoted to solvent activities, only the monodisperse case will be
taken into account here. However, the user has to be aware of the fact that most LLE-data
were measured with polydisperse polymers. How to handle LLE-results of polydisperse
polymers is the task of continuous thermodynamics, Refs. 52-54 Nevertheless, also solutions
of monodisperse polymers or copolymers show a strong dependence of LLE on molar mass
of the polymer, 184 or on chemical composition of a copolymer. 185 The strong dependence on
molar mass can be explained in principle within the simple Flory-Huggins χ-function approach,
please see Equation [4.4.61].
Experimental methods can be divided into measurements of cloud-point curves, of
real coexistence data, of critical points and of spinodal curves:
Due to distinct changes in a number of physical properties at the phase transition border,
quite a lot of methods can be used to determine cloud-points. In many cases, the refractive
index change is determined because refractive indices depend on concentration (with
the seldom exception of isorefractive phases) and the sample becomes cloudy when the
highly dispersed droplets of the second phase appear at the beginning of phase separation.
Simple experiments observe cloud-points visually. More sophisticated equipment applies
laser techniques, e.g., Kuwahara, 186 and light scattering, e.g., Koningsveld and
Staverman. 187 The principle scheme of such a scattering experiment is the same as explained
with Figure 4.4.18. Changes in scattering pattern or intensity were recorded as a function of
decreasing/increasing temperature or pressure. The point, where first deviations from a basic
line are detected, is the cloud-point. Since demixing or phase homogenization need some
time (especially for highly viscous solutions), special care is to be applied for good data.
Around the critical point large fluctuations occur (critical opalescence) and scattering data
have to be measured at 90 o scattering angle. The determination of the critical point is to be
made by independent methods (see below). Various other physical properties have been applied
for detecting liquid-liquid phase separation: viscosity, e.g., Wolf and Sezen, 188 ultrasonic
absorption, e.g., Alfrey and Schneider, 189 thermal expansion, e.g., Greer and Jacobs, 190
dielectric constant, e.g., Jacobs and Greer, 191 or differential thermal analysis DTA, e.g.,
Muessig and Wochnowski. 192
There are only a small number of investigations where real coexistence data were
measured. This is mainly due to very long equilibrium times (usually weeks) which are necessary
for obtaining thermodynamically correct data. A common method is to cool homogeneous
solutions in ampullae very slowly to the desired temperature in the LLE-region and