Handbook of Solvents - George Wypych - ChemTech - Ventech!

148 Christian Wohlfarth
Figure 4.4.1. Typical isotherm for the solvent activity of a homogeneous binary polymer solution.
ods. The ultracentrifuge can also be applied for solutions up to 80 wt% polymer, but this
was only scarcely done in the literature.
(iv) A special problem are polymer solutions with concentrations higher than 90 wt%
up to the limit of the region of Henry’s law. For this purpose, the inverse gas-liquid chromatography
(IGC) is the most useful method. Measurements can be made at infinite dilution of
the solvent for determining the activity coefficient at infinite dilution or Henry’s constant,
but IGC can also be performed at finite solvent concentrations up to 10-15 wt% of the solvent
to get solvent activities for highly concentrated polymer solutions. Some sorption experiments
in this concentration range were reported by piezoelectric quartz crystal
technique; however, thermodynamic equilibrium absorption is difficult to obtain, as discussed
below. At least, melting point depression can be applied in some cases for small
amounts of solvents in semicrystalline polymers, but obtaining reliable results seems to be
difficult.
(v) There is another possibility to measure solvent activities in polymer solutions if
the state of the solution is inhomogeneous, i.e., for the region of liquid-liquid equilibrium.
Binodal and/or spinodal curves can be reduced to solvent activity data by means of a thermodynamic
ansatz for the Gibbs free energy of mixing in dependence on temperature, concentration
(and pressure if necessary), which has to be solved according to thermodynamic
equilibrium conditions. In the case of polymer networks, swelling equilibria can be measured
instead. The solvent activity in a swollen network arises from two parts, a mixing part
with the (virtually) infinite-molar-mass polymer, and a contribution from elastic network
deformation. The second follows from statistical theory of rubber elasticity and also needs
certain model approximations for data reduction.