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Phase Diagrams

A realistic theoretical description of phase diagrams (here this means primarily the modeling
of liquid/liquid but also of liquid/gas and of liquid/solid phase equilibria) requires well
founded and reliable information on composition dependent binary interaction parameters (cf.
the corresponding section). In case the number of components exceeds three, such calculations
also necessitate modified mathematical procedures, because of the high number of
mixed derivatives required on the conventional routes to determine the conditions under
which the chemical potential of the different species becomes equal in the coexisting phases.
The tool that has been found to solve this problem consists in a direct minimization of the
Gibbs energy of the total system.

There are above all two areas where the direct minimization of the Gibbs energy comes in
very handy: The description of the effects of polymolecularity and the modeling of phase diagrams
for flowing systems. In the former case it enables for instance quantitative calculations
on the fundamentals of polymer fractionation via liquid/liquid phase equilibria. In the latter
case it is an indispensable requirement because of the sometimes non-analytical form of the
composition dependence of the (generalized) Gibbs energy.

The central theoretical idea with respect to the modeling of shear influences rests on the
ability of polymer containing systems to store energy while they flows. In most cases the reason
for this ability is of entropic nature and results from chain entanglements (temporary
cross-links), for copolymers there may come in an additional enthalpic mode of energy storage
(via the destruction of quasi-chemical equilibria by flow). Introduction of a generalized
Gibbs energy - consisting of the usual Gibbs energy plus the energy stored in the flowing
system under stationary conditions - did not only allow the modeling of experimental findings
for phase separation into two liquid phases but could also predict new features that were
observed only afterwards. Presently this concept is also successfully applied to describe shear
influences on the crystallization of polymers from solution.

### Publications

For more information, please see the following publications: **233, 229, 221, 203, 192, 190, 176, 172, 173, 168, 145, 139, 112, 109, 30**