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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.



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

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