Athermal binary polymer solution

A very interesting result is the correlative and predictive performance for the UCST of binary polymer solutions with the van der Waals equation of state. Excellent correlation is achieved and reasonable prediction, using an extremely simple equation developed from athermal polymer-solvent VLE (which is simply a linear correlation of the interaction parameter with the molecular weight of the solvent). Two important comments can be made ... 

Similarly to the description of real phase behavior of mixtures of low-molar-mass components, mixture models based on activity coefficients can be formulated. Whereas in the case of low-molar-mass components the models describe the deviations from an ideal mixture, the models for polymer solutions account for the deviations from an ideal-athermic mixture. As a starting point for the development of a model, all segments are placed on a lattice (Figure 10.3). Polymer chains will be arranged on lattice sites of equal size, where the number of occupied lattice sites depends on the segment number r. For a quasi-binary polymer solution, all other places are occupied with solvent segments. 

The term general solution was introduced by Flory to characterize polymer solutions whose enthalpy of mixing is not zero. The model of general solutions borrows the formula of excess enthalpy from regular systems and the excess entropy from athermal solutions. Thus, a treatment of non-ideal polymer solutions arises which is simpler than the conventional methods applied to real systems this allows the deduction, on the basis of the known relationships, of the expressions of functions of deviation from ideality. Thus, for the activity coefficients of components in a binary system the following relations were established ... 

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