Phase diagram correlation with free energies

The construction of the phase diagram of a heteropolymer liquid in the framework of the WSL theory is based on the procedure of minimization of the Landau free energy T presented as a truncated functional series in powers of the order parameter with components i a(r) proportional to Apa(r). The coefficients of this series, known as vertex functions, are governed by the chemical structure of heteropolymer molecules. More precisely, the values of these coefficients are entirely specified by the generating functions of the chemical correlators. Hence, before constructing the phase diagram of the specimen of a heteropolymer liquid, one is supposed to preliminarily find these statistical characteristics of the chemical structure of this specimen. Here a pronounced interplay of the statistical physics and statistical chemistry of polymers is explicitly manifested. 

Fig. 3.16.1. Correlation of a standard phase diagram with the temperature change of free energy curves of simple liquid and solid phases.

To account for this, Rory suggested introducing the van Laar term of the energy of mixing in the form of in the cited free energy equation. This method allows satisfactory considmtion of the isotropic interactions between the components and construction of the complete phase transition diagram in composition-interaction parameter % coordinates. It has usually been assumed that parameter % is correlated with the reciprocal of the temperature by the equation x = a + P/T (where a and p are coefficients). Although this direct correlation is not valid in all cases, it nevertheless holds for most systems. Special cases of the complex dependence of % on T, for example, for systems... 

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