Phenomenological theory of multiply reentrant solubility

A phenomenological approach to the theory of complex phase diagrams in binary liquid mixtures is developed. The random-mixing Flory–Huggins free energy expression is modified by the generalization of local pairwise energies to the corresponding free energies which, for systems with specific interactions such as hydrogen bonds, are described in terms of multiple-level partition functions. The temperature-dependent effective interactions in recent lattice models for these systems appear as special cases of this more general result. While characteristic asymmetries of various interactional correlation functions evaluated in the coexisting phases are found to parallel those of the interactions themselves, the symmetry of the phase diagram is not affected by such interactions, in contrast to the results of decorated-lattice calculations. A heuristic explanation of this is given, supporting a recent suggestion that the description of interaction-driven asymmetric coexistence curves requires an enlarged space of statistical variables which includes density fluctuations.