’’Exactly soluble’’ two-component lattice solution with upper and lower critical solution temperatures

Abstract

A decorated lattice model of a two−component liquid solution is presented which has closed−loop coexistence curves with both upper and lower critical solution temperatures analogous to the behavior found in the nicotine + water and m−toluidine + glycerol systems. The model can be transformed exactly into the spin−1/2 Ising model for which exact results are known in two dimensions and reliable estimates are available in three dimensions. The model exhibits nonclassical critical exponents at both upper and lower critical solution temperatures and has coexistence curves in qualitative agreement with those for real systems. The coexistence curves exhibit characteristic features found in most systems with closed−loop coexistence curves.