A generalization of the three-state binary gas–liquid lattice models and analysis of their critical lines

The concept of a global phase diagram – a diagram in the space of fluid interaction parameters in which regions of similar types of phase behavior are demarcated – has proved very valuable in both theoretical and experimental studies of fluid mixtures. This type of work sheds light on the essential transition mechanism involved in the change of character of the phase diagram, such as multi-critical points and double points, and other phenomena of great practical importance in supercritical fluid extraction processes. The first step in this process is to understand the changes in critical line structure which underlies these differences. In this work, we study and generalize following compressible binary gas–liquid models; the three-state lattice gas, the van der Waals equation for binary mixtures, the Tompa model for polymer solutions, and the modified version of Tompa model for polymer mixture solutions. Then, the critical lines of these models are displayed in the density–density, P, T and T, x planes. The crossing point, a point at which two critical lines meet and exchange branches, is also calculated analytically. The P, T diagrams are discussed according to Scott and van Konynenburg phase diagram classifications.