Critical lines for a generalized three state binary gas–liquid lattice model

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The critical properties of several compressible binary gas–liquid models are described: the three state lattice gas, the Tompa model for polymer solutions, the van der Waals equation for binary mixtures, and an intermediate model. The critical lines are expressed as functions of x1 and x2, the density of type 1 molecules and the density of type 2 molecules, instead of using the pressure and temperature; representative figures are given for each of the models. The general conditions for criticality, stability, and tricriticality are given as functions of x1 and x2 through the intermediary of the spinodal temperature function T(x1,x2). A closed form solution is given for the Berthelot case (geometrical-mean combining rule). All the models exhibit a characteristic intersection of two critical lines, and the behavior near this point is investigated. In the van der Waals case we confirm the coordinates given by van Laar.