A simple gE-model for generating all basic types of binary liquid–liquid equilibria and their pressure dependence. Thermodynamic constraints at critical loci

We survey the types of binary (T,p,x) liquid–liquid phase diagrams that have already been found experimentally or that can be predicted to exist, emphasizing the topological properties of the temperature–pressure relation along their critical loci. We use the simplest gE-model compatible with all known basic behavior. The distinct types of phase diagrams are also discussed in light of simple molecular arguments. These, in turn, will serve to predict the thermodynamics of the mixture, i.e., the underlying excess enthalpic, entropic, and volumetric properties to which the gE-model has to conform. The temperature and pressure dependences of these thermodynamic quantities play a fundamental role. From this functional point of view, all possible (T,p,x) phase diagrams can be reduced to just four types. The model presents six parameters with direct physical meaning. While the slope of the T–p curve for critical demixing permits us to establish a relation between hE and vE, its curvature enables us to obtain information about the mixture's compressibility and heat capacity as well. The last section is devoted to the analysis of more complicated cases than those corresponding to basic types of phase diagrams.