On the classification of generic phenomena in one-parameter families of thermodynamic binary mixtures

Even binary mixtures exhibit surprisingly complex phase equilibria behavior. Understanding their relationships is of primary industrial importance. A tool is the global phase diagram (GPD) i.e. the partition of the space of the external (model) parameters into regions where points represent system such that the corresponding pT diagrams have the same topological type. The boundaries of these regions are hypersurfaces (of codimension 1) in the space of parameters. We present here a complete classification of the local phenomena corresponding to codimension 3 singularities in the pT phase diagrams of proper binary mixtures (i.e. the molar fraction x of one of the species satisfies 0 < x < 1) when a parameter varies so that such a hypersurface is intersected. This work represents a complement to the classification by Nezbeda et al. (I. Nezbeda, J. Kolafa and W. R. Smith, J. Chem. Soc., Faraday Trans., 1997, 93(17), 3073). Following Varchenko’s approach, (A. N. Varchenko, J. Sov. Math., 1990, 52(4), 3305) generic phenomena encountered in binary mixtures when the pressure p and the temperature T change, correspond to singularities of the convex envelope (with respect to the x variable) of the “front” (a multifunction of the variable x) representing the Gibbs potential G[p,T](x). Pressure p and temperature T play the role of external parameters like λ. A total amount of 26 singularities is found (at least 6 of them were not previously described in the literature), and 56 scenarios of evolution of the pT diagram are obtained. As far as possible, we have quoted examples of modeled or real binary mixtures where these singularities appear.