Differential Equations Describing Phase-Equilibrium Displacement During Second-Order (II-Type) Phase Transitions in Multicomponent Systems

In this paper, a generalized thermodynamic description of phase-equilibrium displacement during second-order (II-type) phase transitions in multicomponent systems is developed within the Gibbs-potential metric. The approach is based on the generalized van der Waals equation for phase-equilibrium displacement and accounts for variations in temperature, pressure, and the compositions of coexisting phases. A general system of differential equations is derived for systems with an arbitrary number of components under different thermodynamic constraints, including fixed-composition, isothermal, isobaric, and isothermal–isobaric conditions. The calculated phase-equilibrium relationships are compared with available experimental phase diagram and thermodynamic data. A specific criterion for II-type phase-equilibrium displacement under isothermal–isobaric conditions is also formulated and generalized to systems with an arbitrary number of components.