Simple phenomenological models for phase transitions in a confined geometry. 1: Melting and solidification in a cylindrical pore

A simple phenomenological model is proposed to describe the melting and solidification of a pure component in an infinite cylindrical pore. It is derived within the frame of the Gibbs dividing surface theory. System free energy density is described through usual interfacial tensions and a term taking into account the interaction between interfaces. Metastable melting and equilibrium solidification transitions can then be defined. The temperatures at which they occur reasonably agree with experimental data for confined water. The solid-liquid transition appears to be first order in this model. In agreement with experimental observations, the hysteresis width between melting and solidification decreases as the pore size decreases, and there is a critical pore size for which no hysteresis is observed. An extension of this model to the nucleation of the solid phase allows to take into account finite pore length effect.