Self-diffusion across the liquid-crystal interface

Abstract

We report a theoretical study of the variation of the self-diffusion coefficient across a liquid-crystal interface at equilibrium. The study is based on the assumption that the interface is broad compared to the molecular diameter of the diffusing particle. The structure at the interface is described by a set of position-dependent order parameters which change smoothly across the interface from zero in the pure liquid to nonzero constant values in the pure solid phase. The effective potential experienced by a particle at the interface is expressed in terms of these order parameters. A Smoluchowski equation is used to describe the dynamics in the presence of this effective potential. The calculated self-diffusion coefficient changes sharply over a length of 4-5 molecular layers in the interface and reproduces the essential features observed in recent computer simulations. We find that significant topological ordering takes place on the liquid side of the interface before the self-diffusion coefficient shows any detectable change from its liquid phase value. We discuss the limitations of the present approach and propose future applications of the model.