Dynamics of surface enrichment: A theory based on the Kawasaki spin-exchange model in the presence of a wall

Abstract

A mean-field theory is developed for the description of the dynamics of surface enrichment in binary mixtures, where one component is favored by an impenetrable wall. Assuming a direct exchange (Kawasaki-type) model of interdiffusion, a layerwise molecular-field approximation is formulated in the framework of a lattice model. Also the corresponding continuum theory is considered, paying particular attention to the proper derivation of boundary conditions for the differential equation at the hard wall. As an application, we consider the explicit solutions of the derived equations in the case where nonlinear effects can be neglected, studying the approach of an initially flat (homogeneous) concentration profile, where the surface concentration is the same as in the bulk, towards equilibrium, where some surface enrichment of one component is present. It is shown that the concentration profile shows a transient minimum (the distance of this minimum from the wall diverges as √ as the timet in this “quenching experiment” goes to infinity). Both the lattice theory and the continuum theory are shown to yield equivalent results. Finally, an outlook to possible extensions (dynamics of wetting transition etc.) and further applications is given.