Collective diffusion in the presence of substrate inhomogeneities and particle–particle interactions

A novel variational analytic approach to collective diffusion allowing the density dependent collective diffusion coefficient to be calculated in systems of interacting particles adsorbed on a crystalline substrate is presented. The approach, based on a kinetic lattice gas model extracts the diffusion coefficient directly from the master equations which account for the microscopic kinetics of the system in which microscopic processes underlying the diffusion are particle jumps between neighboring adsorption sites. Variational parameters minimizing the evaluated diffusional eigenvalue of the microscopic rate matrix are ‘geometrical’ and ‘correlational’ phases accounting, for the local potential energy landscape experienced by the adsorbed particle and the local correlations, respectively, i.e. an instantaneous occupation pattern of adsorption sites around the particle. Selected results, collective diffusion as a function of particle coverage, for the system of interacting particles adsorbed on a one dimensional non-homogeneous substrate with steps and for a system of non-interacting particles adsorbed on a two dimensional striped–stepped surface are presented and discussed. It is demonstrated in the latter case that the mean field approach which is known in the literature overestimates the diffusion coefficient and corresponds to the variational result in the limit of infinitely fast hopping kinetics in the direction parallel to steps.