Monte Carlo simulations of surface diffusion at high coverages

Tracer diffusion on a surface is studied by performing Monte Carlo simulations in a two-dimensional noninteracting lattice gas with an emphasis on high coverages. Three different models were investigated: (1) The canonical model (CM), where the background particles on the surface can only diffuse in the parallel direction to the surface. (2) The grand canonical model (GM), where background particles are only allowed to desorb from or adsorb onto the surface (which means that the total number of particles on the surface fluctuates). (3) The combined grand canonic model (CGM), where background particles may both move in parallel (diffusion) or perpendicular (adsorption-desorption) to the surface. In all of these models the tracer is allowed to move only parallel to the surface. The results of the simulations were cast in the form of a correlation factor (the ratio between the calculated diffusion coefficient and the diffusion coefficient of a mean-field approximation). Correlation factors of the tracer were calculated for different surface coverages, and for different ratios between the jump rate of the tracer and the adsorption-desorption rate or/and jump rate of the background particles. In all of the cases, correlation factors showed an identical qualitative behavior: they decreased as surface coverage increases and as background particles became slower. This dependence of the correlation factors on surface coverage and on background particles rate becomes stronger for high surface coverage (above 70%), and for very slow background particles. Comparison to the theory of Harrison and Zwanzig (HZ) shows that it predicts reasonably well the general tendency of the correlation factors in different conditions and even agrees very well with the combined grand canonical simulations (Model 3) when the rates of adsorption-desorption and diffusion of background particles are of the same order.