Abstract
An analysis is presented of the magnitude of some of the potential sources of error in a recently developed diffusion model of surface chemical reactions. Using single absorber Langevin simulations, comparisons are made between the diffusion equation model and the Fokker–Planck equation for the rates of diffusion controlled surface chemical reactions. The diffusion equation is found to predict rates in good agreement with the Fokker–Planck equation for physical values of the diffusion constant. For unphysically large diffusion constants, the rates predicted by the diffusion equation are found to be in error. By employing multiple absorber Langevin simulations errors in the single absorber approximation used in the diffusion model of surface reactions are examined. The single absorber model is found to be accurate for weakly bound adsorbates. For strongly bound adsorbates rate expressions derived from a two-dimensional model are found to be appropriate. The relative rates of Eley–Rideal and Langmuir–Hinshelwood mechanisms are also studied by multiple absorber Langevin simulations. The ratios of the Eley–Rideal to the Langmuir–Hinshelwood rate is found to be in good agreement with the predictions of the diffusion equation model for physically reasonable diffusion constants. The time dependent solution to the diffusion equation considered in a previous publication is given in an appendix.
Highlights
In recent years, diffusion constants for the migration of adsorbates on crystal surfaces have become available both from molecular dynamics calculations[1,2,3,4] and a variety of experimental techniques. 5 The interest in surface diffusion is partially motivated by the fact that diffusion is a primary step in the dynamics of many surface processes
An analysis is presented of the magnitude of some of the potential sources of error in a Iecently developed diffusion model of surface chemical reactions
Using single absorber Langevin simulations. comparisons are made between the diffusion equation model and the Fokker-PIanck equation for the rates of diffusion controlled surface chemical reactions
Summary
Diffusion constants for the migration of adsorbates on crystal surfaces have become available both from molecular dynamics calculations[1,2,3,4] and a variety of experimental techniques. 5 The interest in surface diffusion is partially motivated by the fact that diffusion is a primary step in the dynamics of many surface processes. The model developed in I for diffusion influenced rate expressions for surface reactions contains a number of assumptions the effect of which require further analysis. In contrast to solution kinetics the single absorber model may be inappropriate for surface reactions, because the influence of the absorption boundary conditions on the concentration profile is long range in two dimensions. We analyze the magnitude of the errors in I which arise from the use of the diffusion equation within the Single absorber approximation We carry out this analysis by comparing the expressions derived in I with the results of simulations of diffusive processes using the Langevin equation. We derive the time dependent solution to Eq (1) in the Appendix and develop the behavior of the solution in a number of limits
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