Langevin analysis of the diffusion model for surface chemical reactions

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.