Hybrid treatment of spatio‐temporal behavior in surface reactions with coexisting immobile and highly mobile reactants

For surface reactions on single‐crystal substrates which involve highly mobile adspecies, there is a vast separation in natural time and length scales. Adspecies hop rates can be many orders of magnitude larger than rates for other processes. Strong spatial correlations or ordering can exist on the atomic scale, while spatial pattern formation occurs on a macroscopic scale due to high diffusivity. An efficient analysis of such systems is provided by a ‘‘hybrid treatment’’ which we apply here to the monomer–dimer surface reaction model in the case of coexisting immobile dimer adspecies and highly mobile monomer adspecies. Specifically, we combine a mean‐field treatment of the ‘‘randomized’’ mobile adspecies, and a lattice‐gas description of the immobile adspecies. Monte Carlo simulations then reveal bistability and ‘‘critical’’ bifurcation phenomena, while precisely accounting for the influence of correlations in the immobile adspecies distribution. A corresponding analysis of the evolution of macroscopic spatial inhomogeneities is achieved through parallel simulation of the distributed macroscopic points with distinct correlated states and adspecies coverages. These simulations are appropriately coupled to describe diffusive mass transport of the mobile adspecies. In this way, we examine for this model the propagation and structure of chemical waves, corresponding to interface between bistable reactive states, and thereby determine the relative stability of these states.