Chemical diffusivity and wave propagation in surface reactions: Lattice-gas model mimicking CO-oxidation with high CO-mobility

We analyze the spatiotemporal behavior in a lattice-gas model for the monomer-dimer reaction on surfaces. This model, which mimics catalytic CO-oxidation, includes a mobile monomer adspecies (representing CO), an immobile dissociatively adsorbed dimer species (representing O), and a finite reaction rate (for $CO2$ production). We characterize in detail the propagation of the chemical wave or reaction front produced when the stable reactive steady-state of the model displaces the metastable CO-poisoned state. In the regime of high CO-mobility, such propagation can be described directly within a “hydrodynamic” reaction-diffusion equation formalism. However, we show that the chemical diffusivity of CO is dependent on the O coverage, reflecting the percolative nature of CO-transport through a background of immobile O. We also emphasize that gradients in the coverage of immobile O induce a diffusive flux in the highly mobile CO. These features significantly influence wave propagation and reaction front structure. In addition, our analysis accounts for the feature that in this hydrodynamic regime, correlations persist in the distribution of adsorbed immobile O, and that these influence the reaction kinetics, the steady states, and the percolation and diffusion properties. To this end, we utilize a “hybrid” approach which incorporates a mean-field reaction-diffusion treatment of adsorbed CO, coupled with a lattice-gas treatment of adsorbed O [Tammaro et al., J. Chem. Phys. 103, 10277 (1995)].