Kinetics of catalytic reactions with diffusional relaxation

The kinetics of an irreversible monomer-monomer model of heterogeneous catalysis is investigated. In this model, two reactive species, A and B, adsorb onto a catalytic substrate with a rate I and diffuse onto it with a diffusion rate D. Atoms of similar species aggregate to form immobile islands while atoms of dissimilar species combine and desorb from the substrate. In the limit of low coverage we find that the island-size distribution function exhibits a scaling behavior. In particular, a mean-field rate equation analysis shows that the density of the overall number of islands N(t) and the average number of atoms per islands S(t) follow power law behaviors: N∼(${\mathit{I}}^3$t/${\mathit{D}}^2$ ${)}^{1/5}$ and S∼(${\mathit{DIt}}^2$ ${)}^{1/5}$. For the two-dimensional substrate we derive logarithmic corrections to the mean-field predictions, while in one dimension we develop a modified rate-equation approach that gives N∼(${\mathit{I}}^3$t/${\mathit{D}}^2$ ${)}^{1/7}$ and S∼(${\mathit{DI}}^2$ ${\mathit{t}}^3$ ${)}^{1/7}$.