The effect of surface diffusion on surface reaction rates

We present a simple model to explore the role of surface diffusion on the rate of reaction between a surface diffusing species and a set of fixed randomly distributed reactive sites. A Langmuir adsorption/desorption term is used to describe the influence of the bulk phase on the surface. Reaction is modeled by a fast, with respect to surface diffusion, absorption on the perimeters of the reactive sites. A general effective medium theory is formulated for this model and solved approximately for the rate kf and diffusion coefficient D, which characterize the transport of the reactive density on a scale large compared with intersite dimensions. We find that surface diffusion can be an important contributing factor to the rate of reaction. In particular, when surface diffusion is rapid relative to the Langmuir adsorption/desorption rate, the reaction rate increases strongly with increasing reactive site surface concentration relative to its value for low surface site concentration.