Rate Expressions in Mean Field Microkinetic Models Incorporating Multiple Types of Active Sites

It is well known that heterogenous catalysts exhibit a distribution of sites/structures, some more active than others but more than one often being important to the underlying reaction mechanism(s). The inclusion of this reality in mean field microkinetic models has been largely avoided in favor of lattice-based models like cluster expansions where in principle different types of sites can be explicitly defined. Here, we develop a thermodynamically self-consistent theory of multi-site microkinetics from the first principles of statistical mechanics to show how multiple site types can be represented in mean field microkinetic models. The theory incorporates local enthalpies and entropies, lateral molecular interactions, and global entropy; generating thermodynamic activities for any number of site types that deviate significant from those of idealized models. We provide the resultant rate expressions for rates of adsorption/desorption and surface diffusion between the site types. Contrary to what is typically assumed, even when a species has access to many different sites or binding configurations, only one rate, which is driven by the average adlayer chemical potential, can be defined for desorption from the surface. The approach in this work correctly describes adsorption/desorption and diffusion for a multi-site model of a heterogenous catalyst and differs from the commonly used law of mass action.