title: Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.
abstract: While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.
authors.affiliation: Center for Catalytic Science and Technology (CCST) and Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716, USA.
authors.forename: Abhijit
authors.initials: A
authors.lastname: Chatterjee
authors.forename: Dionisios G
authors.initials: DG
authors.lastname: Vlachos