Monte Carlo simulations of diffusion in zeolites and comparison with the generalized Maxwell-Stefan theory

Abstract

Diffusion in zeolites is studied by means of Monte Carlo methods and the generalized Maxwell-Stefan theory of irreversible thermodynamics. The influence of the surface occupancy, the surface structure, and the surface chemical potential on one- and multicomponent surface diffusion has been investigated. Mass transfer has been simulated in one- and two-dimensional zeolitic channel structures. For the description of the sorption process two different models have been applied, a Langmuir model and a model with repulsive interactions between sorbed molecules. The one-component Fick diffusion coefficient, in the case of the Langmuir adsorption model, is found to be independent of the surface occupancy and depends weakly on the dimension of the lattice. Tracer diffusion on a one-dimensional lattice shows a linear dependence between the mean square displacement of labelled molecules and the square root of time. The mean square displacement in the case of tracer diffusion on the two-dimensional lattice follows the Einstein relation. The uptake behaviour of binary mixtures, co- and counter-diffusion, on the two-dimensional lattice as obtained from the Monte Carlo simulations is in agreement with a single-file diffusion model. The single-file diffusion matrix can be considered as a limiting case of the generalized Maxwell-Stefan formulation. The results of the Monte Carlo simulations and the single-file diffusion model show that the zeolitic structure has an influence on mass transfer rates in tracer flow and counterdiffusion. The coupling between surface fluxes present in the case of the transient uptake of a multicomponent mixture is demonstrated.