The dependence of hopping diffusion upon lattice topology, and occupancy by the diffusing molecules, was studied using Monte Carlo simulations. For poorly connected lattices, such as ZSM-5/silicalite, the self-diffusivity deviated strongly from the linear mean-field result; especially at high occupancies. A time-correlation formalism was derived to predict the deviations, which were proportional to the accumulated correlation between the displacement at some time and the first attempted hop. Renormalized deviations depended upon lattice topology, but not upon occupancy, so that the curves for various occupancies could be collapsed into a single curve which could be well approximated by a stretched exponential. The results showed that a mean-field theory with correlated time-steps should work adequately for well-connected lattices, but poor performance was predicted for such poorly connected lattices as ZSM-5.

Effect of Topology and Molecular Occupancy on Self-Diffusion in Lattice Models of Zeolites - Monte-Carlo Simulations. M.O.Coppens, A.T.Bell, A.K.Chakraborty: Chemical Engineering Science, 1998, 53[11], 2053-61