Modeling the concentration dependence of diffusion in zeolites. III. Testing mean field theory for benzene in Na–Y with simulation

Abstract

We have performed kinetic Monte Carlo (KMC) simulations of benzene tracer diffusion in Na–Y for various loadings and temperatures to test the analytical diffusion theory presented in Paper I of this series. Our theory and simulations assume that benzene molecules jump among SII and W sites, located near Na+ ions in 6-rings and in 12-ring windows, respectively. Our diffusion theory is based on a mean field approximation (MFA) which yields Dθ=16kθaθ2, where aθ≅11 Å is the mean intercage jump length and 1/kθ is the mean supercage residence time. KMC simulations of D(θ), kθ, and aθ at 300 and 400 K show that our MFA is essentially exact for loadings that allow SII site vacancies, and that the concentration dependence is controlled by kθ. For higher loadings, the MFA error is independent of temperature, and increases roughly linearly with loading to a maximum value of ca. 25%, resulting from correlated motion. We present an analytical theory for such correlated motion at infinite vacancy dilution, which predicts the corresponding KMC simulated diffusivities to within statistical Monte Carlo error.