Modeling the concentration dependence of diffusion in zeolites .1. Analytical theory for benzene in Na-Y

We have developed an analytical expression for the diffusion coefficient of benzene in Na-Y at finite loadings in terms of fundamental rate coefficients. Our theory assumes that benzene molecules jump among S-II and W sites, located near Na+ ions in 6-rings and in 12-ring windows, respectively. We assume that instantaneous occupancies in different supercages are identical, a mean field approximation yielding D-theta = 1/6k(theta)a(theta)(2) where a(theta) congruent to 11 Angstrom is the mean intercage jump length and 1/k(theta) is the mean supercage residence time, We show that k(theta) = kappa.k(1).P-1, where P-1 is the probability of occupying a W site, k(1) is the total rate of leaving a W site, and kappa is the transmission coefficient for cage-to-cage motion. We assume kappa = 1/2 for all loadings, and derive analytical formulas for the T and theta dependencies of k(1) and P-1, assuming that S-II and W site occupancies are either 0 or 1 and that benzenes do not otherwise interact, Exact expressions for P-1 in the canonical and grand canonical ensembles are related for finite systems with a new correspondence rule. For theta < 2/3, the S-II-->W-->S-II process contributes no loading dependence to k(theta), while the S-II-->W-->W process gives an increasing loading dependence of 1/(2-3 theta), For theta > 2/3, k(theta) initially increases due to enhanced W population, then decreases due to blocking of target W sites. In the article that follows this one we show that our theory agrees quantitatively with simulation, and agrees qualitatively with experiment for low to moderate loadings. (C) 1997 American Institute of Physics.