Analytical theory of benzene diffusion in Na-Y zeolite

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Abstract
We have developed an analytical expression for the diffusion coefficient of benzene in Na-Y at infinite dilution in terms of fundamental rate coefficients, which has been confirmed by extensive kinetic Monte Carlo simulations. This model assumes that benzene jumps among SII and W binding sites, located near Na+ ions in 6-rings and in 12-ring windows, respectively. Our diffusion theory is based on D=16ka2 where a≅11 Å is the intercage length and k is the cage-to-cage rate coefficient. We have determined that k=k(SII→W)⋅12⋅3[1+k(W→W)/k(W→SII)], a finding that has resolved discrepancies between theory and simulation and has suggested new interpretations of benzene diffusion in Na-Y. When α(T)≡k(W→W)/k(W→SII) is between 0 and 1, the factor 3[1+α(T)] counts the number of thermally allowed target sites for cage-to-cage motion. Alternatively, when α(T)≫1, benzene mobility is interpreted as interstitial diffusion, wherein k is controlled by the probability of W site occupancy multiplied by the rate of W→W jump processes. This limit is expected to arise with benzene loadings of four molecules per supercage.