A transition-state theory approach to adsorbate dynamics at arbitrary loadings

There has been much recent interest in using transition-state theory (TST) to extend the time and length scales accessible to molecular-level simulati ons of adsorbate transport in microsporous materials. However, the vast maj ority of this work has been performed on systems at infinite dilution. The objective of this paper is to obtain fundamental rate constants for adsorba te motion at nonzero loadings using multidimensional TST. More specifically , we focus on systems where the adsorption of a molecule is not highly loca lized in a single site, but rather distributed throughout an uncorrugated c age. We develop a theory in which high-dimensional TST integrals are approx imated using exact lower-dimensional information. The evaluation of the res ulting integrals is performed with an importance sampling method involving the insertion of a single molecule, thus improving the statistical quality of the results. The theory is applied to the motion of methane and xenon in the zeolite ZK4, where hopping between alpha cages is the rate-limiting ev ent. Our results show that hopping rates increase with loading in the cage, which is consistent with experimental trends in the diffusivity. Agreement between our theory and corresponding molecular dynamics simulations is exc ellent. (C) 1999 American Institute of Physics. [S0021-9606(99)70130-3].