THE MAXWELL-STEFAN FORMULATION OF DIFFUSION IN ZEOLITES

Abstract

W.C. Conner and J. Fraissard (eds.), Fluid Transport in Nanoporous Materials, 211–240. © 2006 Springer. Printed in the Netherlands. Diffusion in zeolites is fundamentally different from diffusion in bulk fluid phases because it is influenced by molecular loading, �, i, and is anisotropic, in general. Furthermore, correlations between molecular jumps have a significant influence especially on mixture diffusion. From a phenomenological point of view, there are three different approaches to the setting up of the flux – driving force relationship for diffusion in zeolites. In the Fick approach the fluxes Ni are taken to be linearly dependent on the gradients of the loadings (i�, i) of all species with the “constants” of proportionality being the Fick diffusivities Dij; here we allow for coupling between flux of species i with the driving force of species j. The Dij are “practical” in the sense that the Fick relations can be incorporated in the equipment design equations. However, the Dij show complex dependences on loading and mixture compositions. Furthermore, the Fick transport coefficients are also affected by sorption equilibria. In the Onsager approach, based on the theory of Irreversible Thermodynamics (IT), the fluxes are postulated as linear functions of the chemical potential gradients (iµi), with the proportionality constants being the Onsager coefficients Lij. Use of iµi ensures that the sorption equilibria no longer influence the transport coefficients Lij. The Onsager Lij can be determined from Kinetic Monte Carlo (KMC) and Molecular Dynamics (MD) simulations using the Einstein or Green-Kubo formulae. The diagonal elements Lii cannot be identified with the corresponding values for the pure component i . If correlation effects are ignored, we obtain a diagonal matrix of Onsager transport. In general, for multicomponent mixtures (nt 2), all the Lij are influenced by correlation effects. Van t Hoff Institute for Molecular Sciences