Mesoscopic modeling of binary diffusion through microporous zeolite membranes
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Mesoscopic modeling of binary diffusion through microporous zeolite membranes Mark A. Snyder and Dionisios G. Vlachos Department of Chemical Engineering and Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716-3110, U.S.A. ABSTRACT The mesoscopic framework describing single-component diffusion through microporous materials is extended here to characterize binary diffusion in the absence of intermolecular forces. Two diffusion mechanisms, single-file diffusion characteristic of confined pore structures and species-species exchange consistent with diffusion modes in less-confined pore topologies, are incorporated at the Master Equation level. Derived fundamentally via rigorous coarse-graining of the underlying Master Equation, the binary mesoscopic relation is validated via direct comparison to gradient continuous time Monte Carlo (G-CTMC) simulations. We further show the capability of this fundamentally derived model to capture the macroscopic diffusion phenomenon of ‘overshoot’ or ‘roll-up’ in the transient uptake and flux. Exploration of the species-species exchange mechanism reveals its strong effect on the transient ‘overshoot’ behavior through relaxation of the constrained single-file diffusion.
INTRODUCTION A vast body of research has focused on characterizing the diffusion through microporous zeolite membranes in attempts to develop a priori predictive models for rational membrane design. Practical application of these materials requires understanding of multicomponent diffusion phenomena. Perhaps the most widely recognized modeling framework for such insight is the Generalized Maxwell-Stefan relation, extended by Krishna [1] to describe surface and micropore diffusion of single and multi-component mixtures. Intended to overcome the lengthand time-scale limitations of atomistic simulations, the Generalized Maxwell-Stefan (GMS) relations have been successfully employed to qualitatively [2-5] and in some cases quantitatively [1, 5, 6] capture the transient ‘overshoot’ or ‘roll-up’ phenomenon denoted by a species overshooting its steady state flux or uptake. The phenomenological derivation of the GMS theory, however, limits its predictive capabilities. An alternative approach is the application of a fundamentally derived mesoscopic relation to characterize the diffusion on a continuum level while retaining molecular scale information. In this short communication, we validate the mesoscopic theory of binary diffusion in the absence of intermolecular forces, and explore the capabilities of the mesoscopic framework as a fundamental model to predict and characterize macroscopic diffusion phenomena.
MESOSCOPIC FRAMEWORK DESCRIBING BINARY DIFFUSION The diffusion of strongly adsorbing species along the pores of a zeolite is governed by rare event dynamics, where molecules migrate between deep energy wells or binding sites. The pore
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structures of zeolite membranes can, therefore, be accurately represented as a lattice of binding sites, with diffusion along thi
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