Molecular sieve valves driven by adsorbate-adsorbate interactions: hysteresis in permeation of microporous membranes

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

The role of molecular interactions and interfaces in diffusion: Permeation through single-crystal and polycrystalline microporous membranes

In this second paper of a two part series, we investigate the implications of the interfacial phenomenon, caused by adsorbate-adsorbate interactions coupled with the difference in adsorbate density between the zeolite and the gas phase, upon benzene permeation through single-crystal and polycrystalline microporous NaX membranes. The high flux predicted for thin single-crystal membranes reveals that substantially enhanced flux should be expected in submicron films. Simulations also indicate that the standard local equilibrium assumption made for larger scale membranes is inapplicable at the submicron scale associated with nanometer size grains of thin and/or polycrystalline membranes. Apparent activation energies predicted for benzene permeation through NaX membranes via kinetic Monte Carlo (KMC) simulations are in good agreement with laboratory experiments. The simulations also uncover temperature-dependent flux pathways leading to non-Arrhenius behavior observed experimentally. The failure of the Darken approximation, especially in the presence of the interfacial phenomenon, leads to a substantial overprediction of the flux. Simulations of polycrystalline membranes suggest that this same interfacial phenomenon leads to resistance that can reduce flux by an order of a magnitude with only moderate polycrystallinity.

The role of molecular interactions and interfaces in diffusion: Transport diffusivity and evaluation of the Darken approximation

Kinetic Monte Carlo (KMC) simulations are carried out to directly study diffusion of benzene through thin (37-100 nm) NaX zeolite membranes under a gradient in chemical potential. Nonlinearities in adsorbate loading near the membrane boundaries are shown to arise from the difference in adsorbate density between the zeolite and adjacent fluid phase. Direct extraction of the transport diffusivity from gradient KMC simulations enables testing of the Darken approximation. This rigorous approach reveals limitations of the Darken approximation and, for the first time, the potentially complex nonunique functionality and multiplicity of the transport diffusivity for strongly interacting adsorbates. In the companion paper we explore these nonlinear interfacial effects in the context of permeation through both single-crystal and polycrystalline membranes.