Modeling tracer counter-permeation through anisotropic zeolite membranes: from mean field theory to single-file diffusion

Diffusion in anisotropic host-guest systems exhibiting a Langmuir-type adsorption isotherm is investigated using a tracer counter-permeation (TCP) simulation technique. In the TCP simulations, tagged and untagged molecules counter-diffuse through zeolite membranes of finite thickness. Fick's law is used to measure the diffusivities at high equilibrium occupancy, as a function of the membrane thickness, L, and anisotropy, eta. For values of eta much greater than 1, sorbate motion in the plane of the membrane is very rapid and washes out any correlations in the transmembrane direction, so that diffusion is well modeled by mean field theory. As eta is reduced, correlations between the motion of nearby molecules decrease the counter-diffusivity, but diffusion remains "normal" in the sense that the diffusivity is independent of thickness for sufficiently thick membranes. For membranes with eta=0, a single-file mode of diffusion occurs for all membrane thicknesses, and the counter-diffusivity becomes inversely proportional to thickness for thick membranes. Membranes with eta much less than 1 exhibit a single-file diffusion mode for thin membranes that changes over to a normal diffusion mode as the thickness is increased. We have also determined that the rate of transmembrane permeation is controlled by the ratio of the diffusion time to the sorption time, which is given by k(d)L/D where D is the counter-diffusivity and kd is the desorption coefficient. When permeation is diffusion limited, an assumption of local thermodynamic equilibrium is appropriate at the edges, and the permeability coefficient is independent of membrane thickness. On the other hand, when permeation is sorption limited, the edge concentrations are not determined by the isotherm, and the permeability coefficient depends on thickness so that the permeance is itself independent of membrane thickness. (C) 1999 Elsevier Science S.A. All rights reserved.