Modeling tracer counter-permeation through anisotropic zeolite membranes: from mean ®eld theory to single-®le diffusion

Diffusion in anisotropic host±guest systems exhibiting a Langmuir-type adsorption isotherm is investigated using a tracer counterpermeation (TCP) simulation technique. In the TCP simulations, tagged and untagged molecules counter-diffuse through zeolite membranes of ®nite thickness. Fick's law is used to measure the diffusivities at high equilibrium occupancy, as a function of the membrane thickness, L, and anisotropy, . For values of 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 ®eld theory. As 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 suf®ciently thick membranes. For membranes with ˆ0, a single-®le mode of diffusion occurs for all membrane thicknesses, and the counter-diffusivity becomes inversely proportional to thickness for thick membranes. Membranes with 1 exhibit a single-®le 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 kdL/D where D is the counter-diffusivity and kd is the desorption coef®cient. When permeation is diffusion limited, an assumption of local thermodynamic equilibrium is appropriate at the edges, and the permeability coef®cient 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 coef®cient depends on thickness so that the permeance is itself independent of membrane thickness. # 1999 Elsevier Science S.A. All