Modeling permeation through anisotropic zeolite membranes with nanoscopic defects

We have modeled permeation through anisotropic zeolite membranes with nanoscopic defects that create shortcuts perpendicular to the transmembrane direction (x). We have found that the dimensionless ratio D_y/(k_dΔy) can be used to estimate whether the shortcuts contribute significantly to the overall flux. Here D_y is the diffusion coefficient for motion in the plane of the membrane, k_d is the rate of desorbing into defect voids, and Δy is the spacing between adjacent defects. For values of D_y/(k_dΔy)≫1, we find that shortcuts increase the flux by significant amounts. The magnitude of the flux is increased as the imperfection spacing Δy is decreased. For small values of Δy, permeation through shortcuts becomes sorption-limited so that decreasing Δy further does not increase the flux through a single shortcut. However, as Δy is decreased, the concentration of shortcuts increases, thereby increasing the total contribution of the shortcuts to the flux. We have found regimes where increasing Δy or decreasing D_y decreases the overall flux, showing that permeation can be diffusion-limited by motion perpendicular to the transmembrane direction.