Interaction between penetration sites in diffusion through thin membranes

Two models of permeation through thin membranes are proposed: In the first, the membrane is represented as a plate with randomly distributed perforations, and the permeation rate is controlled by the rate at which penetrant diffuses through an external medium; in the second, the penetrant is considered to be adsorbed on one face of the membrane, and the rate controlling process is lateral diffusion across that face to a set of randomly distributed penetration sites. These models are treated by a self−consistent field procedure, and it appears that interaction between penetration sites influences the permeability significantly even when the number of penetration sites per unit area is quite low.