Membranes which contain impermeable flakes or lamellae can show permeabilities much lower than conventional membranes. The variation of membrane permeability with flake volume fraction φ

flake aspect ratio α and slit aspect ratio δ is studied in this paper

and a new diffusion model in the barrier membranes is suggested:D 0/D=1/δ+α2φ2/(1-φ).This model is verified by the diffusion experiments of varying flake volume fraction φ and varying aspect ratio α . It can be concluded that the diffusion is greatly retarded by two factors: the tight slits between the flakes

and the tortuous wiggles to get around the flakes. The 1/δ is the effect of the slits which decreases the cross-sectional area through which diffusion can occur

while the α2φ2/(1-φ) is the effect of the wiggles which both decrease the cross-sectional area and increase the length for diffusion through the barrier membrane.