Diffusion of carbon dioxide through silicone-polycarbonate membranes containing oriented mica flakes is proportional to the square of the volume fraction of the flakes, to the square of the aspect ratio, and to the square of the cosine of the angle at which the flakes are oriented These experiments are consistent with Monte Carlo simulations. The simulations allow investigation of more complex geometries, including other flake orientations and polydisperse flake sizes.