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Thin-film membranes have been made from cavity-containing supramolecular building blocks known as molecular squares and evaluated for simple test separations. Permeation properties of single components and binary gas mixtures were measured through membranes made of several different molecular squares. For a small square with pyrazine edges, permeation increased in the order cyclohexane, consistent with the selectivities predicted from the sorption coefficients. Diffusion rates also play an important role in the permeation selectivity. For a larger square with porphyrin edges, mixture selectivities for 4-picoline over toluene were observed to be around 7–9, depending on the partial pressure. Functionalization of the interior of the porpyrin square allowed a mixture selectivity of 7 for benzene over cyclohexane. Independently measured adsorption isotherms and effective diffusion coefficients proved very helpful in understanding the effects of sorption and diffusion on the observed permeabilities. [Copyright &y& Elsevier]