Entropic selectivity of microporous materials¤

The absorption of hard spheres into narrow pores is examined in the framework of RosenfeldÏs ““ fundamental measure ÏÏ formulation of density functional theory (DFT) for inhomogeneous Ñuids. The inÑuence of the dimensionality of the conÐning geometry is assessed by considering the cases of a spherical cavity, an inÐnite cylindrical channel and an inÐnite slit. The pores are assumed to be in chemical equilibrium with a reservoir which Ðxes the chemical potentials of the various species. The hard sphere mixture is considered as a highly simpliÐed model of aqueous solutions, involving a majority component (solvent) and solutes competing for absorption into the pores. It is shown that excluded volume e†ects alone can lead to very strong selectivities of the pores, for certain ratios of the solute and solvent to pore diameters. The selectivity is strongest for spherical cavities, and is least pronounced in the slit geometry. More complex geometries, including pore edge e†ects, with dimensions typical of simple ion channels through membranes, are also examined within the same DFT framework. The DFT predictions for the density proÐles inside the pores, and the resulting absorbances and selectivities, are tested by grand-canonical Monte Carlo (GCMC) simulations, and good agreement is found.