Entropic selectivity of microporous materials

The absorption of hard spheres into narrow pores is examined in the framework of Rosenfeld's “fundamental measure” formulation of density functional theory (DFT) for inhomogeneous fluids. The influence of the dimensionality of the confining geometry is assessed by considering the cases of a spherical cavity, an infinite cylindrical channel and an infinite slit. The pores are assumed to be in chemical equilibrium with a reservoir which fixes the chemical potentials of the various species. The hard sphere mixture is considered as a highly simplified model of aqueous solutions, involving a majority component (solvent) and solutes competing for absorption into the pores. It is shown that excluded volume effects 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 effects, with dimensions typical of simple ion channels through membranes, are also examined within the same DFT framework. The DFT predictions for the density profiles inside the pores, and the resulting absorbances and selectivities, are tested by grand-canonical Monte Carlo (GCMC) simulations, and good agreement is found.