Lennard-Jones fluid mixtures in contact with semipermeable membranes. A density functional approach

A density functional approach based on Kierlik-Rosinberg theory is applied to a two-component Lennard-Jones mixture in contact with a selectively perm eable membrane. The results of theoretical calculations are compared with t he grand canonical ensemble Monte Carlo simulations. The density profiles o btained for temperatures higher than the critical temperature agree well wi th simulation data if the difference in the diameters of particles of two c omponents is small. We have also obtained that the agreement between the th eory and simulations is reasonable if the particles of the component that p enetrates the membrane are twice larger than the particles of nonpenetratin g component. For other diameter ratios and for the case when the density of the mixture is high, the theory disagrees with simulations. At temperature s lower than the critical temperature the theoretical density profiles also have been evaluated, and a possibility of multiple solutions of the densit y profile equation, corresponding to the existence of different phases, is discussed.