Density Functional Study of a Simple Membrane Using the Solvent Primitive Model

Abstract

The model membrane, whose surfaces are maintained at the differing surface potentials, V1 and V2, on its inner and outer surfaces, that has been studied previously is extended to include explicit solvent molecules. The solvent primitive model, where the solvent molecules are treated as hard spheres, is used. In this study, the electrolyte can interact with the membrane both electrostatically and by means of a short-range van der Waals-like potential that can be attractive or repulsive. The bulk fluid beyond the outer surface is a four-component electrolyte consisting of the hard sphere solvent, two species of cations, and one species of anions. The membrane is impermeable to one of the cation species so that the fluid in the membrane and beyond the inner surface is a three-component electrolyte. Previously, we studied this model membrane by computer simulation and density functional theory (DFT) and found this theory to be quite accurate. Here we report further results, obtained using DFT, from which results can be obtained much more easily than from simulations. The density profiles of the electrolyte near the membrane and the charge–potential relationship of the membrane surfaces under a wider variety of conditions than is possible by simulation are studied. The presence of the solvent molecules leads to a greater excluded volume. As a result, the density profiles are oscillatory, whereas they are monotonic when a molecular model for the solvent is not used. The potential versus charge relationship is strongly influenced by the solvent density. In addition to the electrostatic interactions, the effect of a van der Waals interaction on the solvent molecules is considered.