Application of the charge regulation model to the separation of ions by hydrophilic membranes

Separation of ions from aqueous solutions by the use of hydrophilic membranes can be described by the charge regulation (CR) model. This is an approach in which the Poisson-Boltzmann equation is combined with a boundary condition at the surface that relates the local ion concentrations in the solution next to the surface to the concentration of each of the adsorbed species. Here, we use the CR model in a simple calculation in which we assume thermodynamic equilibrium and calculate the ion concentrations across the radius of a cylindrical pore slice that is far enough from either of the membrane surfaces for axial concentration gradients to be zero. We use an expression for the ion retention that is based on the equilibrium ion profiles in that slice. For a pure, monovalent salt, this expression qualitatively describes the change of ion retention with pore radius, ion concentrations, and pH. The present calculation does not yet incorporate ion transport expressions; hence, it cannot account for the influence of pressure and flux on retention or describe the retention for mixtures of salts. (C) 2001 Academic Press.