Tutorial on the chemical potential of ions in water and porous materials: electrical double layer theory and the influence of ion volume and ion-ion electrostatic interactions

In this tutorial we address the chemical potential of ions in water (i.e., in a salt solution, in an electrolyte phase) and inside (charged) porous materials such as nanoporous membranes. In water treatment, such membranes are often used to selectively remove ions from water by applying pressure (which pushes water through the membrane while most ions are retained) or by current (which transports ions from a feedwater stream through the membrane). Chemical equilibrium across a boundary (such as the solution-membrane boundary) is described by an isotherm for neutral molecules, and for ions is described by an electrical double layer (EDL) theory. EDL theory describes concentrations of ions inside a porous material as function of the charge and structure of the material. There are many contributions to the chemical potential of an ion, and we address several of these in this tutorial, including ion volume and the effect of ion-ion Coulombic interactions.