Tutorial on the chemical potential of ions in water and porous materials: transport, isotherms, and electrical double layer theory

In this tutorial we discuss the chemical potential of ions in water (i.e., in a salt solution, in an electrolyte phase) and inside (charged) nanoporous materials such as porous 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 rejected) or by current (which transports ions 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 by an electrical double layer (EDL) model. An EDL model 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. We also describe transport and chemical reactions in solution, and how they are affected by Coulombic interactions.