McMillan–Mayer theory for solvent effects in inhomogeneous systems: Calculation of interaction pressure in aqueous electrical double layers

Abstract

We demonstrate how to use the McMillan–Mayer theory to include solvent effects in effective solute–solute interactions for inhomogeneous systems, extending a recent derivation [S. Marčelja, Langmuir 16, 6081 (2000)] for symmetric planar double layers to the general case. In the exact treatment, the many-body potential of mean force between the solute molecules can be evaluated for an inhomogeneous reference system in equilibrium with pure bulk solvent. The reference system contains only solvent and a finite number, n, of fixed solute molecules and it has an external potential that in some cases is different from that of the original system. It is discussed how the n-body potential of mean force between the ions for the relevant cases of large n values can be approximated by a sum of effective singlet and pair interactions evaluated in the presence of, on average, all n ions, i.e., at finite concentration. In examples considered in this work we use effective interionic pair potentials evaluated from bulk electrolyte calculations at finite electrolyte concentrations. We calculate the contribution to the double layer interaction pressure arising from the interaction between ions dissolved in aqueous electrolyte. In cases of moderate or high surface charge, calculations show several new effects. At small surface separations one finds attractive and then strongly repulsive contributions. For surface charge density around one negative charge per 70 Å2 the full results for pressures resemble “secondary hydration force” measured in classical experiments in 1980s. When there is a tendency for ions to adsorb at the surfaces there is a marked change in behavior. The force is then oscillatory, reminiscent of results obtained with the surface force apparatus at low electrolyte concentration.