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

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. Marcelja, 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 e...