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 effe cts in effective solute-solute interactions for inhomogeneous systems, exte nding a recent derivation [S. Marcelja, Langmuir 16, 6081 (2000)] for symme tric planar double layers to the general case. In the exact treatment, the many-body potential of mean force between the solute molecules can be evalu ated for an inhomogeneous reference system in equilibrium with pure bulk so lvent. The reference system contains only solvent and a finite number, n, o f fixed solute molecules and it has an external potential that in some case s 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 lar ge n values can be approximated by a sum of effective singlet and pair inte ractions evaluated in the presence of, on average, all n ions, i.e., at fin ite concentration. In examples considered in this work we use effective int erionic pair potentials evaluated from bulk electrolyte calculations at fin ite electrolyte concentrations. We calculate the contribution to the double layer interaction pressure arising from the interaction between ions disso lved in aqueous electrolyte. In cases of moderate or high surface charge, c alculations show several new effects. At small surface separations one find s attractive and then strongly repulsive contributions. For surface charge density around one negative charge per 70 Angstrom (2) the full results for pressures resemble "secondary hydration force" measured in classical exper iments in 1980s. When there is a tendency for ions to adsorb at the surface s there is a marked change in behavior. The force is then oscillatory, remi niscent of results obtained with the surface force apparatus at low electro lyte concentration. (C) 2001 American Institute of Physics.