Forces between like-charged walls in an electrolyte solution: A comparison of McMillan–Mayer results for several models

Abstract

The interaction of like-charged walls immersed in aqueous solutions with monovalent counterions is investigated at the McMillan–Mayer (MM) level of description. The net pressure acting between the walls is obtained by applying the anisotropic hypernetted-chain theory. The MM approach requires solvent-averaged ion–ion potentials of mean force as input. Results based on “realistic” models for Na+ and Cl− in water are available in the literature and these are used in the present calculations. The wall–wall interactions obtained can differ dramatically from the primitive model (dielectric continuum solvent) case. For some models attractive wall–wall forces are observed at small separations. The MM theory is found to be rather sensitive to details of the counterion–counterion potential of mean force, and different models for the same counterion can give qualitatively different results. At present it is difficult to evaluate the relative accuracy of the different models that have been proposed. However, the results presented here give at least an idea of the interesting possibilities that lie in the physically realistic range.