The transition from a molecular to a continuum solvent in electrical double layers showing ion–ion correlation effects

Abstract

We analyze, using Monte Carlo simulations, how a dielectric medium, modeled as a Stockmayer fluid, modulates the force between two similarly charged surfaces. A major objective is to provide a basis for understanding the strengths and weaknesses of the primitive model. The system studied has uniformly charged walls separated by counterions and solvent, where the latter is kept at constant chemical potential as the separation between the walls is varied. For two different types of Stockmayer fluids, one with a “low” (ε_r ≃ 4.4) and one with a “high” (ε_r ≃ 20) relative dielectric permittivity, the size of the solvent molecules is varied systematically. As the size of the solvent molecules becomes smaller one approaches the continuum limit, where the primitive model should give an increasingly more accurate representation. We find that having an explicit description of the solvent gives rise to an oscillatory component in the force between the surfaces. The wavelength of the oscillations reflects the diameter of the solvent molecules. The smaller the solvent molecules the smaller are the amplitudes of the oscillations. On integrating the force curves to yield interaction free energies the oscillatory features become less apparent. For the smallest solvent size studied the interaction curves show clear similarities with those obtained from the primitive model. The qualitative effect of the dielectric screening is recovered. It is found that the deviations from the mean field description also appear for the molecular solvent. All this suggests that there are no major deviations due to the neglect of many-body contributions in the solvent-averaged potential of the primitive model. This also holds for the incompressibility assumption implicitly applied when using the primitive model.