Charge–cavity and charge–dipole effects in ionic fluids

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Abstract
The contribution of charge–dipole interactions to the thermodynamics and structure of ionic solutions is considered from the standpoint of two models—a quasicontinuum cavity model of charged spheres of dielectric constant ε0 in a continuum of dielectric constant ε as well as a molecular model consisting of charged‐sphere solute particles and dipolar‐sphere solvent particles. With suitable scaling of the interaction potentials one expects to obtain the cavity‐model description from the molecular model in the limit σd/σi→0, where σd and σi are the ion and dipolar‐particle diameters, respectively. We recover for the first time the full r−4 ‘‘cavity‐term’’ of the ion–ion cavity‐model pair potential in such a limit as well as a corresponding screened r−4 term in the solvent‐averaged direct correlation function, which is screened by the factor e−2λr and multiplied by the prefactor (1+λr)2, where λ is the ion–ion inverse screening length. Here, r is the distance between a pair of ions. We also show that if one makes the usual approximation of pairwise additivity of the n‐ion potentials of mean force at infinite dilution, one loses both the screening and the prefactor, recovering an earlier result in G. Stell, Phys. Rev. A 45, 7628 (1992). This is thermodynamically significant; if there were no screening of the r−4 term, there could not be a critical point in the ionic fluid if ε0<ε, while if ε0≳ε, the critical point would be mean‐field‐like if there were no screening, as pointed out in the earlier work.