On the "Born" term used in thermodynamic models for electrolytes

In the literature, many expressions for the Helmholtz or Gibbs energy of electrolyte solutions have included a term that takes into account the variation of the solution permittivity with the composition of solution (e.g., within the statistical-associated fluid theory formalism). This contribution is often called the "Born" term because it was inspired by the classic expression established by Born to describe the solvation energy of an ion. The present work is an attempt to get more physical insight into this semiempirical "Born" term. The way in which it has been used in the literature is briefly examined, and its typical magnitude is evaluated. Next, it is proposed to use the nonprimitive mean spherical approximation model to calculate the chemical potential of an ion in a solution composed of charged hard spheres (HSs) (the ions) and dipolar HSs (the solvent). The cation and the anion are monovalent monoatomic ions of equal diameter. The dipoles have a different size and mimic water molecules. The theoretical expressions for this model were found to fulfill the Gibbs-Duhem relation, which suggests that they are correct. A rescaled ion-dipole contribution is introduced, in a form that is suitable for inclusion in electrolyte models. It is compared with a "Born" term expressed in the same framework. It is found that the former is in general not well estimated by the latter. The two might even be of opposite signs in the case of ions of sufficiently small size.