Ion-Pair Theory of Concentrated Electrolytes. III. Variational Principle

Abstract

Two major contributions are devised for that theory of concentrated electrolytes which by convention regards the ions as completely paired into uncharged dipolar “molecules.” First, a more satisfactory expression is obtained for the wavelength‐dependent static dielectric “constant” $\mathrm{\epsilon (k)}$ . Second, a variational principle for Helmholtz free energy $F$ is displayed whose minimization with respect to the ion‐pair size distribution $p^{\text{(1)}}$ serves to determine both $F$ and $p^{\text{(1)}}$ . In anticipation of future numerical applications, a binary collision approximation is specified for the short‐range interaction aspect of the functional ${\mathrm{F[p}}^{\text{(1)}}]$ .