Ion-Pair Theory of Concentrated Electrolytes. I. Basic Concepts

The statistical thermodynamics of symmetrical “primitive-model” electrolytes is formulated in such a way that all ions are uniquely paired. The behavior of the resulting fluid of “polar molecules” may conveniently be described by a wavelength-dependent dielectric constant ε(k). A rigorous formula of the Kirkwood type for ε(k) is derived. Since ion-atmosphere mean charge densities may be obtained from ε(k), this dielectric function is utilized in construction of an electrolyte free-energy expression Eq. (50), as well as to establish an exact second-moment condition on the ion atmospheres Eq. (73). From the latter it is demonstrated that for rigid spherical ions of diameter a, the ion atmospheres necessarily each have nonuniform charge sign when κa 61 / 2 (κ− 1 = Debye length).