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).