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 $\mathrm{\epsilon (k)}$ . A rigorous formula of the Kirkwood type for $\mathrm{\epsilon (k)}$ is derived. Since ion‐atmosphere mean charge densities may be obtained from $\mathrm{\epsilon (k)}$ , 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 ${\text{κa\hspace{0.17em}>\hspace{0.17em}6}}^{\text{1\hspace{0.17em}/\hspace{0.17em}2}}{\mathrm{(\kappa }}^{\text{−\hspace{0.17em}1}}\mathrm{\hspace{0.17em}=\hspace{0.17em}}\mathrm{Debye\; length})$ .