Paired ions: Dipolar pairs as subset of diffusion pairs

Previous models for which theories of electrolytic conductance have been developed are reviewed. Discrepancies between theoretically derived values of parameters and parameters characteristic of real physical systems suggested the following revised model. Ions are counted as diffusion pairs if their center-to-center distance r is in the range a </= r </= R, in which a is contact distance and R is the diameter of the Gurney cosphere. A fraction alpha of these pairs diffuse to contact to form nonconducting dipolar pairs; alpha/(1-alpha) = exp(-E(s)/kT), in which E(s) is the difference in energy between a diffusion pair at r = R and a contact pair, k is the Boltzmann constant, and T is the absolute temperature. This model permits separate treatment of long-range and short-range interionic effects. The former (relaxation field and electrophoresis) depend on R and the values of the dielectric constant and viscosity of the pure solvent. The latter (formation of dipolar pairs) is described by E(s), or alternatively by K(s) = exp(-E(s)/kT) in which K(s) is the constant describing the steady state between solvent-separated diffusion pairs and dipolar (contact) pairs. For solutions of the alkali halides, a simple empirical correlation is found between R and the Pauling radii of the cations, and also between E(s) and the sum of the radii of cation and anion.