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Earlier theories of electrolytic conductance are reviewed; all of these, with the exception of the Arrhenius-Ostwald theory, are based on physical models. Their theory failed to describe the conductance of strong electrolytes because it did not include the effects (then unsuspected) of long-range forces on mobility. Thermodynamic derivations are independent of model; applied to the postulated equilibrium A(+) + B(-) right arrow over left arrow A(+)B(-) between free ions and nonconducting paired ions, the thermodynamic pairing constant K(a) equals a(p)/(a+/-)(2), and DeltaG, the difference in free energy between paired ions (activity = a(p)) and free ions (activity = a(+/-)), equals (-RT ln K(a)). Converting to the molarity scale, K(a) = (1000 rho/M)[1 - gamma)/cy(2)(y(+/-))(2)]. Here rho is the density of the solvent of molecular weight M, c is stoichiometric concentration of electrolyte (mol/liter), gamma is the fraction of solute present as unpaired ions, and y(+/-) is their activity coefficient. The corresponding conductance function Lambda = Lambda(c;Lambda(0),R, big up tri, openG)involves three parameters: Lambda(0), the limiting equivalent conductance; R, the sum of the radii of the cospheres of the ions; and DeltaG. Conductance data for cesium bromide and for lithium chloride in water/dioxane mixtures and for the alkali halides in water are analyzed to determine these parameters. Correlations between the values found for R and DeltaG and properties characteristic of salt and solvent are then discussed.

It is shown that three and only three parameters are sufficient to generate a function Lambda (c; Lambda(0), K(A), R) which reproduces observed equivalent conductance Lambda as a function of concentration c within experimental error up to concentrations of about 2 x 10(-7)D(3) eq/liter (D = dielectric constant). The three parameters are: Lambda(0), the limit of Lambda(c) at zero concentration; K(A), the association constant; and R, a distance. Realization that conductance data can provide only one distance parameter suggests a model for electrolytic solutions in which R is defined as the radius of the sphere inside of which a unique partner can be found for a paired ion, and outside of which continuum theory may be applied. All system-specific effects (ion-ion and ion-solvent interactions, and the inherent spatial discontinuity of real solutions) appear within the spheres of radius R centered at the cations of the ion pairs. The association constant therefore depends not only on electrostatic attraction but also on the multiplicity of molecular parameters that are needed to describe short range interactions.

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

The conductance of 0.02-0.10 N potassium chloride in poly(vinyl alcohol)-water mixtures at 25 degrees decreases by about 50% as the polymer content increases from zero to 20% by weight, while the bulk viscosity increases from 0.0089 to over 1000 poises. Further increases in polymer concentration transform the highly viscous liquid into an elastomeric solid, in which the conductance still remains relatively high; it decreases significantly only after the glass composition (75% polymer at 25 degrees ) is reached. The internal viscosity, which controls ionic mobility, was estimated from the conductance data: it ranges from 0.01 to about 0.14 over the range 0-55% polymer, similar to the viscosity of many ordinary liquids. Rates of diffusion-controlled processes involving small molecules in macromolecular media can, therefore, be expected to be similar to those in usual solution.

By the addition of n-butyl bromide to a 1:19 copolymer of 4-vinylpyridine and styrene, water-insoluble, strong polyelectrolytes can be prepared. The addition of a hydrocarbon plasticizer permits the casting of flexible films in which large polycations are immobilized but in which bromide ions (or other small anions) are free to move. Electrical measurements on these membranes showed that they could be represented by a complex admittance: an electrolytic conductance in parallel with a pure A. C. impedance. The latter gives a circular arc when real component is plotted against imaginary. These synthetic membranes thus resemble in their electrical behavior that found by Cole for a variety of biological membranes.