Formation of Charge Carriers in Liquids.

After presenting a brief historical overview of the classic contributions of Faraday, Arrhenius, Kohlrausch, Bjerrum, Debye, Hückel and Onsager to understanding the conductivity of true electrolytes in aqueous solutions, we present an in-depth review of the 1933 work of Fuoss & Kraus who explored the effect of the solvent on electrolyte dissociation equilibria in either polar or nonpolar media. Their theory predicts that the equilibrium constant for dissociation decays exponentially with the ratio of the Bjerrum length λ to the ion-pair size a. Fuoss & Kraus experimentally confirmed the dependence on λ of the solvent, while more recent experiments explored the dependence on a. We also present an in-depth review of the charge-fluctuation theory used to explain the sharp increase in conductivity with added water for water-in-oil microemulsions stabilized by ionic surfactants. Water swells the droplets making a greater fraction of them charged. At least for low-water content, the same exponential dependence on λ/a is predicted, provided a is chosen as the size of the polar core of the droplet or inverted micelle. Potential electrolytes like alcohols acquire charge by exchanging a proton. The dissociation equilibrium of the resulting ion-pair in mixtures of toluene and alcohol appears to be well modelled by the Fuoss theory. Solutions of inverted micelles are also thought to acquire charge by exchanging a small ion between two net-neutral micelles. Except for the dissociation of true electrolytes, all of the charging scenarios described above can be represented by a two-reaction sequence: 1) the disproportionation of charge between two neutral molecules, inverted micelles or droplets; followed by 2) the dissociation of the "ion"-pair intermediates. (The dissociation of true electrolytes involves only the second.) For each of the above charging theories, the extent of the second reaction decays exponentially with λ/a.