Extension to the charge fluctuation model for the prediction of the conductivity of apolar, reverse micellar systems

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_B to the ion-pair size a. Fuoss & Kraus experimentally confirmed the dependence on λ_B 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_B/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_B/a.

Temperature Effects on Micelle Formation and Particle Charging with Span Surfactants in Apolar Media

This paper examines the effects of temperature on the micellization and particle charging behavior of the Span surfactant series in an apolar environment. The critical micelle concentrations of each of six surfactants at five temperatures were measured by conductometric techniques. The thermodynamic properties of micellization were calculated using Gibbs-Helmholtz analysis. Magnesia particles were then dispersed in solutions of these surfactants, and their electrophoretic mobilities were measured at three temperatures. Preliminary small-angle neutron scattering (SANS) experiments were conducted to measure the size of aggregates (referred to as reverse micelles) of three of the surfactants. It was found that for all but one of the surfactants the critical micelle concentration (CMC) increased by as much as an order of magnitude across a 40 °C range of temperature. One of the surfactants exhibited a decrease in CMC upon increasing temperature, likely due to a decrystallization of the tails upon reverse micelle formation. The maximum particle mobilities decreased upon increasing temperature due to the increased electrostatic screening by charged reverse micelles at higher temperatures.

The role of acid-base effects on particle charging in apolar media

The creation and stabilization of electric charge in apolar environments (dielectric constant≈2) have been an area of interest dating back to when an explanation was sought for the occurrence of what are now known as electrokinetic explosions during the pumping of fuels. More recently attention has focused on the charging of suspended particles in such media, underlying such applications as electrophoretic displays (e.g., the Amazon Kindle® reader) and new printing devices (e.g., the HP Indigo® Digital Press). The endeavor has been challenging owing to the complexity of the systems involved and the large number of factors that appear to be important. A number of different, and sometimes conflicting, theories for particle surface charging have been advanced, but most observations obtained in the authors' laboratory, as well as others, appear to be explainable in terms of an acid-base mechanism. Adducts formed between chemical functional groups on the particle surface and monomers of reverse micelle-forming surfactants dissociate, leaving charged groups on the surface, while the counter-charges formed are sequestered in the reverse micelles. For a series of mineral oxides in a given medium with a given surfactant, surface charging (as quantified by the maximum electrophoretic mobility or zeta potential obtained as surfactant concentration is varied) was found to scale linearly with the aqueous PZC (or IEP) values of the oxides. Different surfactants, with the same oxide series, yielded similar behavior, but with different PZC crossover points between negative and positive particle charging, and different slopes of charge vs. PZC. Thus the oxide series could be used as a yardstick to characterize the acid-base properties of the surfactants. This has led directly to the study of other materials, including surface-modified oxides, carbon blacks, pigments (charge transfer complexes), and polymer latices. This review focuses on the acid-base mechanism of particle charging in the context of the many other factors that are important to the phenomenon, including the presence of water, of other components (e.g., synergists and contaminants), and of electric field effects. The goal is the construction of a road map describing the anticipated particle charging behavior in a wide variety of systems, assisting in the choice or development of materials for specific applications.