Pseudolattice theory of charge transport in ionic solutions: Corresponding states law for the electric conductivity

A statistical mechanical framework for charge transport in ionic liquid–solvent mixtures based on the existence of a statistical lattice structure (pseudolattice) throughout the whole range of concentration is reported. The ion distribution is treated in a mean-field Bragg–Williams-like fashion, and the ionic motion is assumed to take place through hops between cells of two different types separated by non-random-energy barriers of different heights depending on the cell type. Assuming non-correlated ion transport, the electrical conductivity is shown to have a maximum, arising from the competition between the concentration of charge carriers in the bulk medium and their mobilities in the pseudolattice. An explicit expression for the concentration at which this maximum occurs is given in terms of microscopic parameters, and the electrical conductivity normalized by its maximum value (κ/κ_max) is shown to follow rather closely a universal corresponding states law in concentration space when represented against the ionic concentration scaled by its value at the conductivity maximum (?_α/?_max). Ion–ion and ion–solvent interactions are explicitly considered combining the path probability method for charge transport in solid electrolytes and the Bragg–Williams approximation for interparticle interactions, and their impact on the deviations of experimental data from the universal behavior of non-correlated transport analyzed. The theoretical predictions are shown to satisfactorily predict experimental values of electrical conductivity of aqueous solutions of conventional electrolytes and of mixtures of room temperature molten salts with typical solvents.