(452f) Simplified Universal Equation for Ionic Conductivity of Concentrated Multicomponent Mixtures

Nernst-Einstein equation can provide a reasonable estimate of ionic conductivity of dilute solutions. For concentrated solutions, alternate methods such as Green-Kubo relations and Einstein relations are more suitable to account for ion-ion interactions. Such computations can be expensive for multicomponent systems. Simplified mathematical expressions like the Nernst-Einstein equation do not exist for concentrated multicomponent mixtures. Newman's treatment of multicomponent concentrated solutions yields a conductivity relation in terms of species concentration and Onsager phenomenological coefficients. However, the estimation of these phenomenological coefficients is not straightforward. Here, mathematical formulations that relate the phenomenological coefficients with the friction coefficients are developed, leading to a simplified, ready-to-use version of conductivity relations that can be used for a wide range of ionic mixtures. This approach involves spectral decomposition of the matrix of Onsager phenomenological coefficients. The general conductivity expression is simplified for binary electrolytes, and analytical solutions are provided for ternary and quaternary mixtures with ion dissociation.