Role of Stefan-Maxwell fluxes in the dynamics of concentrated electrolytes.

Abstract

This theoretical analysis quantifies the effect of coupled ionic fluxes on the charging dynamics of an electrochemical cell. We consider a model cell consisting of a concentrated, binary electrolyte between parallel, blocking electrodes, under a suddenly applied DC voltage. It is assumed that the magnitude of the applied voltage is small compared to the thermal voltage scale, RT/F, where R is the universal gas constant, T is the temperature and F is the Faraday's constant. We employ the Stefan-Maxwell equations to describe the hydrodynamic coupling of ionic fluxes that arise in concentrated electrolytes. These equations inherently account for asymmetry in the mobilities of the ions in the electrolyte. A modified set of Poisson-Nernst-Planck equations, obtained by incorporating Stefan-Maxwell fluxes into the species balances, are formulated and solved in the limit of weak applied voltages. A long-time asymptotic analysis reveals that the electrolyte dynamics occur on two distinct time scales. The first is a faster "RC" time, τ_RC = κ^-1L/D_E, where κ^-1 is the Debye length, L is the length of the half-cell, and D_E is an effective diffusivity, which characterizes the evolution of charge density at the electrode. The effective diffusivity, D_E, is a function of the ambi-polar diffusivity of the salt, D_a, as well as a cross-diffusivity, D_+-, of the ions. This time scale also dictates the initial exponential decay of current in the external circuit. At times longer than τ_RC, the external current again decays exponentially on a slower, diffusive time scale, τ_D∼L²/D_a, where D_a is the ambi-polar diffusivity of the salt. This diffusive time scale is due to the unequal ion mobilities that result in a non-uniform bulk concentration of the salt during the charging process. Finally, we propose an approach by which our theory may be used to measure the cross-diffusivity in concentrated electrolytes.