Thermodynamic models for a concentration and electric field dependent susceptibility in liquid electrolytes

Abstract

The dielectric susceptibility χ is an elementary quantity of the electrochemical double layer and the associated Poisson equation. While most often χ is treated as a material constant, its dependency on the salt concentration in liquid electrolytes is demonstrated by various bulk electrolyte experiments. Moreover, it is theoretically well accepted that the susceptibility declines for large electric fields. An analysis based on non-equilibrium thermodynamics reveals that, compared to the case of a constant χ, non-obvious generalizations of the model equations are required if the susceptibility is a function of species concentrations and the electric field. Particular attention needs to be paid to the consistent coupling of the Poisson equation, the momentum balance and the chemical potentials functions. In a numerical study, we systematically analyze the effects of a concentration and field dependent susceptibility on the double layer of a planar electrode|electrolyte interface. We observe that the field dependence can cause strong reduction of the boundary layer width. Concentration dependent susceptibility can prevent complete removal of the solvent from the interface and combination of field and concentration dependency can further change the qualitative behavior of the boundary layer model such that profiles of the ion concentrations are non-monotonous. Both dependencies of χ have the tendency to reduce the capacitance maxima height.