Impedance of an electric double layer capacitor with a multi-component electrolyte

Abstract

I derive the impedance response of an ideal electrolyte containing an arbitrary number of mobile ionic species between blocking planar electrodes, described by the Poisson--Nernst--Planck equations. By transforming the linearized equations to a charge--salt basis, the response is written in terms of a multi-component diffusion--migration matrix and its eigenvalues/eigenvectors. When all diffusivities are equal, the charge mode decouples from the neutral concentration subspace and the classical binary-electrolyte result is recovered. In contrast, unequal diffusivities couple charge relaxation to one or more neutral composition modes. For a ternary electrolyte with two cations and one anion, this coupling produces additional diffusive features and broadens the crossover between resistive and capacitive regimes. The results found in this paper provide a minimal continuum explanation for why mixed electrolytes can display impedance spectra that cannot be interpreted as a simple binary electrolyte with an averaged diffusion coefficient.