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Impedance of an electric double layer capacitor with a multi-component electrolyte
Phys. Rev. E 114, 045413 – Published 27 October, 2026
DOI: https://doi.org/10.1103/ywds-cdzm
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 description, the response is written in terms of a multi-component diffusion-migration matrix and its eigenvalues and 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.
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