WIAS Preprint No. 2906, (2021)

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


  • Landstorfer, Manuel
    ORCID: 0000-0002-0565-2601
  • Müller, Rüdiger
    ORCID: 0000-0003-2643-722X

2020 Mathematics Subject Classification

  • 65N30 78A57 80A17


  • Electrochemistry, double layer, dielectric susceptibility




The dielectric susceptibility $chi$ is an elementary quantity of the electrochemical double layer and the associated Poisson equation. While most often $chi$ is treated as a material constant, its dependency on the salt concentration in liquid electrolytes is demonstrated by various bulk electrolyte experiments. This is usually referred to as dielectric decrement. Further, it is theoretically well accepted that the susceptibility declines for large electric fields. This effect is frequently termed dielectric saturation. We analyze the impact of a variable susceptibility in terms of species concentrations and electric fields based on non-equilibrium thermodynamics. This reveals some non-obvious generalizations compared to the case of a constant susceptibility. In particular the consistent coupling of the Poisson equation, the momentum balance and the chemical potentials functions are of ultimate importance. 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 compute the differential capacitance and the spatial structure of the electric potential, solvent concentration and ionic distribution for various non-constant models of $chi$.

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