General aperiodic equivalent circuit for charge permeable thin-layer cells of symmetric or asymmetric types Part 3 Mixed conductance, polymer electrolyte asymmetric cells

Abstract

This paper presents forms of single species flux equation: Barker, Nernst–Planck, and electron hopping. The latter two are converted into responses I or jvs. φ functions that define T circuit elements. Two forms arise that define the implicit R_i or R_e, and C_i or C_e per unit length (i=ion, e=electron), and the corresponding explicit R and C. The analysis uses as examples (1) a single dissolved, inert electrolyte salt M⁺ X^-, and (2) a redox polymer electrolyte radical cation and anion, also M⁺, X^-, undergoing second-order electron hopping from M to M⁺. The corresponding forms for the Rs and Cs are derived. Case 2 is the mixed conductance asymmetric cell which is illustrated to show how the dc bias changes the polymer cation, anion composition, and so determines different R_e and C_e at each composition through the effective second-order, concentration-dependent electron hopping.

In Part 1, Barker–Brumleve–Buck (BBB) sub-circuit units, were illustrated, viz., the conventional two-feature mass transport-controlled impedance was generated. This finite two-port, four-terminal network for a single salt system, replaced the classical one-port, two-terminal cable transmission line analog because the latter covers only the Warburg feature. Results were specifically used to compare BBB impedances with shorted and open finite cables to show conditions of equivalence. Both symmetric and asymmetric cell results depend only on the ion or electron terminals used. In Part 2, the usual three-feature impedance plane plots for each ion requiring activation to cross the interface are generated and illustrated. In addition, residual cell solution resistance and total cell geometric capacitance were included to generate the four-feature impedance plots.

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