Multi-component diffusion approach to transport across electroactive-polymer films with two mobile charge carriers

This paper aims to apply general relations between the thermodynamical forces (gradients of electrochemical potentials) and resulting fluxes of the species to transport phenomena in a uniform film of the electroactive polymer in contact with some other conducting media, metal(s) and/or solution(s), in the case of a low-amplitude perturbation imposed. Two kinds of mobile charged species are assumed to be present inside the film, the ''electronic'' and ''ionic'' ones. The coefficients in the above relations (friction coefficients) are expressed through the experimentally measurable macroscopic transport parameters, the total high-frequency conductivity, migration transference numbers, binary diffusion coefficient and differential redox capacitance of the film. The non-stationary diffusion equation is found to be valid for several local characteristics of the film, in particular for electron or ion charge density, or for the low-frequency current density. This equation has been solved analytically for three usual geometries of the system, metal/film/metal, metal/film/solution and solution/film/solution, upon a sinusoidal variation of the electrode potential. The final expressions for complex impedance contain contributions of the bulk film, interfacial charge-transfer resistances and (in contact with solution(s)) bulk solution. The functional form of their frequency dependence as well as the shape of complex-impedance plots has turned out to be highly simple for all geometries, being in accordance with those derived earlier within the framework of the Nernst-Planck-Einstein equations. However, the parameters of those dependences have a form different with respect to the previous expectations, leading to a modification of the procedure to interpret experimental data.