Treatment of the Impedance of Mixed Conductors Equivalent Circuit Model and Explicit Approximate Solutions

The electrochemical impedance of a mixed conductor with two charge carriers sandwiched between two equal electrodes is modeled phenomenologically. A simple analytical approximation is found which applies in a very broad materials parameter window (arbitrary carrier mobilities and concentrations) as long as linear response is guaranteed and the sample thickness is great compared to the Debye length. The approximation is applicable to reversible, selectively blocking as well as to partially blocking electrodes. The validity of the approximation is justified by comparison with the exact solution of Nernst-Planck-Poisson set of equations as given, e.g., by Macdonald. The analytical approximation describes the typical Warburg response as well as the single-carrier behavior as limiting cases. Finite interfacial resistances (not perfectly blocking or not perfectly reversible electrodes) lead to additional semicircles and/or to distorted Warburg responses.