Inductive behaviour by charge-transfer and relaxation in solid-state electrochemistry

We discuss a model system of electroactive material containing heterogeneity or energy disorder, in which charge accumulation and transfer is governed mainly by chemical potentials of species in the solid material. The equivalent circuit for impedance spectroscopy is composed of parallel combination of the electrochemical capacitances of the phases and charge-transfer resistances between the phases. The origin of the circuit elements is analysed using the principle of detailed balance and the master equation, as a generalization of different systems, such as intercalation batteries, electrochromics and solar cells based on nanostructured semiconductors, and systems with traps. The Butler-Volmer type equation for interfacial charge-transfer at the solid-solid interface is derived. The model is extended with the relaxation of charge in one of the phases providing an inductive behaviour at high frequency. Experimental results of intercalation of Li into nanostructured TiO2, in the configuration TiO2/room temperature ionic liquid/PEDOT show the inductive behaviour.