Doubling exponent models for the analysis of porous film electrodes by impedance.: Relaxation of TiO2 nanoporous in aqueous solution

The paper is concerned with the small signal ac impedance of porous film electrodes in contact with solution. An overview is presented of the standard transmission line model with two transport channels and a crosswise element. The simplest configurations are discussed: a single resistance in one of the channels, and either an interfacial capacitor or a RC transfer circuit at the pore's wall. The resulting relaxation functions are classified in terms of two characteristic frequencies: one for coupled transport and interfacial polarization and another one for the interfacial reaction. Subsequently, these models are extended in order to describe porous electrodes where the interfacial polarization displays complex properties, i.e,, frequency dispersion. The capacitive element is described by a constant-phase element (CPE), and it is shown that the fractionary exponent provides an additional and measurable degree of freedom in the parameter space of the relaxation function, whose determination can be exploited as a supplementary tool for analysis. The analysis of impedance measurements of TiO2 nanoporous photoelectrodes in negative bias voltage shows that the suggested approach is capable of identifying two characteristic relaxation frequencies in a frequency-resolved measurement on this system.