Application of a transmission line model to impedance studies on a poly(vinylferrocene)-modified electrode

The impedance of a poly(vinylferrocene)-modified electrode fits a transmission line model that has two resistances R1 and R2 and a capacitance CΣ. The low-frequency resistance, R1, passes through a minimum as the coat is oxidised. This is explained in terms of bimolecular electron-exchange reactions between redox centres. The redox composition of the coat can be determined from values of R1. The high-frequency resistance, R2, decreases as the coat is oxidised, which is explained by the build up of the anion concentration. A theoretical description, including the development of Donnan exclusion, is presented. The theory divides the coat into two phases, the polymer and the aqueous pores. The Donnan potential at the polymer/electrolyte interface can be calculated from results for R2 and R1. The capacitance CΣ does not contain a significant Feldberg capacitance. As the coat is oxidised, the capacitance passes through a maximum. This behaviour is described with a Nernst term and a Donnan term describing the charging of the electrode/polymer and of the polymer/electrolyte interfaces, respectively. By combining all the results, values for the ratio of the volume of the polymer phase to that of the aqueous pores, for the thickness, L, of the coat and for D which describes the electron-exchange process can be obtained. From the value for D a value for k, the second-order rate constant describing the electron exchange, can be deduced.