Tafel current at fractal electrodes: Connection with admittance spectra

Abstract

Various types of fractal electrode/electrolyte interfaces are investigated in the presence of an electrode reaction, the rate of which is described by the Butler-Volmer equation in a wide range of overpotentials. Applying scaling analysis, an interesting connection between the Tafel current at a fractal electrode, both in the limit of high and small overpotentials on the one hand and the admittance behaviour of the same electrode on the other, reveals itself. In particular, from Tafel plots in the limit of high overpotentials the effective transfer coefficients are seen to be modified by a geometrical factor α which is equal to the exponent appearing in the description of the CPE frequency dependence found in admittance measurements. Furthermore, at small overpotentials the current is shown to contain information on the exchange current density in a way which applies to all electrode geometries which give rise to CPE behaviour, i.e. not specifically to fractal electrodes.