Fractal dimension and fractional power frequency-dependent impedance of blocking electrodes

Abstract A general treatment of the effect of surface roughness on the impedance of ideally polarizable (blocking) electrodes is proposed. In terms of fractal geometry, surface irregularities are characterized solely by the effective fractional dimension, D . The advantage of this approach is that the structure of the irregularities is irrelevant if the surface is self-similar. The admittance, Y , of self-similar blocking electrodes is shown to depend on the frequency ω as Y = σ( i ω) α , ie , any blocking electrode with fractal surface behaves as a constant phase element (CPE) observed experimentally in many and diverse systems. The fractional exponent α is directly related to D as α = 1 ( D − 1) , hence α can be regarded as a measure of surface roughness. The coefficient σ is shown to be a simple explicit function of electrolyte conductivity and double-layer capacitance thus enabling one to study the latter even when the interface behaves as a CPE instead of being an ideal capacitance.