ELECTROCHEMICAL IMPEDANCE OF BLOCKING QUASI-FRACTAL 3-D ELECTRODES

The response of ideally polarizable electrodes often exhibts a behavior such as Z approximately k (jw)-eta where k is a constant and eta a number smaller than one. Recently an expression for the impedance of two-dimensional (2-d) self-similar electrodes, based on the iteration of a simplified equivalent circuit, has been proposed and experimentally verified. These developments, extended to 3-d objects, allow us to predict the impedance and quantitatively interpret previous results for ramified electrodes. The impedance response presents two frequency domains. In the low-frequency range, a behavior similar to that of planar electrodes is observed with a surface equal to the total area of the object. At high frequencies, a fractal constant phase angle behavior is found to be quantitatively compatible with our theoretical prediction.