Electrochemistry at fractal interfaces: the coupling of ac and dc behaviour at irregular electrodes

Abstract

Impedance models pertaining to the ideally polarizable (blocking) fractal interface and those describing diffusion-limited charge transfer across fractal surfaces are reviewed. In the blocking case no general prediction can be made: although the non-trivial frequency dispersion often exhibits constant phase angle behaviour, the frequency exponent, α, is not uniquely related to the fractal dimension of the interface. In contrast, the generalized diffusion impedance (or Contrell response) is universal, owing to the fact that the time-dependent “yardstick”—the diffusion length—measures the fractal dimension proper. After discussing some consequences of these models, a new conjecture is presented: the ac behaviour of the blocking interface and the Tafel slope of the dc polarization curve measured in the presence of an electroactive material are interrelated at fractal electrode surfaces. Three examples are given where the modified Tafell slope of the irregular electrode is in fact the original value—which is characteristic to the electrode reaction and which is observed at smooth, planar interfaces—multiplied by the frequency exponent, α, of the blocking impedance.