Fractal dimension of Li insertion electrodes studied by diffusion-controlled voltammetry and impedance spectroscopy

We show that a unique fractal dimension can be obtained for Li insertion electrodes by applying two different electrochemical methods to samples of porous Sn oxide and Ti oxide. The first method relies on the assumption that the current recorded in voltammetric experiments, conducted in a Li containing electrolyte, is limited by Li diffusion from the fractal working electrode surface into the oxide matrix. The second method is based on the capacitance dispersion observed in impedance spectroscopy. Simple scaling arguments show that this capacitance dispersion is related to the fractal structure of surface roughness