Impedance of constant phase element (CPE)-blocked diffusion in film electrodes

Abstract

Abstract We construct a model of ac impedance response to blocked linear diffusion that has a sloped low frequency region in the impedance plot. The approach is based on the transmission line analogy to linear diffusion, and it is equivalent to solving Fick’s law with a boundary condition that allows us to set an arbitrary impedance response at low frequencies. We argue that roughness at the blocking interface gives rise to constant phase element (CPE) response at low frequencies, and we give an impedance model function that can fit data along the whole frequency range when such a CPE is found. This is tested in an experiment of Li + insertion in Nb 2 O 5 . The model should be of significance for metal oxide thin film electrodes and modified polymer electrodes.