Locating the Frequency of Turnover in Thin-Film Diffusion Impedance

Abstract

The impedance of diffusion is an important tool to investigate a wide variety of systems, including electrochemical devices such as Li-ion batteries, porous electrodes, and solar cells. The classical impedance model for diffusion in a thin layer with a blocking boundary contains two separate regimes: Warburg diffusion at high frequency and capacitive charging at low frequency. Here, we provide a physical criterion for the transition between these two regimes, as the point of closest approach between early- and late-time approximations of the exact diffusion current. The resulting frequency is (π2/2)ωd with respect to the natural frequency ωd = Dn/L2, with Dn being the diffusion constant and L being the thickness of the layer.