Influence of Finite Diffusion on Cation Insertion-Coupled Electron Transfer Kinetics in Thin Film Electrodes

Materials that undergo ion-insertion coupled electron transfer are important for energy storage, energy conversion, and optoelectronics applications. Cyclic voltammetry is a powerful technique to understand electrochemical kinetics. However, the interpretation of the kinetic behavior of ion insertion electrodes with analytical solutions developed for ion blocking electrodes has led to confusion about their rate-limiting behavior. The purpose of this manuscript is to demonstrate that the cyclic voltammetry response of thin film electrode materials undergoing solid-solution ion insertion without significant Ohmic polarization can be explained by well-established models for finite diffusion. To do this, we utilize an experimental and simulation approach to understand the kinetics of Li⁺ insertion-coupled electron transfer into a thin film material (Nb₂O₅). We demonstrate general trends for the peak current vs scan rate behavior, with the latter parameter elevated to an exponent between limiting values of 1 and 0.5, depending on the solid-state diffusion characteristics of the film (diffusion coefficient, film thickness) and the experiment timescale (scan rate). We also show that values < 0.5 are possible depending on the cathodic potential limit. Our results will be useful to fundamentally understand and guide the selection and design of intercalation materials for multiple applications.