Modeling the Electrochemical Impedance Spectra of Electroactive Pseudocapacitor Materials

Abstract

Measured electrochemical impedance spectra of porous electrodes comprised of redox-active ruthenium oxide and inert niobium hydroxide are compared with the results of structurally consistent mathematical models describing coupled processes of electron transport in the solid matrix, ion transport in the electrolyte, proton transport within the ruthenium oxide particles, and redox reaction on particle surfaces. Addition of moderate amounts of niobium to crystalline ruthenium oxide is found to improve the frequency response due to enhanced intraparticle proton transport. However, excessive niobium reduces ion and electron transport through the electrode thickness, reducing the available capacitance. Thus, an optimum composition is needed to achieve the best balance in transport properties. Near this optimum, the intraparticle proton transport undergoes a transition from a constant phase element (CPE) response for Ru-rich materials to a classical Warburg diffusion response for Nb-rich compositions. The CPE regime is analyzed in detail to identify fractal-like structures as well as alternative radial distributions of intraparticle proton diffusivity consistent with measured response. The models involving variations in radial diffusivity appear most probable and have nearly exponential decreases in radial diffusivity with distance from particle surfaces similar to a Debye distribution of charge carriers in an electric double layer.