Second Harmonic Nonlinear Warburg Admittance Analysis Eliminates Information Loss from Linearization in Traditional EIS: Theory and Experimental Validation

Abstract

Low-frequency impedance or admittance experiments of reversible redox couples in well-supported quiescent electrolyte are normally analyzed using a linearized semi-infinite Warburg element with a single lumped parameter. Because each species of a redox couple has a distinct diffusivity, one cannot determine individual diffusivities by fitting a spectrum with one parameter; linearization causes information loss. Weakly nonlinear theory and experiments presented here extend traditional Warburg admittance analysis to the higher harmonic currents generated from single-sine potential modulations at a Pt electrode in well-supported ferri-/ferro-cyanide electrolyte. Complex harmonic current data from our commercial instrument is processed to enable direct fitting of theory to measurements. We show that complex first and second harmonic currents are measurable for ΔE ≥ 5 mVrms, whereas a good compromise between experimental signal quality and leading-order model accuracy is found at ΔE ≈ 10 mVrms. Higher-order corrections to theory are required at larger potential modulation amplitudes to remove amplitude dependency from fits, until ΔE × FRT> 1, when weakly nonlinear theory breaks down. Fitting the first and second harmonic experimental spectra to theory provides the mean diffusivity and a diffusion asymmetry parameter (deviations from mean), respectively, enabling unique determination of the individual ferricyanide and ferrocyanide diffusivities. Theory also shows that even harmonics disappear in the high-symmetry case of equal species diffusivities. In short, analyzing the first and second harmonics generated with moderate amplitude modulations eliminates information loss from linear Warburg analysis of the first harmonic alone.