Impedance data obtained from measurements on solid electrodes are often modeled with a Constant-Phase-Element (CPE) to describe the influence of time-constant or frequency dispersion. However, the physical origin of frequency dispersion over a broad range of frequencies is not fully understood.

Hirschorn et al.¹ showed that a power-law distribution of resistivity through a film produces a CPE response. The power-law-model approach has been used successfully to extract a film capacitance and associated parameters for a variety of systems. However, the power-law model cannot explain frequency dispersion in cases where a normal distribution of resistivity does not exist. In early experiments on solid electrodes, surface roughness was believed to be a possible cause of frequency dispersion. However, Pajkossy² showed experimentally that annealing can reduce the degree of frequency dispersion even though the roughness of the surface remained the same. Alexander et al.³determined that the frequency at which frequency dispersion occurs due to roughness is inversely proportional to the square of the roughness factor. For large roughness factors, the electrode behaves as a porous electrode.

Brug et al.⁴ developed an expression for an effective capacitance as a function of CPE parameters suggesting that the CPE behavior was attributed to a surface distribution of capacitance. Kurtyka and de Levie⁵ showed that surface heterogeneity due to a distribution of capacitance only induced frequency dispersion over a limited range of frequencies. Alexander et al.⁶determined that frequency dispersion associated with a surface distribution of capacitance only occurs at frequencies greater than the frequency associated with time-constant dispersion due to the geometry of the disk electrode within an insulating plane.

Simulations performed for a distribution of charge-transfer resistance did not yield frequency dispersion for single-step reactions.⁷ However, Wu et al.⁸showed, for disk electrodes, that reactions involving adsorbed intermediates yielded frequency dispersion at low frequencies due to the potential dependence of the surface coverage. The object of the present work is to explore the impedance response of recessed disk electrodes with surface distributions of rate constants for coupled faradaic reactions involving adsorbed intermediates. Finite-element simulations show that frequency dispersion is observed at low frequencies due to the heterogeneity of the reaction rates and surface coverage. This work suggests that a physical explanation for frequency dispersion over a broad range of frequencies may be provided by a distribution of rate constants for reactions coupled by adsorbed intermediates.

References

1. B. Hirschorn, M. E. Orazem,  B. Tribollet,  V. Vivier,  I. Frateur, and M. Musiani, J. Electrochem. Soc., 157 (2010), C452-C457.
2. T. Pajkossy, Solid State Ionics, 176 (2005), 1997-2003.
3. C. L. Alexander, B. Tribollet, and M. E. Orazem, Electrochim. Acta. 173 (2015) 416-424.
4. G. J. Brug, A. L. G. van den Eeden, M. Sluyters-Rehbach, and J. H. Sluyters, J. Electroanal. Chem., 176 (1984), 275-295.
5. B. Kurtyka and R. de Levie, J. Electroanal. Chem., 322 (1992) 63-77.
6. C. L. Alexander, B. Tribollet, and M. E. Orazem, Electrochim. Acta, in press.
7. C. L. Alexander, B. Tribollet, and M. E. Orazem, Electrochim. Acta, submitted.
8. S.L. Wu, M.E. Orazem, B. Tribolet, and V. Vivier, J. Electrochem. Soc., 156 (2009), C28-C38.