Electrical circuits invoking constant-phase elements (CPE) are often used to fit impedance data arising from a broad range of experimental systems. The CPE is often used simply as a way to improve the fit of a model to impedance data, justified by a vague assertion that a distribution of time constants is present in the system under investigation. The development in the present work shows that the CPE parameters have a physical meaning. The CPE may be seen as a special case of time-constant dispersion in which the time constants follow a particular distribution. The interpretation of CPE parameters in terms of physically meaningful properties such as capacitance requires an understanding of the nature of the time-constant distribution. This presentation provides a review of recent work on the interpretation of constant-phase elements. A power-law distribution of resistivity in the direction normal to the electrode surface is shown to yield CPE behavior.[1-5] A formula developed by Brug et al. yields physical parameters for time–constant distributions along the surface of an electrode.[6] Work is underway to explore the physical origin of surface distributions that may give rise to a CPE.[7-9] It should be noted that not all time-constant distributions can be described by a constant-phase element. For example, the impedance of the passive layer for a stainless steel electrode presented by Frateur et al.[10] shows CPE behavior; whereas, the time-constant distribution associated with a niobium oxide covered niobium electrode [11] is not a CPE.References B. Hirschorn, M. E. Orazem, B. Tribollet, V. Vivier, I. Frateur, and M. Musiani, Journal of the Electrochemical Society, 157 (2010) C452–C457.B. Hirschorn, M. E. Orazem, B. Tribollet, V. Vivier, I. Frateur, and M. Musiani, Journal of the Electrochemical Society, 157 (2010) C458–C463.M. E. Orazem, B. Tribollet, V. Vivier, S. Marcelin, N. Pébère, A. L. Bunge, E. A. White, D. P. Riemer, I. Frateur, and M. Musiani, Journal of the Electrochemical Society, 160 (2013) C215–C225.S. Amand, M. Musiani, M. E. Orazem, N. Pébère, B. Tribollet, and V. Vivier, Electrochimica Acta, 87 (2013), 693-700.M. Musiani, M. E. Orazem, N. Pébère, B. Tribollet, and V. Vivier, Progress in Organic Coatings, 77 (2014) 2076–2083.G. J. Brug, A. L. G. van den Eeden, M. Sluyters-Rehbach, and J. H. Sluyters, Journal of Electroanalytical Chemistry, 176 (1984) 275–295.C. L. Alexander, B. Tribollet, and M. E. Orazem, Electrochimica Acta, 173 (2015) 416–424.C. L. Alexander, B. Tribollet, and M. E. Orazem, Electrochimica Acta, 188 (2016) 566–573.C. L. Alexander, B. Tribollet, and M. E. Orazem, Electrochimica Acta, (2016) in press.I. Frateur, L. Lartundo-Rojas, C. M´ethivier, A. Galtayries, and P. Marcus, Electrochimica Acta, 51 (2006) 1550–1557.S. Cattarin, M. Musiani, and B. Tribollet, Journal of the Electrochemical Society, 149 (2002) B457–B464.
Read full abstract