(Invited) Numerical Simulation of Ohmic Impedance

Abstract

Impedance spectroscopy measurements are often confounded by high-frequency phenomena associated with frequency-dependent ohmic resistance. Newman introduced the concept of frequency dispersion to account for the effect of the disk electrode geometry on the impedance response [1]. The phenomenon described by Newman in terms of frequency-dependent capacitance and ohmic resistance may be considered as an ohmic impedance, a transfer function associated with the resistance of the electrolyte to passage of current under the influence of geometry-induced (and frequency-dependent) non-uniform current and potential distributions [2].Two kinds of models are described in the presentation. Finite-element models account for the influence of geometry on the impedance response for a disk electrode. These models demonstrate the ohmic impedance. The second model is an interpretation model used to extract properties from impedance data. For most cases, data are truncated to avoid being confounded by ohmic impedance. On rare instances, the ohmic impedance may be extracted by regression to data.Gharbi et al. [3] suggested that the ohmic impedance follows the form of the Havriliak-Negami equation. The Havriliak-Negami equation was found to provide a good fit to the ohmic impedance calculated for different electrode geometries, including interdigitated electrodes [4] as well as disk electrodes [3].The ohmic impedance was obtained by Levenberg-Marquardt regression of a process model that accounted for the ohmic impedance [5]. The experiments were performed using ferri/ferrocyanide redox species (10 mM each) in a 0.5 M KCl solution. The working electrode consisted of a 5-mm-diameter Au disk rotating at 800 rpm. A Pt gauze (4 cm2) was used as the counterelectrode, a saturated Ag/AgCl electrode was used as a reference electrode, and the temperature of double-walled electrochemical cell was held at 25 ±0.1°C.The process model was expressed in terms of an ohmic impedance and an expression that accounted for the influence of a local constant-phase element on the faradaic reaction and the convective diffusion impedance, expressed in terms of a series expansion following the work of Tribollet and Newman [6]. Regressions were weighted by the experimentally determined error structure of the data, and the resulting parameters characteristic of the ohmic impedance were in excellent agreement with numerical simulations.References J. S. Newman, J. Electrochem. Soc., 117 (1970), 198.V. Huang, V. Vivier, M. E. Orazem, N. Pébère, and B. Tribollet, J. Electrochem. Soc., 154 (2007), C81-C88.O. Gharbi, A. Dizon, M. E. Orazem, M. T.T. Tran, B. Tribollet, and V. Vivier, Electrochim. Acta, 320 (2019), 134609.A. Dizon and M. E. Orazem, Electrochim. Acta, 337 (2019), 135000.W. Watson and M. E. Orazem, EIS: Measurement Model Program, ECSArXiv, 2020, https://ecsarxiv.org/kze9x/.B. Tribollet and J. S. Newman, J. Electrochem. Soc., 130 (1983), 2016.