Ohmic Impedance: Myth or Reality?
Authors: Gharbi Oumaïma , Orazem Mark E , Tran Mai , Tribollet Bernard , Vivier Vincent 
Published: February 2020

In his seminal work on the impedance response of a blocking electrode, Newman developed the concept of frequency dispersion1 accounting for the geometric effect of the electrochemical system on the primary current distribution. More recently, this approach has been revisited for different cases, including an ideally blocking electrode,2 a blocking electrode with a local constant-phase element behavior,3and a disk electrode with faradaic reactions.4-5 It was shown that the frequency dispersion results in a high-frequency time constant that can be associated to an ohmic impedance with a non-zero imaginary component in the high frequencies.6 Interestingly, the development of local electrochemical impedance spectroscopy (LEIS) has allowed the experimental validation of this concept.7-9

However, from a practical point of view, most of the experimental work reported in the literature deals with global impedance measurements and usually neglects the contribution of current and potential distributions. This is certainly due to the fact that these contribution requires the simultaneous solution of the interfacial kinetics and Laplace’s equation in the electrochemical cell, which makes it difficult to analyze the results when comparing this approach to what can be done with equivalent electrical circuits. However, the analysis of high-frequency domains is needed for all electrochemical systems and is of special interest for many practical applications dealing with the detailed analysis of capacitive behavior of an electrode, such as supercapacitors, Mott-Schottky analysis, thin oxide films, or coatings. This analysis requires a good understanding of the processes in the high-frequency domain, including its resistive component.
In this work, a particular attention has been paid to the ohmic contribution observed in the high-frequency domain both for capacitive and faradaic electrochemical responses. We introduce a detailed description of the ohmic impedance first based on synthetic data in order to devise an analytical expression as a quantity that can be easily used in any fitting procedure. An example of the ohmic impedance obtained for blocking electrodes is presented in Fig. 1. In a second step, we propose an experimental validation of our new development by studying three different electrochemical systems: the response of a blocking electrode investigated using a gold disk-electrode in a sodium sulfate solution; the CPE response due to a thin oxide film using an aluminum as electrode material in a sodium sulfate solution, and the electrochemical response of a faradaic system using the dissolution of pure iron in sulfuric acid solution.

References

Newman, J., Frequency dispersion in capacity measurements at a disk electrode. J. Electrochem. Soc.
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117(2), 198-203.

Huang, V. M.-W.; Vivier, V.; Orazem, M. E.; Pebere, N.; Tribollet, B., The apparent constant-phase-element behavior of an ideally polarized blocking electrode a global and local impedance analysis. J. Electrochem. Soc.
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154(2), C81-C88.

Huang, V. M.-W.; Vivier, V.; Frateur, I.; Orazem, M. E.; Tribollet, B., The global and local impedance response of a blocking disk electrode with local constant-phase-element behavior. J. Electrochem. Soc.
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Huang, V. M.-W.; Vivier, V.; Orazem, M. E.; Pebere, N.; Tribollet, B., The apparent constant-phase-element behavior of a disk electrode with Faradaic reactions. A global and local impedance analysis. J. Electrochem. Soc.
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Orazem, M. E.; Tribollet, B., Electrochemical Impedance Spectroscopy. 2 ed.; Wiley: Hoboken, New Jersey, 2017; p 768.

Frateur, I.; Huang, V. M.; Orazem, M. E.; Tribollet, B.; Vivier, V., Experimental Issues Associated with Measurement of Local Electrochemical Impedance. J. Electrochem. Soc.
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Blanc, C.; Orazem, M. E.; Pebere, N.; Tribollet, B.; Vivier, V.; Wu, S., The origin of the complex character of the Ohmic impedance. Electrochim. Acta
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Huang, V. M.-W.; Wu, S.-L.; Orazem, M. E.; Pebere, N.; Tribollet, B.; Vivier, V., Local electrochemical impedance spectroscopy: A review and some recent developments. Electrochim. Acta
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Figure1: Nyquist representation ohmic impedance, Ze, determined for the calculated impedance response of a blocking electrode with a pure capacitance (red circles) and a local CPE (blue triangles). The crosses correspond to the fitting of each impedance diagram with the Havriliak-Negami equation. K is the dimensionless frequency defined as K=Qωαr0/κ.

Figure 1