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Electrochemical impedance spectroscopy

Nature Reviews Methods Primers volume 1, Article number: 41 (2021) Cite this article

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Abstract

Electrochemical impedance spectroscopy (EIS) is a powerful tool to investigate properties of materials and electrode reactions. This Primer provides a guide to the use of EIS and a comparison with other electrochemical techniques. The analysis of impedance data for reduction of ferricyanide in a KCl supporting electrolyte is used to demonstrate the error structure for impedance measurements, the use of measurement and process models, and the sensitivity of impedance to the evolution of electrode properties. This Primer provides guidelines for experimental design, discusses the relevance of accuracy contour plots to wiring and instrumentation selection, and emphasizes the importance of the Kramers–Kronig relations to data validation and analysis. Applications of EIS to battery performance, metal and alloy corrosion, and electrochemical biosensors are highlighted. Electrochemical impedance measurements depend on both the mechanism under investigation and extrinsic parameters, such as the electrode geometry. Experimental complications are discussed, including the influence of non-stationary behaviour at low frequencies and the need for reference electrodes. Finally, emerging trends in experimental and interpretation approaches are also described.

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Fig. 1: Required steps to acquire an EIS measurement.
Fig. 2: Guidelines for EIS measurements.
Fig. 3: EIS data of an ideally polarizable electrode obtained for a redox couple in solution.
Fig. 4: Sample analysis of impedance data.
Fig. 5: Typical EIS spectra and the corresponding physical processes.
Fig. 6: Use of EIS measurements at different temperatures to extract activation energy.
Fig. 7: Use of EIS to detect the concentration of breast cancer cells.
Fig. 8: Influence of pore size distribution on impedance behaviour.
Fig. 9: Measurement model analysis to identify the error structure of impedance data.

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References

  1. Bard, A. J. & Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications 2nd edn (Wiley, 2001).

  2. Orazem, M. E. & Tribollet, B. Electrochemical Impedance Spectroscopy 2nd edn (Wiley, 2017). This book is a good introduction to hypothesis-driven modelling of impedance spectroscopy.

  3. Macdonald, D. D. Transient Techniques in Electrochemistry (Plenum, 1977).

  4. Gabrielli, C. Identification of Electrochemical Process by Frequency Response Analysis (Solartron Electronic Group, 1980).

  5. Barsoukov, E. & Macdonald, J. R. Impedance Spectroscopy:  Theory, Experiment, and Applications 2nd edn (Wiley, 2005).

  6. Deleebeeck, L. & Veltze, S. Electrochemical impedance spectroscopy study of commercial Li-ion phosphate batteries: a metrology perspective. Int. J. Energy Res. 44, 7158–7182 (2020).

    Google Scholar 

  7. Bredar, A. R. C., Chown, A. L., Burton, A. R. & Farnum, B. H. Electrochemical impedance spectroscopy of metal oxide electrodes for energy applications. ACS Appl. Energy Mater. 3, 66–98 (2020).

    Google Scholar 

  8. Xu, Y. et al. A review of impedance measurements of whole cells. Biosens. Bioelectron. 77, 824–836 (2016).

    Google Scholar 

  9. Bahadir, E. B. & Sezgintürk, M. K. A review on impedimetric biosensors. Artif. Cells Nanomed. Biotechnol. 44, 248–262 (2016).

    Google Scholar 

  10. Bandarenka, A. S. Exploring the interfaces between metal electrodes and aqueous electrolytes with electrochemical impedance spectroscopy. Analyst 138, 5540–5554 (2013).

    ADS  Google Scholar 

  11. Sacco, A. Electrochemical impedance spectroscopy: fundamentals and application in dye-sensitized solar cells. Renew. Sustain. Energy Rev. 79, 814–829 (2017).

    Google Scholar 

  12. Margarit-Mattos, I. C. P. EIS and organic coatings performance: revisiting some key points. Electrochim. Acta 354, 136725 (2020).

    Google Scholar 

  13. Macdonald, D. D. Reflections on the history of electrochemical impedance spectroscopy. Electrochim. Acta 51, 1376–1388 (2006).

    Google Scholar 

  14. Gabrielli, C. Once upon a time there was EIS. Electrochim. Acta 331, 135324 (2020). This article presents a detailed description of EIS history, especially the evolution of EIS measurement equipment.

    Google Scholar 

  15. Kohlrausch, F. & Nippoldt, W. A. Ueber die Gültigkeit der Ohm’schen Gesetze für Elektrolyte und eine numerische Bestimmung des Leitungswiderstandes der verdünnten Schwefelsäure durch alternirende Ströme [German]. Ann. Phys. 214, 280–298 (1869).

    Google Scholar 

  16. Kohlrausch, F. Ueber die elektromotorische Kraft sehr dünner Gasschichten auf Metallplatten [German]. Ann. Phys. 224, 143–154 (1873).

    MATH  Google Scholar 

  17. Wien, M. Ueber die polarisation bei Wechselstrom [German]. Ann. Phys. 294, 37–72 (1896).

    Google Scholar 

  18. Warburg, E. Ueber die polarisationscapacität des platins [German]. Ann. Phys. 311, 125–135 (1901).

    Google Scholar 

  19. Hickling, A. Studies in electrode polarisation. Part IV.—The automatic control of the potential of a working electrode. Trans. Faraday Soc. 38, 27–33 (1942).

    Google Scholar 

  20. Koutecky, J. & Levich, V. G. The use of a rotating disk electrode in the study of electrochemical kinetics and electrolytic processes. Zh. Fiz. Khim. 32, 1565–1575 (1958).

    Google Scholar 

  21. de Levie, R. On porous electrodes in electrolyte solutions: I. Capacitance effects. Electrochim. Acta 8, 751–780 (1963).

    Google Scholar 

  22. de Levie, R. On porous electrodes in electrolyte solutions — IV. Electrochim. Acta 9, 1231–1245 (1964).

    Google Scholar 

  23. Gerischer, H. & Mehl, W. Zum mechanismus der kathodischen wasserstoffabscheidung an quecksilber, silber und kupfer [German]. Z. Elektrochem. Berichte Bunsenges. Physikalische Chem. 59, 1049–1059 (1955).

    Google Scholar 

  24. Gerischer, H. Intermediates in electrochemical reactions. Faraday Discuss. Chem. Soc. 56, 7–15 (1973).

    Google Scholar 

  25. Klahr, B., Gimenez, S., Fabregat-Santiago, F., Hamann, T. & Bisquert, J. Water oxidation at hematite photoelectrodes: the role of surface states. J. Am. Chem. Soc. 134, 4294–4302 (2012).

    Google Scholar 

  26. Wang, H., Guerrero, A., Bou, A., Al-Mayouf, A. M. & Bisquert, J. Kinetic and material properties of interfaces governing slow response and long timescale phenomena in perovskite solar cells. Energy Environ. Sci. 12, 2054–2079 (2019). This article presents a comprehensive review of perovskite solar cells, with emphasis on the use of impedance spectroscopy for studying kinetics of bulk and interface processes.

    Google Scholar 

  27. Epelboin, I., Gabrielli, C., Keddam, M. & Takenouti, H. Model of the anodic behavior of iron in sulfuric acid medium. Electrochim. Acta 20, 913–916 (1975).

    Google Scholar 

  28. Keddam, M., Mattos, O. R. & Takenouti, H. Reaction model for iron dissolution studied by electrode impedance. I. Experimental results and reaction model. J. Electrochem. Soc. 128, 257–266 (1981). This article presents a detailed description of the procedure to follow for EIS interpretation in the case of complex mechanisms, using iron dissolution as an example.

    ADS  Google Scholar 

  29. Baril, G. et al. An impedance investigation of the mechanism of pure magnesium corrosion in sodium sulfate solutions. J. Electrochem. Soc. 154, C108–C113 (2007).

    Google Scholar 

  30. Gomes, M. P. et al. On the corrosion mechanism of Mg investigated by electrochemical impedance spectroscopy. Electrochim. Acta 306, 61–70 (2019).

    Google Scholar 

  31. de Levie, R. in Advances in Electrochemistry and Electrochemical Engineering Vol. 6 (eds Delahay, P. & Tobias, C.W.) 329–397 (Wiley, 1967). This pioneering work develops an EIS model for a porous electrode.

  32. Lasia, A. in Electrochemical Impedance Spectroscopy and its Applications 1–367 (Springer, 2014).

  33. Lasia, A. Impedance of porous electrodes. J. Electroanal. Chem. 397, 27–33 (1995).

    ADS  Google Scholar 

  34. Barcia, O. E. et al. Further to the paper “Application of the impedance model of de Levie for the characterization of porous electrodes” by Barcia et al. [Electrochim. Acta 47 (2002) 2109]. Electrochim. Acta 51, 2096–2097 (2006).

    Google Scholar 

  35. Orazem, M. E. & Tribollet, B. A tutorial on electrochemical impedance spectroscopy. ChemTexts 6, 12 (2020).

    Google Scholar 

  36. Savéant, J. M. Elements of Molecular and Biomolecular Electrochemistry: An Electrochemical Approach to Electron Transfer Chemistry (Wiley-VCH, 2006).

  37. Costentin, C., Drouet, S., Robert, M. & Saveant, J. M. A local proton source enhances CO2 electroreduction to CO by a molecular Fe catalyst. Science 338, 90–94 (2012).

    ADS  Google Scholar 

  38. Oleinick, A., Svir, I. & Amatore, C. A few key theoretical issues of importance in modern molecular electrochemistry. Curr. Opin. Electrochem. 13, 33–39 (2019).

    Google Scholar 

  39. Manbeck, G. F., Fujita, E. & Concepcion, J. J. Proton-coupled electron transfer in a strongly coupled photosystem II-inspired chromophore–imidazole–phenol complex: stepwise oxidation and concerted reduction. J. Am. Chem. Soc. 138, 11536–11549 (2016).

    Google Scholar 

  40. Garreau, D., Saveant, J. M. & Tessier, D. Potential dependence of the electrochemical transfer-coefficient — impedance study of the reduction of aromatic-compounds. J. Phys. Chem. 83, 3003–3007 (1979).

    Google Scholar 

  41. Saveant, J. M. & Tessier, D. Variation of the electrochemical transfer-coefficient with potential. Faraday Discuss. 74, 57–72 (1982).

    Google Scholar 

  42. Corrigan, D. A. & Evans, D. H. Cyclic voltammetric study of tert-nitrobutane reduction in acetonitrile at mercury and platinum electrodes: observation of a potential dependent electrochemical transfer coefficient and the influence of the electrolyte cation on the rate constant. J. Electroanal. Chem. 106, 287–304 (1980).

    Google Scholar 

  43. Sluyters-Rehbach, M. Impedances of electrochemical systems: terminology, nomenclature and representation — part I: cells with metal electrodes and liquid solutions (IUPAC Recommendations 1994). Pure Appl. Chem. 66, 1831–1891 (1994).

    Google Scholar 

  44. Newman, J. S. & Thomas-Alyea, K. E. Electrochemical Systems 3rd edn 647 (Wiley, 2004).

  45. Bockris, J. O. M., Reddy, A. K. N. & Gamboa-Aldeco, M. Modern Electrochemistry: Electrodics 2nd edn Vol. 2A 764 (Kluver Academic, 2000).

  46. Talaie, E. et al. Methods and protocols for electrochemical energy storage materials research. Chem. Mater. 29, 90–105 (2017).

    Google Scholar 

  47. Bard, A. J., Inzelt, G. & Scholz, F. Electrochemical Dictionary (Springer Science & Business Media, 2008).

  48. Song, J. Y., Lee, H. H., Wang, Y. Y. & Wan, C. C. Two- and three-electrode impedance spectroscopy of lithium-ion batteries. J. Power Sources 111, 255–267 (2002).

    ADS  Google Scholar 

  49. Engebretsen, E. et al. Localised electrochemical impedance measurements of a polymer electrolyte fuel cell using a reference electrode array to give cathode-specific measurements and examine membrane hydration dynamics. J. Power Sources 382, 38–44 (2018).

    ADS  Google Scholar 

  50. Sone, Y., Ekdunge, P. & Simonsson, D. Proton conductivity of Nafion 117 as measured by a four-electrode AC impedance method. J. Electrochem. Soc. 143, 1254–1259 (1996).

    ADS  Google Scholar 

  51. Deslouis, C., Musiani, M. M. & Tribollet, B. Free-standing membranes for the study of electrochemical reactions occurring at conducting polymer/electrolyte interfaces. J. Phys. Chem. 100, 8994–8999 (1996).

    Google Scholar 

  52. Keddam, M., Novoa, X. R. & Vivier, V. The concept of floating electrode for contact-less electrochemical measurements: application to reinforcing steel-bar corrosion in concrete. Corros. Sci. 51, 1795–1801 (2009).

    Google Scholar 

  53. Samec, Z. Electrochemistry at the interface between two immiscible electolyte solutions (IUPAC technical report). Pure Appl. Chem. 76, 2147–2180 (2004).

    Google Scholar 

  54. 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. 154, C81–C88 (2007).

    Google Scholar 

  55. Shchukin, E. D., Vidensky, I. V. & Petrova, I. V. Luggin’s capillary in studying the effect of electrochemical reaction on mechanical properties of solid surfaces. J. Mater. Sci. 30, 3111–3114 (1995).

    ADS  Google Scholar 

  56. Newman, J. S. Resistance for flow of current to a disk. J. Electrochem. Soc. 113, 501–502 (1966).

    ADS  Google Scholar 

  57. Tran, A. T., Huet, F., Ngo, K. & Rousseau, P. Artefacts in electrochemical impedance measurement in electrolytic solutions due to the reference electrode. Electrochim. Acta 56, 8034–8039 (2011). This article is a key paper on the way to circumventing the artefact linked to the reference electrode in the high-frequency mode.

    Google Scholar 

  58. Hills, G. & Payne, R. Improved method for measuring the double layer capacity at a dropping mercury electrode. Application to measurements at high pressure. Trans. Faraday Soc. 61, 316–325 (1965).

    Google Scholar 

  59. EG&G Princeton Applied Research. A lock-in primer. EG&G Princeton Applied Research https://www.physik.uni-wuerzburg.de/fileadmin/physik-fpraktikum/_imported/fileadmin/11999999/Lock-In_Primer.pdf (1986).

  60. Wellstead, P. Frequency Response Analysis (Solartron Instruments, 1983).

  61. Pilla, A. A. A transient impedance technique for the study of electrode kinetics: application to potentiostatic methods. J. Electrochem. Soc. 117, 467 (1970).

    ADS  Google Scholar 

  62. Itagaki, M., Ueno, M., Hoshi, Y. & Shitanda, I. Simultaneous determination of electrochemical impedance of lithium-ion rechargeable batteries with measurement of charge–discharge curves by wavelet transformation. Electrochim. Acta 235, 384–389 (2017).

    Google Scholar 

  63. Gamry Instruments. Accuracy contour plots — measurement and discussion. Gamry https://www.gamry.com/application-notes/EIS/accuracy-contour-plots-measurement-and-discussion/ (2020).

  64. Zhong, G., Koh, C. K., Roy, K. in IEEE/ACM Int. Conf. Computer Aided Design. ICCAD-2000. IEEE/ACM Digest of Technical Papers (Cat. No. 00CH37140) 406–411 (IEEE, 2000).

  65. Wojcik, P. T., Agarwal, P. & Orazem, M. E. A method for maintaining a constant potential variation during galvanostatic regulation of electrochemical impedance measurements. Electrochim. Acta 41, 977–983 (1996).

    Google Scholar 

  66. Wojcik, P. T. & Orazem, M. E. Variable-amplitude galvanostatically modulated impedance spectroscopy as a tool for assessing reactivity at the corrosion potential without distorting temporal evolution of the system. Corrosion 54, 289–298 (1998).

    Google Scholar 

  67. Hirschorn, B., Tribollet, B. & Orazem, M. E. On selection of the perturbation amplitude required to avoid nonlinear effects in impedance measurements. Isr. J. Chem. 48, 133–142 (2008).

    Google Scholar 

  68. Hirschorn, B. & Orazem, M. E. On the sensitivity of the Kramers–Kronig relations to nonlinear effects in impedance measurements. J. Electrochem. Soc. 156, C345–C351 (2009).

    Google Scholar 

  69. Van Ingelgem, Y., Tourwé, E., Blajiev, O., Pintelon, R. & Hubin, A. Advantages of odd random phase multisine electrochemical impedance measurements. Electroanalysis 21, 730–739 (2009).

    Google Scholar 

  70. Dokko, K. et al. Kinetic characterization of single particles of LiCoO2 by AC impedance and potential step methods. J. Electrochem. Soc. 148, A422 (2001).

    Google Scholar 

  71. Agarwal, P., Crisalle, O. D., Orazem, M. E. & Garcia-Rubio, L. H. Application of measurement models to impedance spectroscopy. II. Determination of the stochastic contribution to the error structure. J. Electrochem. Soc. 142, 4149–4158 (1995).

    ADS  Google Scholar 

  72. Agarwal, P., Orazem, M. E. & Garcia-Rubio, L. H. Application of measurement models to impedance spectroscopy. III. Evaluation of consistency with the Kramers–Kronig relations. J. Electrochem. Soc. 142, 4159–4168 (1995). This article introduces the use of Voigt measurement models to assess the consistency of impedance data to the Kramers–Kronig relations.

    ADS  Google Scholar 

  73. Watson, W. & Orazem, M. E. Measurement model program. ECSArXiv https://doi.org/10.1149/osf.io/kze9x (2020).

    Article  Google Scholar 

  74. Orazem, M. E., Pebere, N. & Tribollet, B. Enhanced graphical representation of electrochemical impedance data. J. Electrochem. Soc. 153, B129–B136 (2006).

    Google Scholar 

  75. Ivers-Tiffée, E. & Weber, A. Evaluation of electrochemical impedance spectra by the distribution of relaxation times. J. Ceram. Soc. Jpn. 125, 193–201 (2017). This article is a significant contribution showing the interest in using the distribution function of relaxation times to identify the different time constants of EIS spectra.

    Google Scholar 

  76. Wan, T. H., Saccoccio, M., Chen, C. & Ciucci, F. Influence of the discretization methods on the distribution of relaxation times deconvolution: implementing radial basis functions with DRTtools. Electrochim. Acta 184, 483–499 (2015).

    Google Scholar 

  77. Dierickx, S., Weber, A. & Ivers-Tiffée, E. How the distribution of relaxation times enhances complex equivalent circuit models for fuel cells. Electrochim. Acta 355, 136764 (2020).

    Google Scholar 

  78. Nara, H., Yokoshima, T. & Osaka, T. Technology of electrochemical impedance spectroscopy for an energy-sustainable society. Curr. Opin. Electrochem. 20, 66–77 (2020).

    Google Scholar 

  79. Huang, J., Li, Z., Ge, H. & Zhang, J. Analytical solution to the impedance of electrode/electrolyte interface in lithium-ion batteries. J. Electrochem. Soc. 162, A7037–A7048 (2015).

    Google Scholar 

  80. Huang, J. & Zhang, J. Theory of impedance response of porous electrodes: simplifications, inhomogeneities, non-stationarities and applications. J. Electrochem. Soc. 163, A1983–A2000 (2016). This article presents a general framework of EIS models that can be applicable to the porous electrodes in lithium-ion batteries, fuel cells and capacitors.

    Google Scholar 

  81. Fuller, T. F., Doyle, M. & Newman, J. Simulation and optimization of the dual lithium ion insertion cell. J. Electrochem. Soc. 141, 1–10 (1994).

    ADS  Google Scholar 

  82. Gruet, D., Delobel, B., Sicsic, D., Lucas, I. T. & Vivier, V. On the electrochemical impedance response of composite insertion electrodes — toward a better understanding of porous electrodes. Electrochim. Acta 295, 787–800 (2019).

    Google Scholar 

  83. Amatore, C. & Maisonhaute, E. When voltammetry reaches nanoseconds. Anal. Chem. 77, 303A–311A (2005).

    Google Scholar 

  84. Popkirov, G. S. & Schindler, R. N. A new impedance spectrometer for the investigation of electrochemical systems. Rev. Sci. Instrum. 63, 5366–5372 (1992).

    ADS  Google Scholar 

  85. Wiegand, G., Neumaier, K. R. & Sackmann, E. Fast impedance spectroscopy: general aspects and performance study for single ion channel measurements. Rev. Sci. Instrum. 71, 2309–2320 (2000).

    ADS  Google Scholar 

  86. Macdonald, J. R., Schoonman, J. & Lehnen, A. P. Applicability and power of complex nonlinear least squares for the analysis of impedance and admittance data. J. Electroanal. Chem. 131, 77–95 (1982).

    Google Scholar 

  87. Box, G. E. P. & Draper, N. R. Empirical Model-Building and Response Surfaces (Wiley, 1987).

  88. Draper, N. R. & Smith, H., S. Applied Regression Analysis (Wiley, 1981).

  89. Orazem, M. E., Durbha, M., Deslouis, C., Takenouti, H. & Tribollet, B. Influence of surface phenomena on the impedance response of a rotating disk electrode. Electrochim. Acta 44, 4403–4412 (1999).

    Google Scholar 

  90. Brug, G. J., van den Eeden, A. L. G., Sluyters-Rehbach, M. & Sluyters, J. H. The analysis of electrode impedances complicated by the presence of a constant phase element. J. Electroanal. Chem. 176, 275–295 (1984).

    Google Scholar 

  91. Hirschorn, B. et al. Constant-phase-element behavior caused by resistivity distributions in films: I. Theory. J. Electrochem. Soc. 157, C452–C457 (2010).

    Google Scholar 

  92. Wu, S. L., Orazem, M. E., Tribollet, B. & Vivier, V. The influence of coupled faradaic and charging currents on impedance spectroscopy. Electrochim. Acta 131, 2–12 (2014).

    Google Scholar 

  93. Gabrielli, C. & Group, S. I. Identification of Electrochemical Processes by Frequency Response Analysis (Solartron Electronic Group, 1980).

  94. Tuller, H. L., Litzelman, S. J. & Jung, W. Micro-ionics: next generation power sources. Phys. Chem. Chem. Phys. 11, 3023–3034 (2009).

    Google Scholar 

  95. Huang, J. et al. Impedance response of porous electrodes: theoretical framework, physical models and applications. J. Electrochem. Soc. 167, 166503 (2020). This article is a systematic review of physics-based EIS models for porous electrodes with substantial mathematic details that may help model development.

    ADS  Google Scholar 

  96. Keddam, M., Mattos, O. R. & Takenouti, H. Reaction model for iron dissolution studied by electrode impedance. II. Determination of the reaction model. J. Electrochem. Soc. 128, 266–274 (1981).

    ADS  Google Scholar 

  97. Pivac, I. & Barbir, F. Inductive phenomena at low frequencies in impedance spectra of proton exchange membrane fuel cells — a review. J. Power Sources 326, 112–119 (2016).

    ADS  Google Scholar 

  98. Roy, S. K., Orazem, M. E. & Tribollet, B. Interpretation of low-frequency inductive loops in PEM fuel cells. J. Electrochem. Soc. 154, B1378 (2007).

    Google Scholar 

  99. Huang, J. et al. An analytical three-scale impedance model for porous electrode with agglomerates in lithium-ion batteries. J. Electrochem. Soc. 162, A585–A595 (2015).

    Google Scholar 

  100. Sabet, P. S. & Sauer, D. U. Separation of predominant processes in electrochemical impedance spectra of lithium-ion batteries with nickel–manganese–cobalt cathodes. J. Power Sources 425, 121–129 (2019).

    ADS  Google Scholar 

  101. Boillot, M. et al. Effect of gas dilution on PEM fuel cell performance and impedance response. Fuel Cell 6, 31–37 (2006).

    Google Scholar 

  102. Harrington, D. A. & Conway, B. E. AC impedance of faradaic reactions involving electrosorbed intermediates. 1. Kinetic theory. Electrochim. Acta 32, 1703–1712 (1987). This paper presents a systematic methodology to construct EIS models from a multistep reaction mechanism.

    Google Scholar 

  103. Epelboin, I., Keddam, M. & Lestrade, J. C. Faradaic impedances and intermediates in electrochemical reactions. Faraday Discuss. Chem. Soc. 56, 264–275 (1973).

    Google Scholar 

  104. Gabrielli, C. & Keddam, M. Heterogeneous reactions coupled by diffusion. Multiple stationary states, impedance, and stability. J. Electroanal. Chem. 45, 267–277 (1973).

    Google Scholar 

  105. Bertocci, U. & Ricker, R. E. in ASTM Special Technical Publication 1154 143–161 (ASTM International, 1992).

  106. Losiewicz, B., Jurczakowski, R. & Lasia, A. Kinetics of hydrogen underpotential deposition at polycrystalline platinum in acidic solutions. Electrochim. Acta 80, 292–301 (2012).

    Google Scholar 

  107. Wang, S. S., Sun, Y., Huang, F. S. & Zhang, J. B. Freezing site of super-cooled water and failure mechanism of cold start of PEFC. J. Electrochem. Soc. 166, F860–F864 (2019).

    Google Scholar 

  108. Takahashi, M., Tobishima, S., Takei, K. & Sakurai, Y. Reaction behavior of LiFePO4 as a cathode material for rechargeable lithium batteries. Solid State Ion. 148, 283–289 (2002).

    Google Scholar 

  109. Vieil, E., Maurey-Mey, M. & Cauquis, G. Current log-transform vs reactant concentration as a tool for chemical reaction order and electrochemical mechanisms determination — I. General theory in steady-state voltammetry and application to electro-oxidation of thianthrene in presence of water. Electrochim. Acta 27, 1565–1583 (1982).

    Google Scholar 

  110. Laidler, K. J. The development of the Arrhenius equation. J. Chem. Educ. 61, 494 (1984).

    Google Scholar 

  111. Hong, P., Xu, L. F., Jiang, H. L., Li, J. Q. & Ouyang, M. G. A new approach to online AC impedance measurement at high frequency of PEM fuel cell stack. Int. J. Hydrog. Energy 42, 19156–19169 (2017).

    Google Scholar 

  112. Zhu, J. G., Sun, Z. C., Wei, X. Z. & Dai, H. F. A new lithium-ion battery internal temperature on-line estimate method based on electrochemical impedance spectroscopy measurement. J. Power Sources 274, 990–1004 (2015).

    ADS  Google Scholar 

  113. Khan, M. Z. H., Hasan, M. R., Hossain, S. I., Ahommed, M. S. & Daizy, M. Ultrasensitive detection of pathogenic viruses with electrochemical biosensor: state of the art. Biosens. Bioelectron. 166, 112431 (2020).

    Google Scholar 

  114. Prodromidis, M. I. Impedimetric immunosensors — a review. Electrochim. Acta 55, 4227–4233 (2010).

    Google Scholar 

  115. Seven, B. et al. Impedimetric biosensor for cancer cell detection. Electrochem. Commun. 37, 36–39 (2013).

    ADS  Google Scholar 

  116. Abe, T., Sagane, F., Ohtsuka, M., Iriyama, Y. & Ogumi, Z. Lithium-ion transfer at the interface between lithium-ion conductive ceramic electrolyte and liquid electrolyte — a key to enhancing the rate capability of lithium-ion batteries. J. Electrochem. Soc. 152, A2151–A2154 (2005).

    Google Scholar 

  117. Song, H.-K., Jung, Y.-H., Lee, K.-H. & Dao, L. H. Electrochemical impedance spectroscopy of porous electrodes: the effect of pore size distribution. Electrochim. Acta 44, 3513–3519 (1999).

    Google Scholar 

  118. Song, H.-K., Hwang, H.-Y., Lee, K.-H. & Dao, L. H. The effect of pore size distribution on the frequency dispersion of porous electrodes. Electrochim. Acta 45, 2241–2257 (2000).

    Google Scholar 

  119. Suthar, B., Landesfeind, J., Eldiven, A. & Gasteiger, H. A. Method to determine the in-plane tortuosity of porous electrodes. J. Electrochem. Soc. 165, A2008–A2018 (2018).

    Google Scholar 

  120. Ritter, S. et al. Results of an international round-robin exercise on electrochemical impedance spectroscopy. Corros. Eng. Sci. Technol. 56, 254–268 (2020).

    Google Scholar 

  121. Tait, W. S. Using electrochemical measurements to estimate coating and polymer film durability. J. Coat. Technol. 75, 45–50 (2003).

    Google Scholar 

  122. Boukamp, B. A. A linear Kronig–Kramers transform test for immittance data validation. J. Electrochem. Soc. 142, 1885–1894 (1995).

    ADS  Google Scholar 

  123. You, C., Zabara, M. A., Orazem, M. E. & Ulgut, B. Application of the Kramers–Kronig relations to multi-sine electrochemical impedance measurements. J. Electrochem. Soc. 167, 020515 (2020).

    ADS  Google Scholar 

  124. Allagui, A., Freeborn, T. J., Elwakil, A. S. & Maundy, B. J. Reevaluation of performance of electric double-layer capacitors from constant-current charge/discharge and cyclic voltammetry. Sci. Rep. 6, 38568 (2016). This article presents a detailed description of the use of a CPE in cyclic voltammetry.

    ADS  Google Scholar 

  125. Gharbi, O., Tran, M. T. T., Tribollet, B., Turmine, M. & Vivier, V. Revisiting cyclic voltammetry and electrochemical impedance spectroscopy analysis for capacitance measurements. Electrochim. Acta 343, 136109 (2020).

    Google Scholar 

  126. Sadkowski, A. Time domain responses of constant phase electrodes. Electrochim. Acta 38, 2051–2054 (1993).

    Google Scholar 

  127. Sadkowski, A. On the ideal polarisability of electrodes displaying CPE-type capacitance dispersion. J. Electroanal. Chem. 481, 222–226 (2000). This article discusses the physical meaning of a CPE.

    Google Scholar 

  128. Orazem, M. E. et al. Dielectric properties of materials showing constant-phase-element (CPE) impedance response. J. Electrochem. Soc. 160, C215–C225 (2013). This article presents an overview of methods used to extract capacitance from CPE parameters, with emphasis on the use of a power-law model to extract the thickness of oxide films.

    Google Scholar 

  129. Newman, J. Frequency dispersion in capacity measurements at a disk electrode. J. Electrochem. Soc. 117, 198–203 (1970).

    ADS  Google Scholar 

  130. 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. 154, C89–C98 (2007).

    Google Scholar 

  131. 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. 154, C99–C107 (2007).

    Google Scholar 

  132. Hirschorn, B. et al. Determination of effective capacitance and film thickness from constant-phase-element parameters. Electrochim. Acta 55, 6218–6227 (2010).

    Google Scholar 

  133. Hirschorn, B. et al. Constant-phase-element behavior caused by resistivity distributions in films: II. Applications. J. Electrochem. Soc. 157, C458–C463 (2010).

    Google Scholar 

  134. Díaz, B., Guitián, B., Nóvoa, X. R. & Pérez, M. C. The effect of chlorides on the corrosion behaviour of weathered reinforcing bars. Electrochim. Acta 336, 135737 (2020).

    Google Scholar 

  135. Hernández, R. D. P. B., Aoki, I. V., Tribollet, B. & De Melo, H. G. Electrochemical impedance spectroscopy investigation of the electrochemical behaviour of copper coated with artificial patina layers and submitted to wet and dry cycles. Electrochim. Acta 56, 2801–2814 (2011).

    Google Scholar 

  136. Capelossi, V. R. et al. Corrosion protection of clad 2024 aluminum alloy anodized in tartaric-sulfuric acid bath and protected with hybrid sol-gel coating. Electrochim. Acta 124, 69–79 (2014).

    Google Scholar 

  137. Bouali, A. C. et al. Layered double hydroxide based active corrosion protective sealing of plasma electrolytic oxidation/sol-gel composite coating on AA2024. Appl. Surf. Sci. 494, 829–840 (2019).

    ADS  Google Scholar 

  138. Calado, L. M., Taryba, M. G., Carmezim, M. J. & Montemor, M. F. Self-healing ceria-modified coating for corrosion protection of AZ31 magnesium alloy. Corros. Sci. 142, 12–21 (2018).

    Google Scholar 

  139. Roggero, A. et al. Thermal activation of impedance measurements on an epoxy coating for the corrosion protection: 2. electrochemical impedance spectroscopy study. Electrochim. Acta 305, 116–124 (2019).

    Google Scholar 

  140. Karden, E., Buller, S. & De Doncker, R. W. A method for measurement and interpretation of impedance spectra for industrial batteries. J. Power Sources 85, 72–78 (2000).

    ADS  Google Scholar 

  141. Costard, J., Ender, M., Weiss, M. & Ivers-Tiffée, E. Three-electrode setups for lithium-ion batteries: II. Experimental study of different reference electrode designs and their implications for half-cell impedance spectra. J. Electrochem. Soc. 164, A80–A87 (2017).

    Google Scholar 

  142. Osaka, T., Mukoyama, D. & Nara, H. Review — development of diagnostic process for commercially available batteries, especially lithium ion battery, by electrochemical impedance spectroscopy. J. Electrochem. Soc. 162, A2529–A2537 (2015).

    Google Scholar 

  143. Itou, Y., Ogihara, N. & Kawauchi, S. Role of conductive carbon in porous Li-ion battery electrodes revealed by electrochemical impedance spectroscopy using a symmetric cell. J. Phys. Chem. C 124, 5559–5564 (2020).

    Google Scholar 

  144. Ji, G., Macia, L. F., Allaert, B., Hubin, A. & Terryn, H. Odd random phase electrochemical impedance spectroscopy to study the corrosion behavior of hot dip Zn and Zn-alloy coated steel wires in sodium chloride solution. J. Electrochem. Soc. 165, C246–C257 (2018).

    Google Scholar 

  145. Sanchez, B., Fernandez, X., Reig, S. & Bragos, R. An FPGA-based frequency response analyzer for multisine and stepped sine measurements on stationary and time-varying impedance. Meas. Sci. Technol. 25, 015501 (2014).

    ADS  Google Scholar 

  146. Gabrielli, C., Huet, F. & Keddam, M. Comparison of sine wave and white noise analysis for electrochemical impedance measurements. J. Electroanal. Chem. 335, 33–53 (1992).

    Google Scholar 

  147. Chang, B. Y. & Park, S. M. Electrochemical impedance spectroscopy. Annu. Rev. Anal. Chem. 3, 207–229 (2010).

    Google Scholar 

  148. Smulko, J. M., Darowicki, K. & Zielinski, A. On electrochemical noise analysis for monitoring of uniform corrosion rate. IEEE Trans. Instrum. Meas. 56, 2018–2023 (2007).

    Google Scholar 

  149. Cottis, R. A. Interpretation of electrochemical noise data. Corrosion 57, 265–285 (2001).

    Google Scholar 

  150. Abada, S. et al. Safety focused modeling of lithium-ion batteries: a review. J. Power Sources 306, 178–192 (2016).

    ADS  Google Scholar 

  151. Deslouis, C., Tribollet, B., Mengoli, G. & Musiani, M. M. Electrochemical behavior of copper in neutral aerated chloride solution. II. Impedance investigation. J. Appl. Electrochem. 18, 384–393 (1988). This article presents a comprehensive analysis of EIS and transfer functions applied to the corrosion of copper in chloride solution.

    Google Scholar 

  152. Robertson, B., Tribollet, B. & Deslouis, C. Measurement of diffusion coefficients by DC and EHD electrochemical methods. J. Electrochem. Soc. 135, 2279–2284 (1988).

    ADS  Google Scholar 

  153. Tribollet, B., Newman, J. & Smyrl, W. H. Determination of the diffusion coefficient from impedance data in the low frequency range. J. Electrochem. Soc. 135, 134–138 (1988).

    ADS  Google Scholar 

  154. Antano-Lopez, R., Keddam, M. & Takenouti, H. A new experimental approach to the time-constants of electrochemical impedance: frequency response of the double layer capacitance. Electrochim. Acta 46, 3611–3617 (2001).

    Google Scholar 

  155. Cachet, H. et al. Capacitance probe of the electron displacement in a dye sensitized solar cell by an intermodulation technique: a quantitative model. Electrochim. Acta 49, 2541–2549 (2004).

    Google Scholar 

  156. Larios-Duran, E. R. et al. Dynamics of double-layer by AC modulation of the interfacial capacitance and associated transfer functions. Electrochim. Acta 55, 6292–6298 (2010).

    Google Scholar 

  157. Antaño-López, R., Keddam, M., Turmine, M. & Vivier, V. The impedance response of a passive film revisited by a double modulation technique. ChemElectroChem 6, 202–210 (2019).

    Google Scholar 

  158. Zou, F., Thierry, D. & Isaacs, H. S. A high-resolution probe for localized electrochemical impedance spectroscopy measurements. J. Electrochem. Soc. 144, 1957–1965 (1997). This study reports the design of dual microelectrodes for performing local EIS to enhance the spatial resolution of the technique.

    ADS  Google Scholar 

  159. Ferrari, J. V. et al. Influence of normal and radial contributions of local current density on local electrochemical impedance spectroscopy. Electrochim. Acta 60, 244–252 (2012).

    Google Scholar 

  160. de Abreu, C. P. et al. Multiscale electrochemical study of welded Al alloys joined by friction stir welding. J. Electrochem. Soc. 164, C735–C746 (2017).

    Google Scholar 

  161. Shkirskiy, V., Volovitch, P. & Vivier, V. Development of quantitative local electrochemical impedance mapping: an efficient tool for the evaluation of delamination kinetics. Electrochim. Acta 235, 442–452 (2017).

    Google Scholar 

  162. Gharbi, O., Ngo, K., Turmine, M. & Vivier, V. Local electrochemical impedance spectroscopy: a window into heterogeneous interfaces. Curr. Opin. Electrochem. 20, 1–7 (2020).

    Google Scholar 

  163. Creason, S. C. & Smith, D. E. Fourier transform Faradaic admittance measurements: I. Demonstration of the applicability of random and pseudo-random noise as applied potential signals. J. Electroanal. Chem. 36, A1–A7 (1972).

    Google Scholar 

  164. Stoynov, Z. B. & Savova-Stoynov, B. S. Impedance study of non-stationary systems: four-dimensional analysis. J. Electroanal. Chem. 183, 133–144 (1985).

    Google Scholar 

  165. Itagaki, M. et al. In situ electrochemical impedance spectroscopy to investigate negative electrode of lithium-ion rechargeable batteries. J. Power Sources 135, 255–261 (2004).

    ADS  Google Scholar 

  166. Huang, J., Li, Z. & Zhang, J. B. Dynamic electrochemical impedance spectroscopy reconstructed from continuous impedance measurement of single frequency during charging/discharging. J. Power Sources 273, 1098–1102 (2015).

    ADS  Google Scholar 

  167. Wiezell, K., Holmstrom, N. & Lindbergh, G. Studying low-humidity effects in PEFCs using EIS II. modeling. J. Electrochem. Soc. 159, F379–F392 (2012).

    Google Scholar 

  168. Setzler, B. P. & Fuller, T. F. A physics-based impedance model of proton exchange membrane fuel cells exhibiting low-frequency inductive loops. J. Electrochem. Soc. 162, F519–F530 (2015).

    Google Scholar 

  169. Kulikovsky, A. A. Analysis of Damjanovic kinetics of the oxygen reduction reaction: stability, polarization curve and impedance spectra. J. Electroanal. Chem. 738, 130–137 (2015).

    Google Scholar 

  170. Schneider, I. A., Kramer, D., Wokaun, A. & Scherer, G. G. Oscillations in gas channels — II. Unraveling the characteristics of the low frequency loop in air-fed PEFC impedance spectra. J. Electrochem. Soc. 154, B770–B782 (2007).

    Google Scholar 

  171. Kuhn, H., Andreaus, B., Wokaun, A. & Scherer, G. G. Electrochemical impedance spectroscopy applied to polymer electrolyte fuel cells with a pseudo reference electrode arrangement. Electrochim. Acta 51, 1622–1628 (2006).

    Google Scholar 

  172. Raccichini, R., Amores, M. & Hinds, G. Critical review of the use of reference electrodes in Li-ion batteries: a diagnostic perspective. Batteries 5, 24 (2019).

    Google Scholar 

  173. Hoshi, Y. et al. Optimization of reference electrode position in a three-electrode cell for impedance measurements in lithium-ion rechargeable battery by finite element method. J. Power Sources 288, 168–175 (2015).

    ADS  Google Scholar 

  174. Solchenbach, S., Pritzl, D., Kong, E. J. Y., Landesfeind, J. & Gasteiger, H. A. A gold micro-reference electrode for impedance and potential measurements in lithium ion batteries. J. Electrochem. Soc. 163, A2265 (2016).

    Google Scholar 

  175. Chu, Z. Y. et al. Testing lithium-ion battery with the internal reference electrode: an insight into the blocking effect. J. Electrochem. Soc. 165, A3240–A3248 (2018).

    Google Scholar 

  176. Orazem, M. E. Electrochemical impedance spectroscopy: the journey to physical understanding. J. Solid State Electrochem. 24, 2151–2153 (2020).

    Google Scholar 

  177. Agarwal, P., Orazem, M. E. & Garci-Rubio, L. H. Measurement models for electrochemical impedance spectroscopy. I. Demonstration of applicability. J. Electrochem. Soc. 139, 1917–1927 (1992).

    ADS  Google Scholar 

  178. Liao, H. et al. Physical properties obtained from measurement model analysis of impedance measurements. Electrochim. Acta 354, 136747 (2020).

    Google Scholar 

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Authors and Affiliations

  1. School of Vehicle and Mobility, Tsinghua University, Beijing, China

    Shangshang Wang & Jianbo Zhang

  2. Sorbonne Université, CNRS, Laboratoire Interfaces et Systèmes Electrochimiques (LISE), Paris, France

    Oumaïma Gharbi & Vincent Vivier

  3. Department of Chemical Engineering, University of Florida, Gainesville, FL, USA

    Ming Gao & Mark E. Orazem

Authors
  1. Shangshang Wang
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  4. Vincent Vivier
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Contributions

Introduction (S.W., J.Z., O.G., V.V., M.G. and M.E.O); Experimentation (S.W., J.Z., O.G., V.V., M.G. and M.E.O); Results (S.W., J.Z., O.G., V.V., M.G. and M.E.O); Applications (S.W., J.Z., O.G., V.V., M.G. and M.E.O); Reproducibility and data deposition (S.W., J.Z., O.G., V.V., M.G. and M.E.O); Limitations and optimizations (S.W., J.Z., O.G., V.V., M.G. and M.E.O); Outlook (S.W., J.Z., O.G., V.V., M.G. and M.E.O); Overview of the Primer (M.E.O.).

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Correspondence to Mark E. Orazem.

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Nature Reviews Methods Primers thanks S. Ciampi, A. Lasia and I. Shitanda for their contribution to the peer review of this work.

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Glossary

Cyclic voltammetry

An electrochemical technique in which the current response of an electrochemical system is measured as a function of the potential, which is swept in positive and negative directions at a given rate.

Chronoamperometry

An electrochemical technique in which a potential step is applied to a working electrode and the current response is recorded as a function of time.

Chronopotentiometry

An electrochemical technique in which a current step is applied to a working electrode and the potential response is recorded as a function of time.

Scanning electrochemical microscopy

A local electrochemical technique that allows sensing of the surface topography and reactivity.

Interfacial capacitance

The capacity of the electrical double layer or the double layer in series with a thin film on the electrode surface (measured in farads per square metre).

Potentiostat

Electronic hardware for electrochemical experiments maintaining a constant potential difference between the working electrode and the reference electrode.

Rotating disk electrode

A set-up allowing control of the rotation rate of a disk electrode embedded in an insulating circular plane in order to enhance and tune mass transport by generating a thin diffusion layer with uniform thickness.

Complex number

An ordered pair of real and imaginary numbers.

Resistance

The real part of the impedance of an electrical circuit (measured in ohm square metres).

Reactance

The imaginary part of the impedance of an electrical circuit (measured in ohm square metres).

Ohmic resistance

An ionic resistance of the electrolyte and electronic resistance of the electrode, wire and connection (measured in ohm square metres).

Capacitance

The ability of the electrochemical system, specifically the electrode–electrolyte interface, to hold electrical charge (measured in farads per square metre).

Frequency decade

A unit for measuring frequency ratios on a logarithmic scale, with one decade corresponding to a ratio of ten between two frequencies (an order of magnitude difference).

Oscilloscope

Electronic hardware monitoring the time-domain signals that are processed in the impedance measurement (for example, Lissajous plot).

Warburg semi-infinite diffusion impedance

An impedance element describing the diffusion behaviour of the electrolyte in the absence of convection with a diffusion layer that can spread to infinity.

Simplex regression

A robust mathematical algorithm used to solve non-linear least-squares curve-fitting problems that is less sensitive to initial values but does not provide confidence intervals for the resulting parameter estimates.

Levenberg–Marquardt regression

A mathematical algorithm used to solve non-linear least-squares curve-fitting problems that is sensitive to initial values and provides confidence intervals for the resulting parameter estimates.

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Wang, S., Zhang, J., Gharbi, O. et al. Electrochemical impedance spectroscopy. Nat Rev Methods Primers 1, 41 (2021). https://doi.org/10.1038/s43586-021-00039-w

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