(297d) Systematic Model Development for Electrochemical Impedance Spectroscopy | AIChE

(297d) Systematic Model Development for Electrochemical Impedance Spectroscopy

Authors 

Orazem, M. E. - Presenter, University of Florida
Impedance spectroscopy represents a rich and inter-related area of science that is applied to a large number of important areas of research including corrosion and corrosion control by coatings, electrochemical kinetics and mechanisms, energy storage systems such as batteries and capacitors, fuel cells, and biological, biocellular, and biomedical systems. While electrical circuit analogues are commonly employed, interpretation of impedance spectra is best achieved by developing a model that accounts for the chemistry and physics of the system under study. The objective of this presentation is to describe a systematic approach to model development that includes use of graphical methods to guide model development, use of electrical circuits to account for the geometry of a given system, and use of a phasor notation to facilitate calculation of a faradaic impedance based on proposed reaction mechanisms and mass transfer.

  1. A preliminary graphical inspection of tM. he data includes use of the traditional Nyquist and Bode formats. Estimates for parameters such as capacitance, ohmic resistance and polarization resistances may be extracted from the plots. Knowledge of the ohmic resistance allows preparation of ohmic-resistance-corrected Bode plots. Values of the extracted capacitance, the shape of the ohmic-resistance-corrected Bode plots, and the shape of the Nyquist plots guide development of a preliminary model. If a set of spectra are obtained at different elapsed times or different conditions, superposition of scaled plots may be used to determine whether the differences may be attributed to changes in system chemistry or to simply changes in parameters such as active area.
  2. Evaluation of consistency with the Kramers-Kronig relations allows determination of the frequency range suitable for analysis. Replicated measurements allow determination of error structure, useful for the regression of experimental data. The measurement model, developed by our group, provides a useful tool for evaluating the error structure of impedance data.1-3
  3. Graphical methods may be used to extract parameters. This step is an extension of the preliminary graphical approach, but has emphasis on the self-consistent part of the spectrum. Plots of complex capacitance may be used to extract meaningful values for capacitance.4-5 An estimate for the characteristic frequency associated with geometrical effects may be established for well-defined cell geometries.6
  4. The interpretation or process model development takes place in two stages: development of circuit analogues and derivation of the faradaic impedance. Electrical circuits are prepared to account for the geometry of the electrochemical system under study. These circuits provide a framework for the faradaic impedance which is developed based on the proposed reaction chemistry. Models for the faradaic impedance are prepared for proposed reaction kinetics. The faradaic impedance includes the influence of mass transfer, coupled reactions, and even homogeneous reactions.7
  5. The process model is regressed to the Kramers-Kronig-consistent portion of the spectrum. Simplex regression is insensitive to initial guessed values for parameters, but does not provide confidence intervals for the regressed parameters. Thus, regression by simplex algorithms may yield values for parameters that are statistically insignificant. Levenberq-Marquardt regression algorithms provide confidence intervals that can be used to assess the statistical significance of parameter values. The limitation of Levenberq-Marquardt regression is that it is very sensitive to initial parameter values. Some regression programs provide simplex algorithms to obtain initial parameter values and Levenberq-Marquardt algorithms to yield final values and their respective confidence intervals.

Impedance spectroscopy is not a stand-alone technique, and models for impedance are not unique. The model identified by the procedure described in this presentation represents a process model intended to account for the hypothesized physical and chemical character of the system under study. The objective of the model is not to provide a good fit with the smallest number of parameters. The objective is rather to use the model to gain a physical understanding of the system. The model should be able to account for, or at least be consistent with, all experimental observations. The proposed model can suggest experiments needed to validate model hypotheses.

This approach will be illustrated by a step-by-step analysis of a sample data set, including preliminary graphical inspection of the data, evaluation of consistency with the Kramers-Kronig relations, development of an interpretation or process model, regression of the model to the Kramers-Kronig-consistent portion of the spectrum, and evaluation of the physical meaning of the parameters extracted.

References

  1. P. Agarwal, M. E. Orazem, and L. H. García-Rubio, “Measurement Models for Electrochemical Impedance Spectroscopy: 1. Demonstration of Applicability,” J. Electrochem. Soc., 139 (1992), 1917-1927.
  2. P. Agarwal, Oscar D. Crisalle, M. E. Orazem, and L. H. García-Rubio, “Application of Measurement Models to Electrochemical Impedance Spectroscopy: 2. Determination of the Stochastic Contribution to the Error Structure,” J. Electrochem. Soc., 142 (1995), 4149-4158.
  3. P. Agarwal, M. E. Orazem, and L. H. García-Rubio, “Application of Measurement Models to Electrochemical Impedance Spectroscopy: 3. Evaluation of Consistency with the Kramers-Kronig Relations,” J. Electrochem. Soc., 142 (1995), 4159-4168.
  4. S. Chakri, I. Frateur, M. E. Orazem, E. Sutter, T.T.M. Tran, B. Tribollet,and V. Vivier, "Improved EIS Analysis of the Electrochemical Behaviour of Carbon Steel in Alkaline Solution," Electrochim. Acta, 246 (2017), 924-930.
  5. A. S. Nguyen, N. Caussé, M. Musiani, M. E. Orazem, N. Pébère, B. Tribollet, and V. Vivier, "Determination of Water Uptake in Organic Coatings Deposited on 2024 Aluminium Alloy: Comparison between Impedance Measurements and Gravimetry," Prog. Org. Coat., 112 (2017) 93-100.
  6. V. Huang, V. Vivier, M. E. Orazem, I. Frateur, and B. Tribollet, “The Global and Local Impedance Response of a Blocking Disk Electrode with Local Constant-Phase-Element Behavior,” J. Electrochem. Soc., 154 (2007), C89-C98.
  7. M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy, 2nd edition, John Wiley & Sons, Hoboken, 2017.