# Nonlinear Impedance of Tafelian Electrochemical Systems

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This Demonstration shows the effects of Tafel kinetics, ohmic potential drop, interfacial capacitance, and amplitude/frequency of sinusoidal potential signals on the nonlinear impedance of electrochemical systems.

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Contributed by: Claude Montella and Jean-Paul Diard (October 2014)

(Université Grenoble Alpes, Grenoble, France)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The usual impedance of electrochemical systems, defined under small-signal conditions, depends on the steady-state conditions and the frequency () of sinusoidal perturbation signal. The effective (nonlinear) impedance, depends, in addition, on the amplitude of the input signal, given the electrode potential .

The example of Tafel kinetics, , is dealt with in this Demonstration, together with ohmic drop () and interfacial capacitive () effects. The modifiable parameters are the steady-state potential imposed (), the ohmic resistance (), the amplitude () of the sinusoidal input signal, and its frequency (). The other parameters (, , ) have fixed values.

(a): the steady-state current-potential curve ( versus ), shown in black, is compared to the same curve corrected for ohmic drop ( versus ), shown in orange.

(b): the Lissajous plot (blue), vs. , starting from steady-state conditions (black), is used to observe the linearity or nonlinearity of electrochemical system behavior.

(c): the potential difference at the electrolyte/electrode interface: (orange) is compared to the input signal (blue) under periodic conditions ( cycle). The symbol represents the deviation from steady state.

(d): the periodic current (blue), as well as its fundamental harmonic component (orange), obtained by Fourier series expansion, are plotted over one cycle as a function of dimensionless time.

(e): The faradaic (blue) and capacitive (orange) contributions to the total current variation are plotted under periodic conditions ( cycle).

(f): Shows the Nyquist representation of the usual impedance (black) and the nonlinear impedance (orange) of electrochemical system, with . Both impedances are dimensionless after division by the low-frequency linear resistance .

The influence of nonlinearity of electrochemical systems on the impedance evaluated at low frequency was examined in [1–3]. The influence of signal frequency was dealt with in [4]. The effect of ohmic drop was investigated in [3].

References

[1] J.-P. Diard, B. Le Gorrec, and C. Montella, "Deviation from the Polarization Resistance due to Non-Linearity. I- Theoretical formulation," *Journal of Electroanalytical Chemistry*, 432, 1997 pp. 27–39.

[2] J.-P. Diard, B. Le Gorrec, and C. Montella, "Deviation from the Polarization Resistance due to Non-Linearity. II- Application to Electrochemical Reactions," *Journal of Electroanalytical Chemistry*, 432, 1997 pp. 41–52.

[3] C. Montella, "Combined Effects of Tafel Kinetics and Ohmic Potential Drop on the Nonlinear Responses of Electrochemical Systems to Low-Frequency Sinusoidal Perturbation of Rlectrode Potential - New Approach using the Lambert W-function," *Journal of Electroanalytical Chemistry*, 672, 2012 pp. 17–27.

[4] M. E. Orazem and B. Tribollet, *Electrochemical Impedance Spectroscopy*, Hoboken, NJ: John Wiley & Sons, 2008 p. 134.

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