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 (
), shown in black, is compared to the same curve corrected for ohmic drop (
), shown in orange.
(b): the Lissajous plot (blue),
, 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 (th
(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 . The effect of ohmic drop was investigated in .
 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
, 1997 pp. 27–39.
 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
, 1997 pp. 41–52.
 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
, 2012 pp. 17–27.
 M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy
, Hoboken, NJ: John Wiley & Sons, 2008 p. 134.