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 (

^{th} 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].

[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.