## ELECTROCHEMICAL IMPEDANCE

In the last chapter, we studied the current response of an electrochemical system for different electrode potential excitations (potential step, square wave, etc.). We considered only the influence of the mass transport on the response as a function of time, neglecting the kinetics of the electrode reaction. In other words, we consistently made the hypothesis that the Nernst equation applied to the interfacial concentrations. It is, of course, possible for the techniques studied previously, such as potential step amperometry, cyclic voltammetry, square-wave voltammetry, etc. to take into account kinetic effects by introducing Butler-Volmer type equations as boundary conditions of the diffusion equations. However, even though those techniques just mentioned can be used to study the kinetics of an electrode reaction, the result is often corrupted by sideeffects such as the charging currents of the double layer observed on a time-scale of the order of a millisecond, or by the ohmic drop associated to the experimental setup. We have already seen in chapters 7 and 8 that the response of reversible electrochemical systems studied in the presence of an ohmic drop unfortunately resembled the response of kinetically slow systems. The best way of differentiating the kinetics of an electrode reaction from experimental side-effects is to use an excitation function covering a large time domain. The most common of these techniques is electrochemical impedance where the electrode potential excitation function is a sine wave of variable frequencies.

As a first approximation, we can consider an electrochemical system as linear, i.e. that the current response for small potential perturbations is linear, and the potential response for small imposed current perturbations is also linear. To illustrate this, consider a steady state current-potential curve such as that in Figure 9.1, and let’s examine the system response if we vary the electrode potential sinusoidally at low frequencies around a constant value Ec with a small amplitude E. The current response follow the steady state curve at the same frequency around the constant current value Ic with an amplitude I which reflects the slope of the steady state curve. The two functions have the same frequency, but the current can be dephased with respect to the potential. Thus, basically, we can write