fast process at high frequency (> 10 kHz) and low process such as diffusion at low frequencies (<100 mHz). The modulus $Z$ and phase $\phi$ are the parameters of interest, so the impedance data can be plotted in Bode plot ($Z$ and $\phi$ $vs.$ frequency), but in electrochemistry, the most common plot is the Nyquist plot $-Im(Z)\,vs.\,Re(Z)$.Īs the periodical perturbation is performed at several frequencies, Electrochemical Impedance Spectroscopy (EIS) is capable of characterizing processes that have different time constants i.e.
The small perturbation of the electrode state has the advantage that the solutions of relevant mathematical equations used are transformed in linear forms.
Sometimes, it is forgotten that it is a complex number as it is shown in the topic on the definition of Z. The impedance is given in is a complex number. In the case of Fig. 1, the transfer function is the admittance $Y$ with $Y=1/Z$. If the input is a current sine wave and the output a potential sine wave, then the transfer function is the impedance $Z$. $H(s) = \dfrac$ the Laplace transform, and $s$ the Laplace variable, which is, in our case proportional to the frequency. The transfer function $ H(s)$ of the Linear Time Invariant (LTI) system is defined as: The frequency sweep enables access to all processes taking place at the electrode, from the faster (double-layer charging) to the slower (mass transport). With AC techniques, such as Electrochemical Impedance Spectroscopy (EIS), the response of the system to a potential or current sinusoidal perturbation is studied as a function of the frequency, which is swept over a few decades (Fig. Generally, a constant sampling time is used. In simple terms, with DC techniques, the response of an electrochemical system is studied as a function of time. In electrochemistry, there are two main types of techniques: Direct Current (DC) and Alternative Current (AC) techniques.ĭC techniques mainly include potential or current step and sweep methods such as Chronopotentiometry, Chronoamperometry, Linear Scan Voltammetry or Cyclic Voltammetry. A tentative definition of Electrochemical Impedance Spectroscopy