# Electrochemical Impedance Spectroscopy

Electrochemical Impedance Spectroscopy (EIS) is one of the most complex techniques in electrochemical research. In this section the basics of EIS are explained, i.e. the excitation and the signal as well as the recorded values. The visualization and analysis of the EIS data is explained in the following chapters.

## Electrochemical Impedance Spectroscopy (EIS)

Electrochemical Impedance Spectroscopy (EIS) gained a lot of attention in the last 10 years. Its popularity can be attributed to various reasons. One is that EIS allows separating the influences of different components, meaning the contribution of the electron transfer resistance, double layer capacity, etc.

Another reason is that EIS is very surface sensitive, which makes many changes visible that can’t be perceived with other techniques. Examples are changes in polymer layers due to swelling, surface changes due to protein adsorption or penetration of corrosion protection layers. As a result EIS is interesting for analytical electrochemistry, because molecules can be detected without a redox active marker.

While resistance is the ratio of voltage or potential and current for a DC (direct current) system, the impedance is the ratio of voltage or potential and current for AC (alternating current) systems. The wave nature makes it necessary to define the impedance with two parameters. One is the total impedance Z and the other one is the phase shift Î¦.

If you consider the two periodic waves of current and voltage, the waves have the same frequency, because one wave causes the other. There is a constant time shift between the two waves, which is called the phase shift Î¦. Its unit is degrees (Â°), because usually waves are considered to be vectors in a polar coordinate system or a sine function (see Figure 6.1).

The total impedance is the ratio of the potentialâ€™s amplitude and the currentâ€™s amplitude. The resulting impedance is a complex number. This number can be expressed in the complex plane in polar coordinates by using Z as the length of the vector and Î¦ as the angle. With the common knowledge about calculations for complex numbers the impedance can also be expressed as the real part of the impedance Zâ€™, which is the resistance, and imaginary part Zâ€™â€™ (see Figure 6.2).

The two notations are the origin of the two most popular plots for impedance spectra: the Bode plot and Nyquist plot. More information will be given in chapterÂ Bode and Nyquist Plot.

A potentiostat measures the impedance by applying a potential wave to the working electrode and records the resulting current wave. From these two waves the potentiostat calculates Z, Î¦, Zâ€™ and Zâ€™â€™. The spectrum is made by measuring these parameters for potential waves with different frequencies.

A fixed number of frequencies per decade is usually chosen, because most plots have a logarithmic axis. This means for example 10 frequencies between 10 000Â Hz and 1000Â Hz, 10 between 1000Â Hz and 100Â Hz etc. are chosen, these frequencies are usually equidistant on a logarithmic scale. PSTrace allows you to choose, if you want to define the total number of points through the whole spectrum or the number of points per decade, whatever option you choose, you can always see a list of the chosen frequencies.