Basic Knowledge for Understanding EIS

Ohm s law defines the resistance, R, in terms of the ratio between voltage V and current I. Its use is limited to the ideal resistor for a DC system, which is independent of frequency. The relationship between the resistance, current, and voltage can be expressed as 

However, real electrochemical systems exhibit much more complex behaviours. They are not simply resistive. The electrochemical double layer adds a capacitive term. Other electrode processes, such as diffusion, are time and/or frequency dependent. Therefore, for an actual electrochemical system, impedance is used instead of resistance. The impedance of an electrochemical system (defined as Ziot)) is the AC response of the system being studied to the application of an AC signal (e.g., sinusoidal wave) imposed upon the system. The form of the current-voltage relationship of the impedance in an electrochemical system can also be expressed as 

The technique that measures the AC impedance of a circuit element or an electric circuit is called AC impedance spectroscopy. As described in Section 2.4, the impedances of a resistor (X, ). a capacitor (Zc), and an inductor (ZL) for a sinusoidal system can be expressed, respectively, as follows  

If AC impedance spectroscopy is used in an electrochemical system, this technique is generally called electrochemical impedance spectroscopy, known as EIS. The impedance of an electrochemical system can also be expressed typically in Cartesian coordinates  

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