# What is EIS ?

Latest updated: February 12, 2020

Electrochemical Impedance Spectroscopy (EIS) is a powerful tool enabling the study of processes that occur at the interface of an electrode.

In EIS a periodic signal is applied in current or voltage at several frequencies. The periodic signal is traditionally built with a sinus.

The transfer function H of the system is defined as:

$H(s) = \dfrac{\text{ℒ[Output(}t\text{)}]}{\text{ℒ[Input(}t\text{)}]}$ (1)

ℒ  being the Laplace transform

Measurements as a function of the frequency of the perturbation give an impedance, Z,  (or admittance) diagram. The impedance is given in Ohm as it is the ratio of the voltage vs. the current and is a complex number.

To be valid, the system under study has to be:

• Linear: The response (output) of the cell has to be directly proportional to the input. The small perturbation of the electrode state has the advantage that the solutions of relevant mathematical equations used are transformed in linear forms.
• Time invariant: The state of the cell must not change during the measurements.
• Causal: The output has to be correlated directly with the input.

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).

As the periodical perturbation is performed at several frequencies, EIS is capable of characterizing processes that have different time constants i.e. fast process at high frequency (> 10 kHz) and low process such as diffusion at low frequencies (<100 mHz).

Tutorial I:  Background

## Powerful and sensitive

• Powerful: Electrochemical impedance spectroscopy (EIS) is used to study a wide variety of systems in many fields of electrochemistry such as electrode kinetics, double-layer studies, batteries, corrosion, solid-state electrochemistry, bioelectrochemistry, photovoltaic systems.

Tutorial II: Corrosion

Tutorial III: Battery testing

• Sensitive: It can measure tiny signals, so as with all sensitive techniques, certain precautions should be considered with EIS.

Tutorial IV: Experimental conditions

## How to interpret EIS data

To interpret EIS data, it is common to make an analogy between the experimental data and an equivalent circuit made of capacitor, resistor, inductance and element that mimic diffusion processes, which depends on the electrode reactions. The elements used to build the equivalent circuit have to have a physical meaning.

An EIS data modeling tool is required to be able to withdraw the value of the element of the equivalent circuit.

Below how it looks like in BioLogic EC-Lab software to select the appropriate equivalent circuit:

For more information on the BioLogic EIS modeling tool (ZFit), please have a look at the videos below:

EIS electrochemical impedance spectroscopy transfer function