Electrochemical Impedance Spectroscopy

The electrochemical impedance spectroscopy (often abbreviated as EIS) determines the impedance , i. H. the alternating current resistance of electrochemical systems as a function of the frequency of an alternating voltage or alternating current. Electrochemical systems are e.g. B. galvanic cells or electrolysis cells and contain an electron conductor ( electrode ), and an ion conductor ( electrolyte ). With impedance spectroscopy , valuable information about the system under investigation and the processes taking place in it can be obtained, e.g. B. also via the resistance of an electrolyte .

application areas

In almost all areas of electrochemistry, impedance spectroscopy can be used to examine and assess material or system properties. Areas of application can therefore be:

Energy storage:
- Batteries , e.g. B. Determination of internal resistance . Further goals are to determine the state of charge or the state of aging of the battery.

Biological and Biomedical Systems

Electrochemistry of semiconductors , e.g. B. in photoelectrochemical cells such as the Grätzel cell . Here one must reckon with a significant contribution of the electron conductor to the total impedance.

Investigations into corrosion , corrosion protection and passivation

Surface technology

kinetics

For investigating the sedimentation behavior of particles in liquids

Measurement methods

In most cases, impedance spectroscopy is carried out by applying an alternating voltage, i. That is, the potential of the working electrode is modulated sinusoidally and the current and its phase are measured. There are several options for the mean potential: Either for the resting potential, i.e. H. at equilibrium potential with an open circuit, or at a fixed average potential that is kept at a constant value apart from the voltage modulation by a potentiostat ("potentiostatic impedance spectroscopy"). In the “potentiodynamic method”, the impedance is recorded during a cyclic voltammogram . Alternatively, the impedance spectroscopy can also be carried out with the aid of an impressed alternating current; then the potential and its phase are measured.

The concept of impedance and the complex AC calculation assume that there is a linear relationship between the amplitudes of voltage and current. In electrochemical systems, this is only an approximation for small amplitudes, e.g. B. 1 to 10 mV, the case. Significantly larger amplitudes must therefore not be used for measurement.

Presentation, evaluation and interpretation of the measurement results

The basics of the presentation, evaluation and interpretation of the measurement results are the same as for other impedance spectroscopic methods and are described here .

An aqueous solution of iron (III) and iron (II) ions will be examined as an example. A working and counter electrode are immersed in this solution. If an alternating voltage is applied to the electrodes, several processes take place that can be described with an equivalent circuit :

Equivalent circuit in electrochemical impedance spectroscopy

The ions accumulate or deplete in a double layer on the electrodes. This layer is formed by a plate capacitor with the capacitance C described.
The alternating voltage causes reversible redox reactions at the electrodes . Iron (III) ions are reduced to iron (II) ions through the uptake of electrons and iron (II) ions are oxidized through the release of electrons . The electron uptake or electron release at the electrodes requires activation energy and is described by a resistance R _d .
Ions are transported from the solution to the electrodes or transported away from the electrodes. The resistance of the solution, which is described by an ohmic resistance R , plays a role here . This is independent of the condition of the electrode.
As a result of the alternating voltage, the concentrations of the ions that are reduced or oxidized change at the electrodes. If the positive half sine wave is on the working electrode, the oxidation takes place. Electrons are picked up by the electrode. If the negative half-wave is present, the reduction takes place. Electrons are released from the electrode. The fluctuations in the concentration of iron (III) and iron (II) ions cause a damped wave, which partially propagates in the solution. This resulting impedance can be described using the Warburg impedance model .

The four impedance elements apply to the working electrode, but also to the counter electrode, since the same processes take place there.

In the next step of the evaluation, the frequency-dependent behavior is calculated from assumed output values for each impedance element and compared with the measured data. If there is good agreement, a physico-chemical model is developed that describes the electrochemical system in detail, taking pressure and temperature into account. You can also apply a direct voltage for comparison in order to obtain further information.

theory

Harmonic alternating currents, as used in impedance spectroscopy, can be described by a sine function:

{\ displaystyle U = U_ {0} \ cdot \ sin (\ omega \ cdot t + \ phi _ {U})}

{\ displaystyle I = I_ {0} \ cdot \ sin (\ omega \ cdot t + \ phi _ {I})}

Here, the voltage, the amplitude of the voltage, the current, the amplitude of the current, the phase angle of the voltage, the phase angle of the current and the angular frequency, which can be written as a function of frequency: . The phase shift can be determined by the difference of the two phase angle: . In AC theory, it makes sense to describe the mathematical relationships in complex number space. ${\ displaystyle U}$ ${\ displaystyle U_ {0}}$ ${\ displaystyle I}$ ${\ displaystyle I_ {0}}$ ${\ displaystyle \ phi _ {U}}$ ${\ displaystyle \ phi _ {I}}$ ${\ displaystyle \ omega}$ ${\ textstyle \ omega = 2 \ pi \ cdot f}$ ${\ displaystyle \ phi}$ ${\ textstyle \ phi = \ phi _ {I} - \ phi _ {U}}$

{\ displaystyle {\ widehat {U}} = U_ {0} \ cdot e ^ {i (\ omega \ cdot t + \ phi _ {U})}}

{\ displaystyle {\ widehat {I}} = I_ {0} \ cdot e ^ {i (\ omega \ cdot t + \ phi _ {I})}}

Here is the complex voltage and the complex current. AC resistances are called impedance . The Ohm's law applies by analogy to direct current doctrine . With the complex expressions for the voltage and the current we get: ${\ displaystyle {\ widehat {U}}}$ ${\ displaystyle {\ widehat {I}}}$ ${\ displaystyle {\ widehat {Z}}}$ ${\ textstyle {\ widehat {Z}} = {\ frac {\ widehat {U}} {\ widehat {I}}}}$

{\ displaystyle {\ widehat {Z}} = {\ frac {U_ {0}} {I_ {0}}} \ cdot e ^ {- i (\ phi _ {I} - \ phi _ {U})} = Z_ {0} \ cdot e ^ {- i \ phi}}

Here is the impedance , which expresses the amount of the complex impedance. According to Euler's formula , the impedance can also be represented as a differentiated real and imaginary part:

{\ textstyle Z_ {0} = {\ frac {U_ {0}} {I_ {0}}}}

{\ textstyle e ^ {\ mathrm {i} x} = \ cos (x) + \ mathrm {i} \ sin (x)}

{\ displaystyle {\ widehat {Z}} = Z_ {0} \ cos (\ phi) -iZ_ {0} \ sin (\ phi) = Z'-iZ ''}

Here is the real part and the imaginary part of the complex alternating current resistance. The reciprocal impedance describes the complex conductance, also called admittance. In the Nyquist diagram , the two parts of the impedance are plotted against each other.

{\ displaystyle Z '}

{\ displaystyle Z ''}

Web links

Electrochemical Impedance Spectroscopy Theory: A Primer. Gamry Instruments as of December 28, 2007, archived from the original on February 1, 2009 ; Retrieved August 22, 2011 .
Apparative Methods in Physical Chemistry - Impedance Spectroscopy (PDF file; 244 kB)

Individual evidence

↑ Nikolaus Doppelhammer, Nick Pellens, Christine EA Kirschhock, Bernhard Jakoby, Erwin K. Reichel: Using Moving Electrode Impedance Spectroscopy to Monitor Particle Sedimentation . In: IEEE Sensors Journal . 2020, ISSN 1530-437X , p. 1–1 , doi : 10.1109 / JSEN.2020.3004510 ( ieee.org [accessed July 14, 2020]).
↑ Genady Ragoisha: Potentiodynamic Electrochemical Impedance Spectroscopy. In: ABC Chemistry. 2004, accessed August 15, 2015 .
↑ Basics of EIS: Electrochemical Research-Impedance. Linearity of Electrochemistry Systems. In: gamry.com> Resources> Application Notes> Electrochemical Impedance Spectroscopy. Gamry Instruments, April 17, 2018, accessed September 17, 2019 .
↑ K. Funke: Apparative Methods in Physical Chemistry: Impedance Spectroscopy. 2002, accessed February 28, 2020 .

[1] Nikolaus Doppelhammer, Nick Pellens, Christine EA Kirschhock, Bernhard Jakoby, Erwin K. Reichel: Using Moving Electrode Impedance Spectroscopy to Monitor Particle Sedimentation . In: IEEE Sensors Journal . 2020, ISSN 1530-437X , p. 1–1 , doi : 10.1109 / JSEN.2020.3004510 ( ieee.org [accessed July 14, 2020]).

[2] Genady Ragoisha: Potentiodynamic Electrochemical Impedance Spectroscopy. In: ABC Chemistry. 2004, accessed August 15, 2015 .

[3] Basics of EIS: Electrochemical Research-Impedance. Linearity of Electrochemistry Systems. In: gamry.com> Resources> Application Notes> Electrochemical Impedance Spectroscopy. Gamry Instruments, April 17, 2018, accessed September 17, 2019 .

[4] K. Funke: Apparative Methods in Physical Chemistry: Impedance Spectroscopy. 2002, accessed February 28, 2020 .