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  Electrochemical EIS course (Electrochemical Impedance Spectroscopy Principles.....

Electrochemical impedance spectroscopy Principles and Foundations



EIS (Electrochemical impedance spectroscopy) deal about impedance measurement principles, EIS analysis method, Nyquist Plot analysis, Warburg impedance, AC impedance analysis, and electrochemical impedance and data interpretation etc.


- Understand impedance measurement principles and methods

(same as Impednace Analyzer's principle).


-  Learn how to easily understand equivalent circuits through experimental 

and measured data using impedance measuring equipment (LCR meters).


-  Apply Sine Wave waveforms one by one to samples from high frequencies to low frequencies. And response through samples Measure the amplitude and phase variations according to Sine Wave, and then analyze the impedance.


-  A graph, represented by a complex number with one coordinate drawn at a one frequency, is called the Nyquist Plot(Electrochemistry Nyquist Analysis).


-  It is possible [equivalent circuit extraction of samples] and [each parameter extraction], through Nyquist Plot

- Interpreting Impedance Graphs



-  Besides that, Other changes in electrochemical reactions can be estimated.



Why use impedance?

A constant current and constant voltage based on resistance measurements according to the Potential, can be used for more various analyses.

Differences Between Resistance and Impedance

- Resistance : Indicates the degree to which the electrical flow is 

interrupted about Direct Current (DC). 

     (The amount of current changes is depending on the resistance value)

- Impedance : indicates the degree to which electrical flow is interrupted about alternating current (AC) 

    (Unlike direct current, amplitude and phase changes occur according to frequency) 


Differences in electrical properties between direct current (DC) and alternating current (AC)

- Direct Current : Current varies depending on the voltage applied 

according to Resistance

- Alternating Current : Amplitude and phase change depending on the 

applied voltage and frequency according to Impedance



Amplitude, phase(Affecting the characteristics of the response output about input of electric) and 3 major classifications of related ingredient => Resistance, Capacitors and Inductors.

It utilizes the characteristics of varying amplitude and phase at each frequency according to the combination of resistance, capacitors and inductors (series, parallel, and both).

To unknown samples, other than electrical circuits, If the Electrical Characteristics Analysis is interpreting equivalent in Standard Models such as Electronic Circuit through impedance analysis.

Internal electrical properties can be easily identified.

To learn about the Electrochemical impedance spectroscopy and Nyquist Plot was ordered as follows :

1. Understand the characteristics of R, L and C according to the response 

waveform for the applied waveform in an electrical circuit

2. Change of current respond and phase character (depending on frequency of impedance)is expresse as complex number system

3. Understand Nyquist Plot using complex number expressions


4. Understanding electrochemical samps using Nyquist Plot


1. Definition of R, L and C

Resistance , R

Interrupt current flow, creates electrical position energy differences (potential difference, voltage). and control electrical flow to run as much current as user want..  

Resistance character is requires less current to flow as resistance is greater.


In other words, It can be explained by Ohm's law, which indicates the inverse relationship between resistance and current.

This ohm() is the size of resistance.

V = I  R  [ Ohm's law

For example, if you take a 5 V battery and connect a 1 resistor, you will have a current of 5 A.



In the graph above, only the magnitude changes depending on the size of the resistance, but the phase does not.  

While capacitor or inductance, which constitute different impedance, are factors that cause phase changes, resistance is characterized by no phase changes.


If the resistance grows, the current becomes smaller.


If the resistance is reduced, the magnitude of the current becomes greater. 



Resistance is different in a series circuit and in a parallel circuit, the method of calculating the resistance size present in the circuit.





Capacitor, C

This refers to devices that accumulate electric charges.

In other words, It stores energy in the form of electric fields.

It consists of two electrodes and a thin gene in between.

Here, a gene is not a conductor. but it is a material through which electricity can flow.

This is because (+) and (-) poles flow and [polarization similar to electrostatic induction] occur.

Outside the gene, the arrangement of these charges can be said to polarize by rotating.


The capacitor has the characteristics of separating the DC and AC components and allowing only AC (alternating current) to pass.

Its role is to allow constant currents to flow.

However, it prevents them from passing low frequency voltages.


Put simply, high frequencies do not have enough time to charge them(because flow speed is fast), so they pass through capacitors right away. And low frequencies has sufficient charging time, it is difficult to pass it.


In other words, resistance to voltage with frequency component (to emit a constant current).

Charge is a DC voltage applied to one electrode, positive charge to the charged plate,

Charges accumulate until the negative charges are parallel to the external applied voltage.

Over time, equilibrium results in a state that do not flow electricity.

Discharge of capacitors is opposite process of charging.

Applying resistance instead of voltage causes the electrical charge to be discharged as much as it had been before, and the current to flow.


When discharged, the rate of discharge depends on the size of the resistance and the greater the resistance the longer the discharge time.



* Capacitance


This is a proportional constant that represents [the degree of electrode accumulating electrical charge]. 


According to the equation, the smaller the spacing (d) of metal plates and the larger the area (A), the larger the capacity of capacitors will be.

The higher the voltage, the larger the capacitance, the more the Q will accumulate.

The unit of the Capacitance is the Parat (F).

Where 1F (Parat) represents 1.602 10-19 19 [Charge per electron 1 unit].

As the unit of 1 F is large, mostly use 1 µ F (microfarad).

Where 1 F is the capacity to accumulate 1 (C) of positive and negative charges on the positive plate when the positive plate is approved.

For example, for high-capacity capacitors of 1000 F, when electric charges accumulate by 1 [C], a potential difference of 1000 V between plates is formed.


Therefore, it has a large capacity.

The current flows by a degree of /2
[rad]=90 before the voltage.

Unlike resistance, capacitors are affected by frequency and produce changes in phase.

The phase change is caused by a ' reactance ', a unique resistance that only works with alternating current.


(We will discuss it further behind.)


Inductor , L

Inductor is a device made by winding wires.

Used for high frequency blocking or power-induced coupling.

Inductors act to suppress rapid changes in current and to stabilize current changes.

For example, an increase in current can interfere with current flow, and a decrease in current can increase current flow.

An inductor forms a magnetic field in the direction of track length.

As the current changes the magnetic field also.

So prevents the current from changing.


This may act to inhibit rapid current changes, as induced currents flowing through the inductors by electromagn etic induction are flowing in a direction that prevents them from changing their magnetic flux.



Inductor acts as a kind of resistance that prevents alternating current from flowing. Block the fast flow of signals. (like capacitor.)

And as opposed to capacitors, larger inductors reduce current and pass low frequencies but difficult to pass high frequencies.

In other words, when the capacitor grows, it passes high frequency, makes current flow smoothly, and when the inductor gets bigger, it fails to pass high frequency and prevents current flowing well.

* Inductance

This is the ratio of reverse electromotive force produced by electromagnetic induction as the current in the circuit changes. 

In other words, stop the current from changing when the wire is flowing.

If the current is changing in the direction it is going in or the size of it, the opposite is made by making reverse electromotive force to prevent it from changing.

An electromotive force is the driving force that maintains a constant potential difference between conductors and allows current to flow.

Likewise, reverse electromotive is produced in the opposite direction to voltage of electromotive force.

Inductance occurs on all tracks that have length, the length and size of inductance are proportional.

Therefore, the higher the inductance value, the more difficult it is to pass the high frequency.

To increase the inductance value as much as possible, make the line as long as possible.


Thus the long line coil became the general shape of the inductor..



The current in the inductor is /2[rad]=90 behind the voltage.

The reactance also ingredient that changes the phase difference.

There is a reason why phase difference between voltage and current occurs in the circuit diagram where capacitors and inductors exist.

The Voltage and Current graphs show a 'sin' shaped graph.

When calculating voltage and current values, we must differentiate about time.

A differential in the sin function results in a cos function that produces a 90 degree difference in phase.

That is why there is a phase difference.

2. Reactance and Complex number representation of current response

to voltage, at alternating current

Complex number representation and Reactance

As described above, impedance consists of three major components. Of these, the capacitance and inductance are depending on frequency.

[Complex number representation] is most appropriate to provide a single view of [their characteristics and the influence of each element etc.] at each frequency. 

1. Resistance : ( Z = R )

2. Capacitance : ( Z =1/ jwC )


3. Inductance : ( Z = jwL )

 * Impedance =  Resistance + Inductance + Capacitance

representation as 3 components combined, And again; 

* Impedance  =  Resistance + Reactance (Inductance + Capacitance)

For our comfort, further divided into two categories, Resistance and Reactance, which do not change the phase.

Reactance is a unique resistance that only works with alternating current (AC). It is a component that changes its phase. This applies to capacitance and inductance.

Reactance is associated with frequency. So this explains the phase difference between the capacitor and the inductor.


When expressing impedance as size and phase, expressed in complex number.

Z = R + jX =
R+j(XL-(1/XC))  [ R :
real number, jX : imaginary number]


XL : Inductive reactance


1/XC : Capacitive reactance



* Complex number representation of Capacitor



A higher frequency of alternating current in a capacitor increases the change in +, -. This allows the capacitor no time to charge, so current flows well. 

So when you give a capacitor high frequency, it passes well.

Conversely, low frequency of alternating current slows down the changes in + and -. 

Since changes are slow, charging rate of capacitors is increased since it naturally allows time to charge capacitors. As charging rate increases, current flow becomes slower.


Thus, when the frequency is low, the current flow interruption becomes too great to pass through.

Frequency and XC(capacitive reactance) are inversely related.


* Complex number representation of Inductor




If the frequency of exchange is high in an inductor, changes in + and - rapidly . In other words, the faster the current changes, the greater the induced electromotive force.

Inductive electromotive force is the generation of potential differences to guide current in the direction of purpose.

This is an electromagnetic induction phenomenon caused by magnetic fields, inducing voltages in a circuit.

At high frequencies, the induced electromotive force increases. The inductive electromotive force is proportional to inductance.

Inductance is increased as well.

Also, because the magnitude of the induced reactance is proportional to the frequency of the alternating current, the higher the frequency, the greater the resistance.

Therefore, at high frequencies, current flow from the inductor does not flow well. Conversely, when low frequencies are low, current flows well.


Frequency and XL(Inductive reactance) are proportional.

TIP : resonant frequencies

The frequency at which the reactance becomes zero. The frequency at which the capacitive reactance and inductive reactance are combined equals 0.

At resonance, the impedance is composed only of Z = R [Ohm] net resistance components, where impedance is the minimum impedance value. The current at resonance becomes the applied voltage and the frostbite and is the maximum size that can flow in that circuit.

Because impedance, a type of resistance, is the minimum value, the current become the maximum size.

In order to be a resonance, capacitors and inductors exist and impedance's imaginary number should be zero. This is because the imaginary number is reactance j (XL - XC).

In other words, resonance ; from an energy perspective, L and C are exists simultaneously and make the points at which equilibrium .


It is simple to calculate resonant frequency.


The frequency at which Imaginary number impedance goes to zero is the resonant frequency.


If substitute the reactance and arrange it,



Using resonant frequencies, it is used to analyze impedance later on.





At [ Z = Z = R + jX ] , 

When a resonance is reached by combining frequency and , the reactance value(imaginary number) of X is zero.

Thus, the above can be expressed in the complex number type graph showing the impedance Z size.

There is only a pure resistance value, So it is expressed as a point as above..

3. Equivalent circuit of an electrochemical cell And 

Complex number expression

* Faraday & Non-Faraday Current

- Faraday Current : This is deliver current of electrons directly.

For example, Electro-transferreduction depending on oxidation-reduction reaction of the electrode surface.

Or the movement of an oxidation/ reduction agent in an electrolyte solution.

- Non-Faraday Current : Current due to the accumulation of charge, which is formed when a substance (ion or molecule) that has an electric charge on the interface is collected. For example, two layers of electricity.

In other words,


Voltage is applied to the electrodes. Perform electrode (+), (-) polarity. In a solution, it is guided by static forces and charge builds up on the interface. Two layers are formed with different charges.



Avoid direct ion reactions with non-faraday currents.

To describe the phenomenon at the interface, an equal circuit is expressed using a cell element.

Electrolyte that moves an electric charge represents resistance. And the accumulation of electric charges is a capacitor.

The movement of substances observed only in chemistry is represented by the Warburg impedance at diffusion.

Chemical reactions can be presented electro-chemical.

A high electrolyte concentration means a lower resistance because it accelerates chemical reactions.

A low electrolyte concentration means a relatively slow response, which means high resistance. 


To describe the phenomenon at the interface, expressed in equivalent circuits using cell devices ;



If the experiment of the chemical reaction on the left is expressed electro-chemical, the equivalent circuit shown on the right can be represented using RLC.

The blue shows  Rs the resistance in the electrolyte. 

Red shows the resistance due to the accumulation of charge on the interface to the Rp - and C.

* What is an equivalent circuit?

This is a circuit that combines electrical characteristics of components with resistance, intotter, and capacitor (RLC) etc in series and parallel.

It can also be expressed as an electrochemical equivalent circuit in an experiment with a chemical reaction as previously stated.

This means that by analyzing impedance, equivalent circuits can be identified, thus can be know electrical and electrochemical material properties. This is the fundamental purpose of analyzing impedance.

Complex number representation

* Why express impedance with a complex number?

If express with a complex number,

Components of impedance => Resistance + Reactance

change according to frequency is express on X and Y two axis coordinates, so the changes and effects of the two components can be seen at a glance. In particular, it is easy to observe the effects between each other depending on the frequency of each component. (Especially, Capacitance and Inductance offset each other)

This can be done by adding and subtracting operations, not by complicated calculations.

If it is not expressed as a complex number, it is not easy to obtain AC current values that change phase and it needs to be solved by using complicated differential equations.

But express of the complex number, it can be calculated by changing the shape of the phaser by the impedance polar coordinates.

This simplifies calculation of formulas such as multiplication and division.


In addition, complex number expressions are needed to express the resistive components (capacitors, inductors) taking into account changes in phase from alternating current.






4. Nyquist Plot



When capacitors and resistance are presented solely as impedance polar left type graphs, this is like above.

Note that since the graph of the inductor has the opposite characteristics to that of the capacitor, it may be presented in the opposite form. (Graph slant toward the right)

Based on this, the following graph shows the equivalent circuit with the presence of [capacitors and resistance] in Nyquist plot.


Nyquist plot


When only resistance and capacitors are present, the Nyquist plot can be represented as shown above. The Y-axis shows the imaginary number and X-axis shows the real number, but the Nyquist plot should be understood as a three-dimensional graph (with the axis of frequency components), not a two-dimensional graph.

If interpret this graph simply,


When frequency is high, only pure resistance value R is left because capacitor's effect is almost not affected. So, take the value of Rs in the Zreal axis, and take the value of 0 in Zimege.




If frequencies are high on early, they are not affected by capacitors and have values of pure resistance.

As frequency becomes lower, value of - Zimege increases as capacitor is affected. 

Then, if the frequency reaches zero, the reactance value affected is less.


Thus, the - Zimege value decreases and only the Zreal value remains. So Rs value is derived .



As I mentioned before, since the impedance of the capacitor when the frequency is very high is close to zero, only the value of Rs measurement is given.

And as frequency decreases, it is affected by capacitors and becomes the same graph shape as above.

At this time, the Zimege value is increased to about 45 degree angle due to the Warburg impedance.

The blue dots can be calculated as [ f (frequency) = 1/2RpCp ].

* What is the Warburg impedance here?

It is impedance related to the rate of diffusion of ions in an electrolyte.

The rate of diffusion is relatively slow and is therefore invisible at higher frequencies as it is minimal in effect. And therefore its characteristics appear at lower frequencies.

The Warburg impedance relates to the rate of diffusion of ions and is inversely proportional to the square root of frequency .


The formula for this is as follows.



At high frequencies, the mass transfer of ions is very slow compared to alternating current changes and thus shows no resistance.

Like capacitors, the effect of Warburg impedance is very small.


At low frequencies, mass transport prevents electrical charges from moving because of the slow change in concentration on the electrode surface due to changes in current. Therefore, there is an effect of the Warburg impedance..


The Nyquist plot shows together the size and phase of the frequency response on a plane in polar coordinates. So this is a three-dimensional graph called the polar plot.

In this Nyquist plot, each point from high frequency to low frequency is plotted as a three-dimensional graph.

It can be know the equivalent circuit as analysis this schematic Nyquist plot.

The reason for drawing the Nyquist plot is to identify the equivalent circuit and to understand the electrochemical characteristics of this experiment.

Within the graph are the real number part and the imaginary number part, respectively, for the frequencies to which they are accredited.

This means that the impedance is all represented in the polar plot.

In the Bode plot, it is divided into Magnitude and Phase.

So the Nyquist plot expresses this on the polar plot, and impedance characteristics in one step.

In the electrical circuit, the Nyquist plot analysis is one of the methods of assessing the absolute / relative stability of the control system.

And it is based on the principle of deflection in the complex number theory.

Comparison of Nyquist Plot for samples that different


characteristics each other.



  Comparison of samples with different surface characteristics



Comparison of samples with different electrolyte characteristics




If two circuits are combined