Hello Ahmed Bahloul,

We can calculate capacitance from EIS plot by using following steps:

The impedance of supercapacitive component relates

Z=1/jwC

where Z=impedance, w=2πf, C=capacitance

Now in complex form,

Z=Z'+jZ''

Combining these two, we have, C=1/(jw(Z'+Z''))=-(Z''+jZ')/w|Z|2

In equivalence with, C=C'-jC''

It is derived that

C'=-Z''/w|Z|2 and

C''=Z'/w|Z|2

Now, the capacitance from EIS plot is |C| = √ (C')2+(C'')2

you can check my publications for more details. I've added a few here.

Article Hexagonal VS2 Anchored MWCNTs: First Approach to Design Flex...

Article V2O5 encapsulated MWCNTs in 2D surface architecture: Complet...

Article Free-standing flexible MWCNTs bucky paper: Extremely stable ...

Hello Ahmed Bahloul,

We can calculate capacitance from EIS plot by using following steps:

The impedance of supercapacitive component relates

Z=1/jwC

where Z=impedance, w=2πf, C=capacitance

Now in complex form,

Z=Z'+jZ''

Combining these two, we have, C=1/(jw(Z'+Z''))=-(Z''+jZ')/w|Z|2

In equivalence with, C=C'-jC''

It is derived that

C'=-Z''/w|Z|2 and

C''=Z'/w|Z|2

Now, the capacitance from EIS plot is |C| = √ (C')2+(C'')2

you can check my publications for more details. I've added a few here.

Article Hexagonal VS2 Anchored MWCNTs: First Approach to Design Flex...

Article V2O5 encapsulated MWCNTs in 2D surface architecture: Complet...

Article Free-standing flexible MWCNTs bucky paper: Extremely stable ...

Also, you might find examples[1] for the simple(st) cases of capacitance calculations from EIS. However, for more complicated cases, the better, and the more elegant calculations are based on the equivalent[2,3] circuit model(ing)s for perplexing cases[4] of super, ultra enhanced, new(er) capacitors' electrodes[5,6].

1. Autolab Application Note EIS03 http://www.ecochemie.nl/download/Applicationnotes/Autolab_Application_Note_EIS03.pdf

2. Autolab Application Note EC12: Different approaches for capacitance measurements http://www.ecochemie.nl/download/Applicationnotes/Autolab_Application_Note_EC12.pdf

3. Equivalent Circuit Modeling Using the Gamry EIS300 Electrochemical Impedance Spectroscopy Software https://www.gamry.com/application-notes/EIS/equivalent-circuit-modeling-using-the-gamry-eis300-electrochemical-impedance-spectroscopy-software/

4. Supercapacitor electrical equivalent model https://www.garmanage.com/atelier/index.cgi?path=public&B&Energy_storage/Supercapacitors/Model

5. BU-209: How does a Supercapacitor Work? http://batteryuniversity.com/learn/article/whats_the_role_of_the_supercapacitor

6. Can Supercapacitors Surpass Batteries for Energy Storage? http://www.electronicdesign.com/power/can-supercapacitors-surpass-batteries-energy-storage

Hello Bidhan Bandit,

Thanks for your reply and your articles, it is very interesting.

Now i have plotted the real and imaginary capacitance

vs Log frequency curve, (i give you in attached file, the Pani curve).

How can i calculate the capacitance from the curve? at what frequency?

Cordially

Hello Pr. Ioannis Samaras

Thanks for you reply.

The fitting of the a.c. impedance data was done using electrochemical software the EC-Lab Z fitting. The EIS measurement is interpreted in terms of an equivalent electric circuit (Randles).

After fitting, the calculated double layer capacitance of PANI electrode is 18.03 µF.cm2).

What is the relation between the double layer capacitance obtained by fittng of Nyquist curve and the specific capacitance of supercapacitor electrod? is it the same?

Cordially

Hello Ahmed Bahloul

In EIS, the capacitance depends on frequency. At lower frequency, you'll get high capacitance. According to the plot, you can easily find C' and C'' value separately. as you can see, C'= 0.009 unit and C''=0.004 unit (approx.). So, the capacitance will be C = 0.0098 unit.

If you have taken 1 cm2 as electrode dimension, then the capacitance C=0.0098 unit/cm2.

If u want specific/volumetric capacitance ( unit/gm or unit/cm3 ), just divide 0.0098 by the active electrode mass/volume respectively.

Hello Ahmed Bahloul,

show, please, your equivalent electric circuit[1], as well as the initial parameters (plus error values?) satisfying your fitting[2].

1. In common EDLC (electric double-layer capacitors) electrochemical capacitors you get a single (EDLC-) capacitance.

2. In supercapacitors' cases we customarily add more, not the same (value) elements, in (y)our equivalent electric circuit.

Hello Pr. Ioannis Samaras,

The equivalent circuit is (Randles circuit) :

R1+C2/(R2+W2)

R1 = 9.301 Ohm err. = 0.187

C2 = 18.03e-6 F err.= 0.59e-6

R2 = 36.08 Ohm err. = 0.75

W2 = 117.9 ohm^s-1/2 err.= 1.243

is it satisfiable

Cordially

Hello Bidhan Pandit,

Thank you very much for the explication.

Now, the calculation of the specific capacitance by different techniques show different results:

-Cyclic voltammetry : 176.29 F/g (5 mVs-1, in the range -0.2 to 1 V/SCE)

-Charge-discharge test : 80.74 F/g ( 0.1A/g, in the range 0 to 0.7V)

-EIS: 66.84 F/g (from 100KHz to 100 mHz)

why the results are very different? is there any explication?

Cordially

Firstly try to take same potential window for CV and CD. Otherwise you can't correlate the CV and CD results. More specifically, CD shows same type of plateau with potential as CV curves show in same potential frame.

Look there is no point to match the results. Actually cyclic voltammetry (CV), charge-discharge (CD), and electrochemical impedance spectroscopy (EIS) all give the same electrochemical characteristics at different point of view. For CV, current is measured against fixed potential window and scan rate.  On the other hand, time is measured against fixed potential and current density for CD. And EIS gives frequency dependent impedance/capacitance values.

In supercapacitor study, CD is more reliable. So, focus mainly the CD-derived capacitance values like other researchers.

In spite of that, if you really want to get your CV, CD, and EIS derived capacitance values near to each other, try to use high scan rates and current densities as supercapacitor is related to fast charge-discharge time. To have high capacitance value from EIS, you should calculate capacitance value at minimum frequency. you can also apply VDC near Vmax (from CV) further to have greater capacitance.

Thank you very much, Mr. Bidhan Pandit.

In order to find the maximum (as the Cap. from CV) capacitance value from EIS, you should apply[1] VDC

Thanks to Pr. Ioannis Samaras and

Dr. Bidhan Pandit for your replies