The impedance you measure is between the working electrode and the solution. It is best seen in the Nyquist plot how it is composed of charge transfer resistance and double layer capacitance. In order to measure this, a current (here usually ac) has to flow through the system. This flows between working and counter electrode, while the potential difference applied between the working and the counter electrode is such that the working electrode potential is at a set value with respect to the reference electrode. The potential of the counter electrode is unknown and not of interest. I hope this is not too trivial and addresses your question without having to refer to equivalent circuits.

Hi!

As the three electrodes system is used to compensate the ohmic drop between the working and reference electrodes, FRA measurements allow to measure the impedance located between the working and the counter electrodes. In any case I think that merely the layers adjacent to the electrode surface are detectable.

Hi Lucia,

thanks for your answer.

So, it means that a related equivalent circuit should show all impedance between WE and CE, not that between WE and RE?

If you fit your data with an equivalent circuit and you are working with a three electrodes system you will be able to characterize the electrolyte or self assembled layers adjacent to the electrode surface. If you are interested in the whole region between the working and counter electrodes you have to work in a two electrodes configuration simply cortocircuiting the counter and the reference elctrodes.

what kind of interface are you working with and what are you interested in?

I am working with a 3-electrodes system with diluted H2SO4 electrolyte. in general, I am evaluating the catalytic activity of my catalyst for oxygen reduction reaction (ORR) by different electroanalytical methods. with EIS I am in doubt that the fitted equivalent circuit contains also impedance near to the CE or it just comes from the WE?

and if by study the double layer capacitance values obtained from CPE (constant phase element) in the equivalent circuit, could we judge about the catalyst surface area?

Well, I think you can consider the EIS data you obtain in your three electrodes configuration as referred to the working electrode/solution interface and no interferences should come from your counter electrode. As to the catalyst surface area determined by diffuse layer measurements I am not so expert to help you adequately . In any case I would avoid using CPE elements because of their hybrid nature. I advice to you to model the diffuse layer as a mesh of a resistance and a capacitance in parallel. You should obtain better results.

thank you once again Lucia.

As far as I understand, in impedance measurements you are always measuring the total impedance of the circuit WE-CE. It means that you have the contributions from both electrodes. This is why you need CE with significantly higher surface area. In a serial circuit, total capacity Ct is a combination of reciprocal capacities of WE and CE: 1/Ct = 1/C(WE) + 1/C(CE). So, if C(CE)>>C(WE), 1/Ct approx 1/C(WE), Ct approx C(WE). But only if surface area of CE is much higher than WE.

Also, potentiostat is normally automatically compensating iR drop in CE-WE circuit to the point of the Luggin cappilary. Thus, only R contribution between WE and point of Luggin will remain in the measured impedance. This is why, in this case the only remaining part of circuit measuring is -R-Z(f)-, where R is uncompensated resistance and Z(f) is an impedance of WE/electrolyte interface.

I totally agree with Sergey, the counter electrode should have a greater surface area than the WE (e.g. 100 times to minimize the contribution from the CE to 1%). a large CE surface area means the resistance of this electrode will be very low and the total resistance will be dominated by that on the WE. CPEs are often necessary experimentally; there usage are commonly attributed to surface defects . In order to use an absolute capacitor you need your surface to be atomically flat (e.g. mono-crystalline electrodes).

cheers

nadim

Sergey and Nadim, thanks to both of you.

could you please help me to interpret the relation between the capacitance value and catalyst surface area? specially while there is a big faradaic resistance and we cannot find any sign of reaction. at this condition we counter a big impedance, and I am eager to know if we could compare different catalyst surface areas from the double layer capacitance?

here in follow I bring some of my Impedance results.

If you want to know about the catalytic surface area vs. double layer capacitance, you may want to try using cyclic voltammetry instead. You will be able to calculate the amount of current coming from capacitance using your current electrolyte, and also measure your catalytic surface area using Potassium Ferrocyanide to measure the oxidation and reduction of the Fe2+/Fe3+ redox couple at different scan rates.

There is a paper from Analytical Chemistry that I have attached to this that might help you. If you have any other questions, let me know.

Forgot the attachment.

Hi Micah

first of all thank you for this interesting article; I already did CV and related calculation to measure the double layer charge (anodic and catthodic) to compare different materials, however here I'd like to know if two different catalysts with different real and calculated electrochemical surface areas, under same measuring condition will show different capacitance in impedance measurements or no?

thank you

If you are interested to know that how to calculate the impedance in 3 electrode system, theoretically the equivalent circuit modeling and calculating is always between Reference electrode and Working electrode. Simply, the impedance spectroscopy is like knocking to something which you are interested to know about its material or its quality, obviously you hear the reflected sound from object! then AC current with different range of frequency applied to WE and the feedback current will detected by CE

Dear Ebrahim;

if the disturbance or any input to the system is applied to the WE (which we have all information about that) and the response is detected by CE (which are the measuring data), why we should consider the whole impedance between WE and RE, instead of WE and CE?

I don't understand your meaning! but RE is a reference, so it has the constant potential to measuring of any potential based on it. First, in impedance spectroscopy the AC current with wide range of frequency from high to low applied to working electrode (obviously between WE and RE) then the reflected potential will be detected and measured by CE (the current measure with CE and RE).

you can refer: http://www.gamry.com/assets/Application-Notes/Basics-of-EIS.pdf

the information provided by Gamry instruments.

Hi!

As to my knowledge, the use of three electrodes systems allows to compensate any ohmic drop between working and reference electrodes, as the current is forced to flow between working and counter electrodes. What you can do to test the validity of this statement is to change reference with counter electrode in your system and record EIS spectra. Then you can compare the obtained results with the ones you obtain by using a couple of identical electrodes as reference and counter in one case you can use two electrodes equal to the reference you are using now and then equal to the counter you are using now.

Let me know how it works.

Dear Ebrahim and Luica

Thank you once again for your patience to reply my questions, but unfortunately I have not found an answer for my question yet. I know the mechanism in the EIS measurement and the way of applying voltage (vs. RE) and recording current by CE. You know when we do EIS on a battery, where there is just a cathode side and an anode side and we consider one of them as Working and Ref no.2 and the other side as the both Ref. no.1 and CE, we draw an equivalent circuit to explain the total impedance it is obviously between cathode side and anode side, with a model like that I attached. As I know to measure the impedance we apply a voltage between two points and we measure the current passing exactly between them. So, here in a three electrode cell, I know that the applied potential is between RE and WE, however there is no current to pass through the RE (because of its high polarization), so we obtain the current passing through the CE. Now, we could say that this current passed through WE too, but it is not the current between those two points (WE and RE) that we applied potential.

Under this circumstance if we fit our system with a model like that I brought in the attached file, the first Parallel R/CPE is related to which part of the system? CE or RE?

I really do appreciate if you share your knowledge with me.

Thanks

I think that in this case you can reproduce your experimental data simply using the first resistance and the second mesh as equivalent circuit, no other contribution should be necessary in a three electrodes system. Can you try to do that?

there is no good fitting with just the first R and second part, howevere when we add 3rd part there is a very good fitting.

What I meant was that you should use the first and the third elements in your picture.

Eventually you can replace R with an RC mesh.

Does it work better?

Actually I tried at first, with the first (R) and third (R,W / CPE) elements to fit the experimental data, however, I did not see an appropriate fitting, unless when I used all the terms mentioned above. And for me, this equivalent circuit makes more sense, cause of that I consider the impedance from the WE (with the third part, containing Warburg and CPE impedance) to electrolyte (the first R) and ended at the CE (with parallel resistance and CPE). My question is not about the fitting, it is more about the physical meaning of the equivalent circuit. Has my considered equivalent circuit a physical and logical root or no? If is it right to consider impedance between WE and CE? If not, for which reason?

thanks again

You are right, the physical meaning is fundamental. For this reason I usually avoid to use CPE elements. In any case I think you are right when you consider impedance between WE and CE, but I do not think the redox reaction occurring at the CE gives its own contribution. Can you write your fitting results and may I have your experimental data in TXT? I would like to simulate them with the AUTOLAB sofware.If you prefer you can send them to me by e-mail. Thanks.

Dear Lucia

I do appreciate you take time to let me solve this problem. Here in follow I mentioned the raw data of two of my samples, with the related curves of one of them, besides the fitting curve that I have obtained from the already explained equivalent circuit. As it is obvious there is a good match between experimental data and fitting curve. However I am waiting to see what you suggest to simulate these data with an appropriate equivalent circuit, of course with physical meaning.

Thanks a lot

Nyquist plot

Bode diagram

As I am using Kaleidagraph program for my plots, can you export your xls data in txt.

In the form you attached are not usefull for me

Hi! I am trying to obtain a good fit with your data, but it is not so easy as I cannot fit directly the experimental data, but I can only try to simulate your data with autolab FRA sotware and then compare the fitting results with your data. I am trying to do that just using RC meshes and Warburg impedance.It takes a long time.I am trying to do my best.

Hi Lucia

Honestly, I don’t know How can I thank you for your time and attention to this question. Actually I’ve found the answer of my first question which measuring impedance is between WE and CE. As we apply the voltage between WE and CE, albeit we control the value of the WE potential by the RE, and we measure the passing current through WE and CE, therefore, the measured impedance is for all elements and phenomena between WE and CE. The attached figure explains more precisely what I mean. So, both the voltage perturbance and measured current response are related to two points (WE and CE) and we have to consider all elements between them. Although usually by choosing a high surface area and high conductive material (like Pt mesh) we decrease the impedance related to the CE, and we can imagine that all the impedance is related to the WE and its interface with the electrolyte.

Anyhow, I appreciate if you could simulate these data to find an appropriate equivalent circuit, to compare mine with that. To ensure me that my simulation is correct.

I attached the data on text file, again.

Thank you once again

Ali

U-1100

O-700

I am very curious and the problem you proposed is very intriguing.

Usually I try to avoid using CPE as it is not a real circuit element. Your data are quite complicated to be elaborated through the simple circuit you describe just substituting CPE with capacitance element. As I do not know your system I wonder if you tested the system without redox species. Which is the result at the same applied potential with the electrode in contact with the electrolyte solution?

I wish you all the best for your work.

The impedance you measure is between the working electrode and the solution. It is best seen in the Nyquist plot how it is composed of charge transfer resistance and double layer capacitance. In order to measure this, a current (here usually ac) has to flow through the system. This flows between working and counter electrode, while the potential difference applied between the working and the counter electrode is such that the working electrode potential is at a set value with respect to the reference electrode. The potential of the counter electrode is unknown and not of interest. I hope this is not too trivial and addresses your question without having to refer to equivalent circuits.

Hi! I have tried to reproduce your data with my software, but it is not easy.

In any case from a qualitative point of view I think that an R(RC) circuit for -1100 and R(C[RW]) circuit for -700 shoulb be quite good. Can you try and let me know the values you obtain by using these equivalent circuit.

Thank you

Really Mostafa ????

I knew between WE & CE. Please let me know.

Thanks

Dear Ali

It is an essential that one realize that the A.C impedance is an interfacial parameter of the WE and the solution. The A.C impedance is a vector (has a magnitude & phase)in a comparison to the scalar (only magnitude)DC resistance(polarization resistance) of the interface between the We and the solution. The A.C impedance becomes equivalent to the scalar DC resistance (polarization resistance) at low frequency; f =016 Hz, in the Bode plot; (impedance versus log(angular velocity))when the angular velocity ;w=2Pf=1, where P=3.14 . So log (w)=log((2)x(3.14)x(0.16))=0.

Both A.C. impedance & polarization resistance can only be estimated from Bode plot and linear polarization plot, respectively by extrapolation, interpolation, and so on. Nowadays, one can obtain those parameters by interphasing a computer to the a potentiostat with accessories of A.C. impedance spectroscopy with a software for estimating those parameters.