Could you share an example EIS data that you are trying to fit?

Please see the attached file...Thank you very much

Hello Roshan,

Could you show the Bode plots? Sometimes those plots are better to analyze than Nyquist.

Cheers.

So, from the data you show, it seems that it largely does what you want it to do. It would be nice to see it go to a lower frequency, because I suspect that your Warburg element doesn't show up for that reason (it does seem to be present in two cases). In general, what you see is what you should be getting from the Randle's model: your Rs is the contact resistance and the high frequency incercept on your Nyquist plot (and it looks like it's very small); your CPE and Rct define the reaction in question and the semicirlce, with Rct being the diameter of the semicircle (about 300 kOhm to 1.5MOhm -- large, as you mentioned you were expecting); and your Warburg element, W, is the 45 degree line shooting off at the low frequencies.

There is a nice graphic explaining it here:

http://eel.ecsdl.org/content/2/9/A89/F2.expansion.html

So to get some starting values for your fit, get the Re(Z) of your highest frequency point, and that would be your Rs. Rct, as I said, you can get initial estimate simply by looking at where the semicircle would touch down, were it to continue all the way to the Re(Z) axis. CPE you can estimate from resonance of the RC circuit: angular freq. of max loss w=2pi*f=1/(Rct*C). That frequency is the apex of the circle, or the apex of a corresponding peak on the Body plot, as Othon pointed out. CPE is pretty much imperfect capacitance, and will make for a slightly "flatter" semicircle than a perfect capacitor, and once you start fitting data, you'll see if you'll need to use CPE instead of just C.

It seems that some of the plots you have, you might be able to fit even without W. But to get the easiest way of factoring that in, you will need to go to lower frequencies, until you get a nice 45 degree line. Then you can estimate the Warburg coefficient by traicing it to Re(Z) axis.

Hope this helps.

Can you provide a few papers relevant to the idea that Rct for your system is not an useful parameter ?

Hi Othon,

please see the bode plot attached

Thanks Pavel for your useful comments and suggestions.

Do you recommend using Rct or CPE to plot the dose response curve and interpret my sensor as Rct for my system is very high???

Also I cannot open the link of graphic you added as it needs some login..could you please send me the graphic by some other way?

Hello Roshan,

Your Bode plots do not show any diffusion (see Bode phase tends to zero deg at low frequencies) and the Bode |Z| shows an almost-like parallel RC behavior. As Pavel told up, you can fit your data without using a Warburg element. Maybe using the  parallel R-CPE fit in parallel with CPE can fit your data. 

I have attached picture here to picture out the equivalent circuit I've told about.

As your Bode phase plot is so broad and your are studying a modified electrode, you have to think about:

1 - The modification doesn't cover 100% of the electrode's surface, and

2 - The modification modifies the electrode's double layer composition.

The point 1 can assure a charge transfer within the surface without modification, and point 2 changes the charge into double layer of your electrode, so you can use an CPE element in parallel with parallel R-CPE fit.

You also should verify your impedance data and fit using Kramers-Kroning test. If the chi-squared test is too high (the thumb rule says more than 10-3 units) take a look if there's any issue at your system. Check the cables, the electric contacts with your cell and equipment, the Faraday cage, the current range (if you're running potentistatic mode), etc. The more you know about your system, better you're going to interpret your impedance data. 

Another thing that might help you: try to take the superficial pH for your modified electrode. Take a look at the DOI link above.

Hope this helps you.

http://dx.doi.org/10.1021/ed082p779

I will share some of my data when I get into the lab, but I often find that my Rct is so high (1e12) that I can actually model my interface with just a capacitor in series with a resistor and get a pretty good fit. 

This is for a SAM on gold microelectrode. 

Dear Roshan Khadka,

what is, please, the variable parameter in your attached plots, 2d ago ?

Try to remeasure your EIS, please, changing the VDC polarization parameter, applying a set of over-potentials nDC (= VDC  -  VOCV ) as a parameter (in your EIS).  The Rct (and maybe the Re, also) depend on nDC.

Hi Hunter,

For just bare gold surface and SAM on gold, RC in series can give me good fit as well but when I attach my proteins, I get the Rct (very high) and Randels circuit is the closest fit...yes, could you please share some of your data and the fitting as well please???

Dear Ioannis,

The first plot is the protein immobilized gold surface and the rest (decreasing order) higher concentrations of my target. I have already done a lot of measurements at -0.7 V (10, 000Hz to 0.1 Hz) so remeasuring will make me do a lot of works. 

I can fit my curves with Randles circuit but the question is where does this very high Rct come from as i am measuring them in just aqueous PBS buffer???

Thanks

Dear Roshan Khadka,

ok, thanks. Also[1], the polarization parameter (VDC= -0.7 V) is versus CE[2] or a RE ?

1. What is the prevailing VDC for the (most of your) measurements ? 

2. Counter Electrode (CE) is (bare) gold ?

Hi Ioannis,

1. The Vdc is versus a leakless Ag/AgCl RE. The Vdc for all of my measurements is -0.7.

2. The CE is coiled platinum wire.

Thanks

Dear Roshan Khadka

What proteins are you using, do they have redox centres? Furthermore -0.7 V vs. Ag/AgCl seems to be a non-ideal potential to perform capacitance measurements with gold (thiol from your SAM?) electrodes. I recall this is in the potential range were reductive desorption of the thiol monolayer occurs (depending on the perfection of this layer). Another explanation for the high faradayic impedance is that in fact you are measuring proton reduction, which is low on the perfect monolayer. However when you add proteins the interaction of the proteins with the hydrophobic monolayer will cause a disturbance of this monolayer allowing proton reduction to proceed, and this is possibly also a nucleation for the detoriation of the monolayer. What is the EIS data for the bare unmodified (no SAM) gold electrode at this potential? What are the equilibrium potentials of the respective electrodes and why do you not try to use a perturbation voltage around equilibrium? Results may be a bit less spectacular but possibly make more sense. Also I tended to avoid chlorine when working with gold electrodes.

Best regards, Mike

Roshan,

Here is my data with varying doses of a protein binding to a SAM at a gold electrode. I'd agree with Michael Wijnhoven in that, you likely are seeing redox reactions as a result from either 1) your surface modifications or 2) your proteins. Based on what you're seeing, I'd tend to believe that its most likely your proteins.

I agree that you should be biasing your electrodes around the equilibrium potential. First run a CV to find your cathodic and anodic peak, then average them to find your Eeq. This should be your DC bias vs. Ag/AgCl. I'd recommend running this both with/without your SAM to see if the potential is shifting.

Cheers,

Hunter

Dear Michael and Hunter,

Thanks for your suggestions. Please see attached my CV and EIS for bare gold and SAM modified gold electrode. As my measurement solution is just PBS buffer (no redox species) but I am still getting some oxidation reduction peaks and I am not sure where are they coming from? I tried cleaning the electrodes extensively and also degassing the solution a lot but i couldn't eliminate those peaks. Do you have any idea where are these peaks coming from? Is it the oxidation of gold forming gold oxides at positive cycle and gold oxides reducing to gold at negative scan? Based on your suggestions and my CVs, open circuit potential (0V) seems to be ideal for EIS measurement or maybe 0.1V. Please do comment on this as well.

The SAM I am using is 6-mercaptohexanoic acid and proteins are insect olfactory receptors and I think they do not possess any redox centres or I do not know. Before binding the surface to SAM modified gold electrode, I also activate the COOH end groups of SAM using EDC/NHS chemistry as well.

I look forward for your response.

Thanks,

Roshan

Dear Roshan,

Thank you for running the CV's as Hunter suggested. It is something that should become second nature. The oxidation/reduction of gold is shifted to more negative voltages as a function of increasing pH, and in the presence of chloride it is further decreased (as compared to sulfate) the standard potential being about 1V vs .SHE. So it is likely that some redox activity comes from Au. I assume you are using a solid gold elctrode, so if you scan to more positive potentials you should be able to resolve the full oxidation peaks (if you use thin film electrodes do not try this, in the presence of chloride). Another feature of the CV's is the appearance of a relatively well defined reduction peak at about -0.3 V, followed by a constant current this could be related to Au reduction and limiting proton concentration. From the CV of the modified electrode I see no evidence for any reductive or oxidative desorption of the thiol monolayer (but possibly these are steady state voltammograms). So either this does not occur or the modification is imperfect.

Anyhow, the potential you are using now seems to be fine. So a next step could be the characterization of your monolayer. When you read literature the procedure of fabricating a SAM on gold, seems very easy and sometimes it is just assumed that it is perfect. Of course it is almost never the case. So if possible you could characterize your SAM using a redox couple like Fe(CN)63-/4- (1mM) or Co(phen or bpy)32+/3+ (e.g 0.1 mM). Scan limits about -0.1 to 0.4 V vs. AgCl, and EIS at equilibrium. Possibly you might consider to work at low ionic strength (+- 10 mM), for this. And you can then do the same with the attached proteins. If you find the modification to be unstable you can consider using mixed (mono)layers, in the past I found mercaptopropyl-methyldimethoxysilane very useful for blocking and stabilizing purposes. I used this in conjunction with sodiumborohydride reduced antibodies (without further purification), and it worked fine. For cleaning gold sweeping in 1M H2SO4 is very effective and allows you to determine the surface area of the gold electrode, if this is not possible methanol/HClO4 cleaning was also satisfactory.

Hope this helps,

Kind regards, Mike