Spherical Diffusion in EIS Fitting

[AZuzu]

Good morning,

I have carried out some EIS experiments in order to analyze a biological interaction. I have used a biosensors with a gold working electrode fabricated by thin-film technologies.

When I built the equivalent circuit, I chose the spherical diffusion instead of the linear one because it provides best fitting results and minor errors.

As I use planar electrodes, I was wondering if I must consider the linear diffusion even if it leds to worse fittings.

I have attached an example of the measurements and the equivalent circuit I have used.

Thank you very much.

Kind regards,

Ana Zuzuarregui

[Yevgen Barsukov]

It depends on where is the diffusion acting as a limiting factor. If it is from the electrode to the solution, in this case

you should use planar diffusion.

     It might be however that you have a solid state diffusion in the particles as a limiting step.

For example If you have a porous film, and the particles in the film are spherical (or can be approximated as such) it might be

correct to use spherical diffusion, and use actual particle size information such as radius to calculate the true diffusion coefficient.

Regards,
Yevgen

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[AZuzu]

Thank you very much Yevgen,

I have used a FeCN solution as electrolyte so I thought that the diffusion took place from the solution to the electrode. I thought that when I apply the input signal to the electrodes the ions present in the electrolyte 'difund' from the bulk solution to the interface between the electrode and the solution. I have attached an scheme of the way I thought the sensor works.

Thank you very much again

Kind regards,

Ana Zuzuarregui

[Yevgen Barsukov]

Since you are not using a reference electrode, you effectively measuring 3 different impedances - that

of WE reaction (dependent on applied potential it could be reduction or oxidation), that of CE reaction 

and that of the electrolyte in between. It makes for a complex system. Are you measuring impedance

at open circuit potential, or are you forcing some bias potential between electrodes before measuring?

What is the purpose of the measurement in general?

Regards,
Yevgen

Kind regards,

Ana Zuzuarregui

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[AZuzu]

I am so sorry, I have explained myself really bad.

I actually have a three electrodes biosensor: the gold working electrode, a platinum CE and an silver reference electrode.

I functionalize the working electrode and immoblize a bio-receptor. In that moment I measure the impedance of the system in a FeCN solution obtaining the curve ploted.

Then I add the analyte I want to detect and measure the impedance again. The bio-receptor and the target analyte have both electrostatic and hidrophobic interactions so when I measure the impedance once the analyte has been detected the value of the impedance increases due to the compesation of the electrostaic chrages and the hidrophobic part of the analyte.

As the redox reaction takes place in the electrolyte solution I thought that the diffusion could be considered spherical.

I hope this time I have expressed better my system and the doubts I have.

Thank you very much and sorry again,

Kind regards

Ana Zuzuarregui

[Yevgen Barsukov]

Based on your description, your limiting diffusion is going to be not in the bulk solution but in the film

of your functionalized polymer.

From this point of view it makes more sense to analyse everything based

on finite length diffusion through a layer of your material. You can use "transmissive finite Warburg" element

from MEISP library or code it directly.

Here is a screenshot for the element from MEISP.

Its electric equivalent presentation is a short circuit terminated transmission line,

and it is given by below equation:

Regards,
Yevgen

Ana Zuzuarregui

[Yevgen Barsukov]

just to clarify, it would make sense to put the diffusion element difshort instead of the diffusion

element that you have now in your equivalentn circuit, not to use the circuit that exemplifies its use above because

it does not have serial capacitance and so it will not result in a vertical line in the low frequency part of the impedance 

spectrum that you observed.

Actually, if it is indeed diffusion trough a layer, imaginary part should eventually go down at low frequency.

I wonder - what is the lowest frequency you measured to? It might be that if you go to lower frequency you will

actually observe this behaviour.

Regards,
Yevgen

[AZuzu]

Thank you very much Yevgen,

I have analyzed my data using a Warburg element instead of the spherical diffusion and the results of the fitting is in most cases the same. At least concerning to the value of Rct, which is the one I use to quantify the biochemical interaction.
Can I suppose that the diffusion of the redox species is not limitant in my system?

Thany you again,

Regards

Ana

[Yevgen Barsukov]

I would put it this way - it is possible that the diffusion inside the bulk of the electrolyte is not limiting,

but the diffusion through the active film might still be, and it is affected by any changes in the film such

as these due to the adsorption of the material you are sensing.

Regards,
Yevgen