# Simulation of a double layer capacitance and a warburg impedance with comsol

1. May 27, 2010

### FirePhoenix

Hallo,
i'm trying to implement a comsol simulation of a impedance spectroscopy experiment.
But unfortunatly i'm an absolut beginner in Comsol and i have many problems with this work.

First of all i want to say that i'm using the AC/DC module, more precisely the transient analysis.
At the moment I'm using a simple 2D geometry to try out all equations and boundary conditions.

Now to the first problem:
I tried to simulate only a double layer capacitance between an electrode and a drop of water. The double layer thickness is very small compared to the dimensions of the electrodes, so I didn't want to draw it, but use a distributed impedance for the boundary condition between the electrode and the drop of water.
The other boundary conditions are:
Potential V= sin(10*t) on the left side of the electrode.
Potential V= -sin(10*t) on the right side of the drop of water.
All other boundaries are electrical insulated.
But it wasn't sucessfuly, I always recieve the whole potencial difference over the drop of water and not over the distributed impedance.

The second problem is that I have no idea how to bring the warburg impedance equation into the boundary conditions.
The equation is something like Z= sigma/sqrt(w)*(1-j), but where do I place that and how can i express w?

Finaly remains the question, if it is possible to make the simulations automatic over a defined range of frequencies and to calculate a complex impedance out of the result.

Attachments:
Comsol1: result, up a simulation with a drawed double layer, down the distributed impedance.
Comsol2: the boundary condition for the distributed impedance
Comsol3: the boundary condition of the electrode

and sorry for my bad english

cu FirePhoenix

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• ###### Comsol3.jpeg
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2. Jul 21, 2010

Hi!
I am about to do some simulations of impedance spectroscopy as well. Have you overcome the problems you have mentioned?

Best regards,
Mike

3. Jul 21, 2010

### FirePhoenix

I'm still working on it.

But at the moment it looks good.

You have to define the frequency over the scalar variable: nu_emqvw,
and then define the epsilon_r and the sigma of the doublelayer region as:

A0_CPE= 1e-6; (use the value of your measurements)
psi_CPE= 0.5; (0.5 for warburg impedance)

sigma= (sig_DL+ A0_CPE*(2*pi*frequenz).^psi_CPE*cos(psi_CPE*pi/2));
epsilon_r= e_DL+ A0_CPE/(epsilon_0)*(2*pi*frequenz).^(psi_CPE-1)*sin(psi_CPE*pi/2);

lg
FirePhoenix