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Frequency analysis of an electric double layer

Salvador Gómez Carretero

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Dear COMSOL community,

I have been lately trying to model and simulate the behaviour of an electric double layer. Thanks to the help provided in the forum I have managed to accomplish it using the Electrostatics module, defining an Stern layer with no charge inside and a diffuse layer where the Poisson-Boltzmann equation is employed.

Now I want to go a step further and I want to simulate the result from an EIS (Electrochemical Impedance Spectroscopy) measure, so I want to perform a frequency analysis of that double layer and calculate the impedance of the system as a function of frequency. And I am a bit lost.

As far as I know the Electrostatics module does not allow frequency analysis. The natural module seems to be the Electrical Currents module. But how do I define a space charge density there as I did in the Electrostatics module? Should I couple the physics from the Electrostatic module and the Electrical currents module? Any clue?

Thanks a lot for your help and attention.

Best regards,
Salva

4 Replies Last Post Feb 23, 2017, 3:05 a.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago Apr 19, 2011, 1:29 a.m. EDT
Hi

You are right ES (Elelctro Static) is not set up for harmonic development in the time/frequency domain, you need EC (Electric Current a close cousin) to do that, but that should not hold you back, you will find your BC in there too. Its only that you cannot "exchange" the physics, you must restart a model, but its quickly done, as you might keep the geometry.

If you look carefully at the equations, you will see that there is only the Je that really differs (external current density) (D=epsilon0*epsilonR*E).

I believe you will have to find the most appropriate way to re-express your charges as voltages.remembering that in both physics (Ex,Ey,Ez) = (-dV/dx,-dV/dy,-dV,dz) = (-Vx,-Vy,-Vz) in COMSOL notation, and you solve for the dependent variable V.

Pls note that the notation is slightly confusing here, Ex is the "x" component of the Electric field E (a vector), while Vx is the first derivative along "x" of the Electric Potential V (a scalar)

--
Good luck
Ivar
Hi You are right ES (Elelctro Static) is not set up for harmonic development in the time/frequency domain, you need EC (Electric Current a close cousin) to do that, but that should not hold you back, you will find your BC in there too. Its only that you cannot "exchange" the physics, you must restart a model, but its quickly done, as you might keep the geometry. If you look carefully at the equations, you will see that there is only the Je that really differs (external current density) (D=epsilon0*epsilonR*E). I believe you will have to find the most appropriate way to re-express your charges as voltages.remembering that in both physics (Ex,Ey,Ez) = (-dV/dx,-dV/dy,-dV,dz) = (-Vx,-Vy,-Vz) in COMSOL notation, and you solve for the dependent variable V. Pls note that the notation is slightly confusing here, Ex is the "x" component of the Electric field E (a vector), while Vx is the first derivative along "x" of the Electric Potential V (a scalar) -- Good luck Ivar

Salvador Gómez Carretero

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Posted: 1 decade ago Apr 20, 2011, 3:01 p.m. EDT
Thanks a lot, Ivar, for your response.

So should I then try to transform the charge density to a current source (term "Qj" in the EC module) or to an external current density (term "Je" in EC module)?

I have thought of the following:
1)Calculate the electric field fromm the ES module (es.Ex, es.Ey, es.Ez) with the charge density
2)Calculate the electric field from the ES module (es.Ex, es.Ey, es.Ez) but without the charge density
3)Use the difference of the previous fields, multiplied by the electric conductivity, as an external current density (term "Je" in EC module) in the domain where the charge density was defined in the ES module.

But, on the other hand, the Poisson-Boltzmann equation is not lineal with respect to the potential, since the potential appears inside an exponential function:
(d^2(V))/(dx^2)=-(a1*exp(b1*V)+a2*exp(b2*V))
For two kind of ions ("1" and "2") and being V the electric potential.

So I am not sure if my idea is correct or not, since I am not sure if the superposition principle can be applied here.

Could you please go further in your explanation?

Thanks a lot for your help and attention.

Best regards,
Salva
Thanks a lot, Ivar, for your response. So should I then try to transform the charge density to a current source (term "Qj" in the EC module) or to an external current density (term "Je" in EC module)? I have thought of the following: 1)Calculate the electric field fromm the ES module (es.Ex, es.Ey, es.Ez) with the charge density 2)Calculate the electric field from the ES module (es.Ex, es.Ey, es.Ez) but without the charge density 3)Use the difference of the previous fields, multiplied by the electric conductivity, as an external current density (term "Je" in EC module) in the domain where the charge density was defined in the ES module. But, on the other hand, the Poisson-Boltzmann equation is not lineal with respect to the potential, since the potential appears inside an exponential function: (d^2(V))/(dx^2)=-(a1*exp(b1*V)+a2*exp(b2*V)) For two kind of ions ("1" and "2") and being V the electric potential. So I am not sure if my idea is correct or not, since I am not sure if the superposition principle can be applied here. Could you please go further in your explanation? Thanks a lot for your help and attention. Best regards, Salva

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Posted: 1 decade ago Nov 9, 2011, 5:04 a.m. EST
Dear All,

I'm trying to build exactly the same model and so far I haven't find any solution. I was trying to set the conductivity sigma to 0 and current source to i*omega_emqvw*rho, where rho defines surface charge density. It computes the solution nicely, but the physical description itself is wrong.

Best regards,
Dmitry Momotenko
Dear All, I'm trying to build exactly the same model and so far I haven't find any solution. I was trying to set the conductivity sigma to 0 and current source to i*omega_emqvw*rho, where rho defines surface charge density. It computes the solution nicely, but the physical description itself is wrong. Best regards, Dmitry Momotenko

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Posted: 8 years ago Feb 23, 2017, 3:05 a.m. EST
Hi Salvador,

I am also trying to model and simulate the behaviour of an electric double layer using COMSOL "Electrostatics" module in order to obtain Capacitance vs frequency plot. Were you able to figure out how to do it? Any help would be appreciated.
Hi Salvador, I am also trying to model and simulate the behaviour of an electric double layer using COMSOL "Electrostatics" module in order to obtain Capacitance vs frequency plot. Were you able to figure out how to do it? Any help would be appreciated.

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