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## Modeling a Dielectric as a Real Capacitor

Hello everyone,

I am having trouble modeling something. I would like to look at the conduction/conductance/resistivity of a insulating/conductive composite. It could be thought to be like a polymer/insulating fiber system. Electrically, the polymer itself is referenced in literature to look like a capacitor and resistor in parallel. The capacitor illustrates the ideal dielectric capacitor that one might expect and the resistor illustrates the leakage that actually flows through the capacitor when placed in a potential. The illustration is on Tony Blythe's 2nd edition "Electrical Properties of Polymers" book on page 156. I've attached an image of the equivalent circuit I am talking about(not exactly the image from the book though).

I would like to know the DC electric conduction through the entire composite, so both in the low conductivity areas (the polymer/semi-insulator) and the in the high conductivity areas (which is a fiber/metal). Is there any way I can use components of both the Electostatics and Electric Currents Modules? I want it to take into account both the electrical conductivity and also the relative permittivity of the polymer. If so how can I do this? I've attached a 2D model of the geometry of what I'm talking about.

When I do this geometry in the EC interface, the electric field is not what is expected and when I do this geometry in the ES interface, I do get the correct e-field. I would like for the model to look like the ES does (which is what is expected) but actually have some current go through it.

Thanks in advance for any help you can shed for me!

John

9 Replies Last Post 23/12/2013 18:39 GMT-05:00
Posted: 5 years ago
John,

you don't show us what the EC model looks like, so it is diffcult to give an advice. I saw that the Nylon conductivity is only 1e-12 S/m. That may be a little low. The EC application mode requires some conductivity for all materials. I frequently saw that people use something around 1 S/m for 'insulators'.

Maybe you try playing a little with the conductivity.

Cheers
Edgar

Posted: 5 years ago
Thanks for your advice Edgar. I've attached two models each showing the differences in electric fields. Their conductivity are much different compared to the difference between their permittivity. In literature, an insulator is typically less than 10e-12 S/m where semi-insulators ar 10e-1 to 10e-11, generally.

When you load up the two models, each one has a very different electric field. As far as I see it, the e-field should be for the most part uniform between the two potentials (electrodes), not all "bunched" up between the first terminal and the middle (no potential) electrode.

Posted: 5 years ago
I tried the EC model with a Nylon conductivity of 1 S/m and gives a much more realistic picture. The EC application mode is not for insulators.

Of course 1 S/m is much too high for Nylon but actually the electric field and also the potential does not depend much on the conductivity value in your model. You can solve it with a conductivity setting that is convenient for the solver. Even if you are interested in the current field you can scale it according to a realistically low conductivity.

Cheers
Edgar

Posted: 5 years ago
Thanks for taking a look at my models.

I am beginning to get the hint that the EC is not for insulators or semi-insulators, but how is one supposed to model a (not completely) insulating material, then? Seems to me that there is an option for if the charges are static (ES) and then if the material is > 0.1 S/m you can have a current with the EC. Is there any option for anything in between? Or is there any kind of option for connecting them? I'm sorry if this question is completely naive.

I noticed in a presentation by Christen on the Comsol Conference that uses the Poisson and Continuity Equation together. I've attached a screen shot of the slide. Is there any way I can attach an equation to the ES that will allow for a little bit of current to flow? Maybe this suggestion is completely off base, but I am just trying to figure this something.

Thanks, you've been more than generous with your help,

John

Posted: 5 years ago
John,

I would say that in your model with the copper conductivity of 6e7 S/m and the nylon with 1e-1 S/m it IS just a little bit of current in the 'insulator'. You have 8 orders of magnitude in the model. You could try now to tweak the solver to increase the span.

Which specific question to the model remains unanswered? I don't think the publication you cited is applicable to your question.

Cheers
Edgar

Posted: 5 years ago
Hi

but at least in the latest version under EC you have a domain definition for equivalent ES studies, hence you can use EC (conduction) for those material having a real conduction, and set the others to ES (static = NO conduction) as there is no reason to say conduction is 1E+6 and 1E-6, that is too many orders of magnitude difference in condution to expect the binary numbers to give you any reasonable result without being numerical error/limittion driven.

But mixing EC and ES correctly should give you more resonable results, no ?

--
Good luck
Ivar

Posted: 5 years ago

Hey John,

I had a read through your question

"I am beginning to get the hint that the EC is not for insulators or semi-insulators, but how is one supposed to model a (not completely) insulating material, then? Seems to me that there is an option for if the charges are static (ES) and then if the material is > 0.1 S/m you can have a current with the EC. Is there any option for anything in between? Or is there any kind of option for connecting them? I'm sorry if this question is completely naive.

I noticed in a presentation by Christen on the Comsol Conference that uses the Poisson and Continuity Equation together. I've attached a screen shot of the slide. Is there any way I can attach an equation to the ES that will allow for a little bit of current to flow? Maybe this suggestion is completely off base, but I am just trying to figure this something"

I am modelling an insulator with pollution layer ( hence it will have leakage current flowing through the surface), hence this question is relevant to me as well. So have you found any way in which this dielectric can be modeled using EC but with current flow within it?

Thanks a lot,

Khyati

Posted: 5 years ago
Khyati,

Sorry for my delay in answering your question.

I haven't found a solution. For my problem, I made the conducting parts "Perfect Conductors" (all current flowing into the surface/boundary equals all current flowing out), and gave the very much less conducting parts a conductivity of a polymer/semi-insulator. I'm modeling conductivity through a composite, so this works *pretty well* for me.

Thanks,
John

Posted: 4 years ago
Dear Khyati,

I read your case that you posted it last May,

"I am modelling an insulator with pollution layer ( hence it will have leakage current flowing through the surface), hence this question is relevant to me as well. So have you found any way in which this dielectric can be modeled using EC but with current flow within it?'

Do you have the solution for the above matter as I am trying to solve the same problem as well.

Thank you for your kindness"and advice

Regards,

Hafisoh

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