I was wondering if anyone had any insights on how to estimate or discern the potential drops across a capacitor containing three distinct media between the electrode plates. The system is as follows(adsbygoogle = window.adsbygoogle || []).push({});

Vo-(+) air gap | binary electrolyte phase | plastic phase (-)

The lengths of the air gap is approximately that of the electrolyte phase, with the length of the plastic phase being much smaller. I'm trying to figure out a way to consider the the electric field at the interfaces due to the electrical double layer that should be generated by the potential difference across the capacitor.

Solving Laplace in one dimension gives

I_{1}= Ax+B

I_{2}= Cx+D

I_{3}= Ex+F

Applying boundary conditions I get

I_{1}(x=0)=Vo=B

I_{3}(x=2L)=0=2EL+F => F = -2EL

I_{1}(x=L)=I_{2}(x=L)

AL + Vo = CL + D

I_{2}(x=2L)=I_{3}(x=2L)

2CL + D = EL - 2EL

2CL + D = -EL

from conservation of charge

n*(σ_{1}E_{1}-σ_{2}E_{2}) = 0

σ of air and plastic = 0 thus

E_{2}=0

C=0

leaving me with 3 unknowns and only two equations

AL + Vo = D

D = -EL

Which is why I am trying to see if I can estimate the approximate potential drop due to the air gap, which would allow me eliminate one of my unknowns. Still though, this is only good for determining the potential everywhere within my capacitor, and I am still no closer to determining the electric field due to the double layer at my interfaces. Any ideas?

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# Estimating potential drops within multi-media capacitors

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