2D electric field distribution in electrolyte solution

[CheesyG]

TL;DR Summary

How can I determine the electric field distribution in an electrolyte solution when applying a given potential to electrodes?

Hi there,

How can I determine the electric field distribution from a planar electrode? The known parameters are potential applied to the electrode, ionic strength and dielectric constant of the medium. (E.g. for the most simple case 0.5 mM NaCl in water)

I'm having difficulty finding a straightforward explanation to do this. I'd want to account for the potential drop across the Stern layer and the exponential decay of potential in the diffuse layer to get a complete picture of electric field distribution. BC is potential --> 0 as x --> infinity.

One case would be for an infinite planar electrode, another would be for a small 100nm planar electrode in a cavity.

 

[Borek]

This is more of a physics problem. Sure, chemistry will add its own complications, as the medium is not homogeneous and can change in the electric field, but as the first approximation I would look for physics models for the electric field in vacuum, something around the Poisson equation if memory serves me well (I can be terribly wrong here, haven't visited this territory in ages).

I have problems understanding your setup though, you can't apply potential using a single electrode, and the presence and location of the counter electrode (geometry of the system) is probably crucial element of the system.

 

[CheesyG]

Thanks Borek!

We would apply the potential between the working and counter electrodes.

The problem also needs to account for field screening due to the presence of the electric double layer. (Electric field distribution in vacuum is much more straightforward!)

I would also make a few assumptions :

- The potential decays to 0 in the bulk solution such that we treat the working electrode independently

- we ignore iR drop, or any other effects of solution resistance

I think this should be a straightforward problem, but I’m having a hard time finding a simple expression for electric field distribution taking into account the stern and diffuse layers of the EDL (or figuring out how best to approach this). Then how to approach the problem different electrode geometries or surface areas.

Hope this makes sense,
Cheers!

 

[TeethWhitener]

The equation you’re looking for is the Poisson Boltzmann equation:
https://en.m.wikipedia.org/wiki/Poisson–Boltzmann_equation