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Re: WSN: Dielectric Constant for weak electrolyte solutions (fwd)
Sender: jw@newt.phys.unsw.edu.au (Joe Wolfe)
Subject: Re: WSN: Dielectric Constant for weak electrolyte solutions
Dear Tony,
JR Smith and M Eberl, J.Chem.Soc. Faraday Trans 89 2783-2789 (1993)
treats the Nernst-Plank-Poisson equations in some relevant geometries
and discusses some of the experimental problems in measuring the relevant
parameters.
What is the dielectric constant?
A naive DC measurement would give an absurd result, in the sense that
any conductor could be said to have a very large dielectric constant. (The
dielectric constant is proportional to the ratio of the charge required to
give a particular electric field in a given geometry. If the medium
conducts, then one keeps adding charge and gets no change in the field.)
Provided that the ionic effects are included explicitly, there seems little
reason to use a dielectric constant different from that of water (there
are 55,000 mol of water and only 300 mol of ions in a cubic metre of solution).
I am assuming that you are considering frequencies rather less than MHz. At
low frequencies, you have a high concentration of dipolar molecules (water)
which will dominate the dielectric response, providing that one's definition
of dielectric response does not include the flow of ions.
Including the flow of ions is a nasty problem, however, except in the few simple
cases where analytical solutions exist. Numercial solutions are beset by
the problem that the ion concentrations must be known with great precision
in order to calculate the charge concentration (anions-cations). Double
precision is inadequate, and 30 or so digits may be needed for reasonable
resolution.
Finally, there is spectacular dispersion with frequency, so you should
be careful to specificy frequency.
The addresses of the authors of the article above are:
eberl@maths.mu.oz.au
jrs@newt.phys.unsw.edu.au
Eberl addressed some of the problems that you raise in her doctoral thesis,
and Smith has published several papers on solutions to Nernst-Plank-Poisson
equations.
Good luck,
Joe Wolfe