Iam trying to find effective dielectric constant of two mixtures.i.e. mixing a gas to a nanomaterial. we can use either Maxwell Garnett theory or Bruggeman. In my case the volume fraction is greater than unity. i.e x = Gas / Material is greater than unity which effective medium approximation has to be used Maxwell Garnet or Bruggeman
Dear Senthil, my first question is: what is the geometry of your system? if it is not an aerosol, the solid particles must form a network to hold the structure. If you have an interpenetrating network structure of solid and gas, you may try the Böttcher formula. The volume fraction is never greater than 1. The volume fraction of the gas is (gas volume)/(gas volume + solid volume).
Hi Senthil,
It’s been a while since I’ve worked with these theories, hope this helps a little.
My work was about conductive (i.e. dielectric constant = infinity) particles inside an insulating polymer matrix. It might be a little different if the filler particles are not metallic.
There are 2 major shortcomings of Maxwell-Garnett and Asymmetric-Bruggeman. Both assume spherical filler particles. And they do not represent any frequency dependence.
Maxwell-Garnett Formula is based upon the assumption of spatially separated conductive particles. Therefore, it is only valid for the case of small volume fractions of inclusions. It does not have a particular percolation threshold. The material is assumed to be an insulator until all the host material is replaced by the conductive filler.
Asymmetric Bruggeman shows an extremum of the overall permittivity for a filler fraction of 0.33, no matter what the permittivity of the insulating host or the shape of the inclusions may be (it assumes spherical particles).
Depending on your system, you might want to look into percolation theory. I can recommend this literature:
Gantmakher, V.F., Electrons and disorder in solids. 2005, Oxford; New York: Clarendon Press ; Oxford University Press. x, 225 p.
Zallen, R., The physics of amorphous solids. 1983, New York: Wiley. xi, 304 p.
For a more comprehensive list of mxiture formulas see the attched article
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