Bruggeman models

There is another limitation of the MG approach, consisting in the assumption that the medium was not modified by the insertion of metallic particles. This is of course too crude, and the Bruggeman model, treated next, removes this limitation. 

Fig. 11. The Bruggeman model (BM) lakes into account the modification of the effective medium by the adjunction of metal in the medium. The net effect is a broadening of the resonance peak. The parameters of the metallic spheres in these calculations are fuHp = I eV and fiV = 0.1 eV. The insulating host is defined by ftcOp i = 1 eV and ftf = 1 eV and fidiy = 20 eV. Note that the normal Drude curve is superimposed with the Bruggeman curve with/= 1.

When Maxwell model fails to provide a good mateh with experimental results for higher eoneentration of inelusions, Bruggeman model ean suffieiently be used. 

The symmetric Bruggeman model does not make a distinction between continuous and discontinuous phases and, therefore, the relevant expression is symmetrical in y/u y/2. It seems to have been first applied to the complex variable by Landauer [1978]. Coverdale et al. [1995] give an in-depth discussion of its relevance to impedance spectra of composite materials. The symmetric Bruggeman model is described by Eq. (26). 

The Maxwell equation as written in Eq. (8.32) has been used by many researchers to describe the behavior of MMMs. It was however later suggested that the Maxwell equation is applicable for the low loading level of dispersed phase since it was assumed that the streamline around the dispersed articles were not affected. Instead the Bruggeman model was recommended in which the effect of the particles added to the dilute suspension is considered. The Bruggeman equation is given by... 

Fig. 8.61 Comparison of experimental data for permeability and ideal separation factor for COJ CH gas pair with the predicted values by the Maxwell and the Bruggeman model (Ultem 1000/ CMS MMMs). (From [23])...

The Bruggeman model assumes that the host material is just the EMA dielectric function ( h= ) which is self-consistent. For the Bruggeman model the EMA equation reduces to ... 

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