Effective Medium Approximations for the Description of Multicomponent Composites

We compared several generalizations of the Bruggeman effective medium approach with the use of elliptical cells. Namely, a "uniaxial" anisotropic approximation and two isotropic models with averaging over chaotic orientations and random conductivities of particles were compared, which make it possible to consider multicomponent composites with various filler particles (for instance, carbon nanotubes and graphenes). The expressions for the corresponding percolation thresholds were derived. It was shown that all considered approximations result in the same "additive rule" of the inverse percolation thresholds, which was previously found for a particular case of two-component fillers with the use of estimates of an excluded volume. The correlation of the aforementioned "additive rule" with frequently observed synergic effects was discussed, the description of which requires taking into account near correlations and is beyond purview of the effective medium theories. For the model problem with parameters corresponding to carbon nanotubes in a polymer matrix, the considered models led to qualitatively similar results and resulted in an effective conductivity within the Hashin-Shtrikman bounds. Using the known two-scale averaging technique, taking into account the possibility of agglomeration of the filler particles, we showed that, in the framework of the considered models, agglomeration can lead to both an increase and decrease in the percolation threshold.