Abstract

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.

中文翻译：

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描述多组分复合材料的有效介质近似

摘要

我们将Bruggeman有效培养基方法与使用椭圆细胞的几种方法进行了比较。即，比较了“单轴”各向异性逼近和两个平均模型，这些模型在颗粒的混沌取向和随机电导率上进行了平均，从而可以考虑具有各种填料颗粒（例如碳纳米管和石墨烯）的多组分复合材料。推导了相应的渗透阈值的表达式。结果表明，所有考虑到的近似值都产生反渗透阈值的相同“加法规则”，这是先前在使用排除体积的估计值的两组分填充剂的特殊情况下发现的。讨论了上述“加法规则”与经常观察到的协同效应的相关性，对它的描述需要考虑到近似的相关性，并且超出了有效的媒介理论的范围。对于具有与聚合物基质中的碳纳米管相对应的参数的模型问题，所考虑的模型导致了定性相似的结果，并在Hashin-Shtrikman范围内产生了有效的电导率。使用已知的两级平均技术，考虑到填料颗粒发生团聚的可能性，我们表明，在所考虑的模型框架内，团聚可以导致渗透阈值的增加和降低。考虑的模型导致了定性相似的结果，并在Hashin-Shtrikman范围内产生了有效的电导率。使用已知的两级平均技术，考虑到填料颗粒发生团聚的可能性，我们表明，在所考虑的模型框架内，团聚可以导致渗透阈值的增加和降低。考虑的模型导致了定性相似的结果，并在Hashin-Shtrikman范围内产生了有效的电导率。使用已知的两级平均技术，考虑到填料颗粒发生团聚的可能性，我们表明，在所考虑的模型框架内，团聚可以导致渗透阈值的增加和降低。