A mean‐field model is developed for the electrical conductivity of microcomposites and nanocomposites with polymer matrices. The model accounts for aggregation of filler into clusters (involving both conducting and nonconducting particles) and rearrangement of these clusters with the growth of volume fraction of filler (which leads to a reduction in tunneling resistivity and an increase in the number of bridging contacts between conducting particles). The governing equations involve five material constants with transparent physical meaning: the depolarization factor of clusters, volume fraction of polymer in clusters of filler, effective conductivity of an individual filler particle, and two coefficients characterizing an increase in the effective electrical conductivity of filler driven by the growth of bridging contacts between neighboring particles in clusters. Good agreement is demonstrated between results of simulation and experimental data on the electrical conductivity of epoxy resin reinforced with carbon black and graphite particles, poly(vinyl chloride) reinforced with copper and nickel particles, polypropylene loaded with spherical and spheroidal tin particles, poly(butylene terephthalate) reinforced with graphene nanosheets, and polypropylene loaded with multiwalled carbon nanotubes.

中文翻译：

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用聚集填料模拟聚合物纳米复合材料的电导率

建立了具有聚合物基体的微复合材料和纳米复合材料电导率的均值场模型。该模型考虑了填料聚集到簇中（涉及导电和非导电颗粒）以及随着填料体积分数的增加而重新排列这些簇的情况（这导致隧道电阻率的降低和导电之间的桥式接触数量的增加）。粒子）。控制方程涉及五个具有透明物理意义的材料常数：簇的去极化因子，填料簇中聚合物的体积分数，单个填料颗粒的有效电导率，以及两个系数来表征填料有效电导率的增加，这是由簇中相邻颗粒之间的桥接接触的增长所驱动的。在模拟结果和实验数据之间，在炭黑和石墨颗粒增强的环氧树脂，铜和镍颗粒增强的聚氯乙烯，球形和球形锡颗粒填充的聚丙烯，聚丁烯的电导率的模拟结果与实验数据之间，显示出良好的一致性。对苯二甲酸酯）用石墨烯纳米片增强，聚丙烯用多壁碳纳米管填充。