Modeling electrical conductivity of polymer nanocomposites with aggregated filler

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.