Modeling the electrical percolation behavior of hybrid nanocomposites based on carbon nanotubes and graphene nanoplatelets

An improved three-dimensional percolation model taking into account the random dispersion of nanofillers in a polymer matrix has been developed in order to study the effect of the nanofiller shape and aspect ratio (AR) on the electrical percolation behavior characteristic of nanocomposites. In this new model, two nanofillers of different shape and AR have been considered separately-carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs)-while hybrid systems with different relative ratio of the fillers and various AR have also been investigated. The numerical model is able to predict the electrical percolation threshold assuming a perfect random dispersion and orientation of the nanofillers, while tunneling effects are also accounted for, resulting in a percolation volume of 0.023 and 1.628 vol% for CNTs and GNPs nanocomposites, respectively, showing a quantitative agreement with existing experimental observations. The percolation volume was found to decrease with the AR of CNT and GNP according to different relationships. Hybrid systems incorporating CNTs and GNPs exhibited significant synergistic effects when the two fillers were properly combined. The numerical predictions confirm the applicability of the model to predict the percolation behavior and percolating network morphology by indicating the probability of contact patterns between same and different elements.