Modeling the synergistic electrical percolation effect of carbon nanotube/graphene/polymer composites

Electrical percolation behavior is one major concern for conductive polymer composites (CPCs). Two types of conductive fillers such as one-dimensional (1D) carbon nanotubes (CNTs) and two-dimensional (2D) graphene nanosheets are often simultaneously incorporated into one polymer to yield a synergistic effect in improving electrical percolation behavior but proper analytical models are still lacking for clearly clarifying the synergistic percolation effects of CNT/graphene/polymer composites. In this work, an analytical model based on excluded-volume theory is developed to determine the synergistic percolation threshold of ternary CNT/graphene/polymer composites. Subsequently, parametric studies are performed to examine the effects of the aspect ratio of CNTs and graphene and the relative content ratio of CNTs to graphene on the synergistic percolation threshold of the ternary CNT/graphene/polymer composites. It is suggested that both filler aspect ratios and relative content ratio of CNTs to graphene should be combinedly considered to achieve the strongest percolation synergism. Furthermore, comparisons between modeling predictions and existing experimental data are made to demonstrate the validity of the developed model. This work provides a theoretical basis for understanding the synergistic percolation effect of two types of fillers such as CNTs and graphene nanosheets in CPCs.