Synergic effect of graphene nanoplatelets and carbon nanotubes on the electrical resistivity and percolation threshold of polymer hybrid nanocomposites

A physics-based hierarchical modeling approach considering tunneling resistance through polymer is proposed to predict the percolation threshold and resistivity of carbon nanotube (CNT)/graphene nanoplatelet (GNP)-reinforced polymer hybrid nanocomposites. At first, a method is developed to calculate the resistivity of CNT-polymer nanocomposites. Then, percolation theory model is employed to calculate the percolation threshold of CNT-reinforced nanocomposites. At the end, an analytical model is presented for estimating the resistivity of CNT/GNP hybrid nanocomposites. The effects of barrier height, nanofiller aspect ratio and tunneling distance on the percolation threshold and resistivity of hybrid nanocomposites are extensively investigated. The results show that the percolation threshold depends on many factors such as aspect ratio, electrical conductivity and volume fraction of nanofillers. It is clearly shown that the smaller GNP aspect ratio leads to an increase in percolation threshold and electrical resistivity. The results also indicate the dominant role of nanofiller volume fraction at low tunneling distance. The model results are compared with experimental data in the literature for GNP/CNT hybrid nanocomposites where it is demonstrated that the represented model is able to explain the impact of electrical tunneling on the resistivity of polymer nanocomposites.