Predicting the electrical conductivity in polymer carbon nanotube nanocomposites based on the volume fractions and resistances of the nanoparticle, interphase, and tunneling regions in conductive networks

Some limited models have been suggested to determine the conductivity of polymer carbon nanotube (CNT) nanocomposites (PCNTs). However, earlier models (e.g., the Kovacs model) cannot properly consider the roles of the interphase regions or tunneling properties on the percolation threshold and subsequent conductivity of PCNTs. In this paper, the Kovacs model is further developed by assuming that the CNT, interphase, and tunneling regions are separate phases. Also, some simple equations are provided to calculate the percolation threshold as well as the volume fractions and resistances of the CNT, interphase, and tunneling regions in conductive networks. The experimental conductivity results for several samples are compared with the predictions of the developed model. In addition, the calculations of the developed model at different parameter levels are explained and justified. The conductivity calculations show good agreement with the experimental data. Moreover, the developed model reasonably explains the roles of the different parameters on the conductivity. For example, long, thin, and straight CNTs efficiently improve the conductivity because they form large networks in the nanocomposites. Additionally, a thick interphase enlarges the conductive networks, resulting in a desirable conductivity. The conductivity of PCNTs only depends on the tunneling resistance; this is the case because the poor resistance/significant conductivity of the CNT and interphase regions do not influence the conductivity. The developed equations can replace conventional approaches for predicting the conductivity of nanocomposites.