A multistep methodology for calculation of the tensile modulus in polymer/carbon nanotube nanocomposites above the percolation threshold based on the modified rule of mixtures

A multistep model is proposed for calculating the tensile modulus values of polymer/carbon nanotube (CNT) nanocomposites (PCNTs) based on the modified rule of mixtures, assuming a percolated network of nanoparticles. In the first step, the network of nanoparticles is considered as a new phase with a novel volume fraction and Young's modulus. Then, the volume fraction of the filler network in the PCNTs is correlated to the density of the network. Also, the percolation of the nanoparticles is related to the aspect ratio of the nanoparticles. Finally, a new model is proposed based on the modified rule of mixtures (the Riley model) of the properties of the filler network. The predictions of the proposed model are compared with experimental results and the roles of the nanoparticles and network properties in the modulus values of nanocomposites are determined. The proposed model presents acceptable predictions when compared with the experimental data. Moreover, the density and modulus of the filler network, as well as the aspect ratio and diameter of the nanoparticles was found to directly affect the moduli of the nanocomposites.