A multistep methodology based on developed Takayanagi, Paul and Ouali models for tensile modulus of polymer/carbon nanotubes nanocomposites above percolation threshold assuming the contribution of interphase regions

In this study, a multi-step technique is suggested to estimate the tensile modulus of polymer/carbon nanotubes (CNT) nanocomposites (PCNT) assuming the percolating effect of interphase regions. At the first step, Paul model calculates the modulus of regions containing dispersed nanoparticles and surrounding interphase. Secondly, the modulus of interphase-networked CNT is predicted by Ouali model. Finally, the developed Takayanagi model estimates the modulus of PCNT using the moduli of supposed regions. Additionally, some parameters such as the fraction of nanoparticles in the network (f) and the percolation threshold of interphase regions are formulated. The predicted modulus shows good agreement with the experimental results of samples. The thinnest and the longest CNT as well as the thickest and the strongest interphase cause the highest modulus. However, the interphase properties more significantly affect the modulus compared to material characteristics.