Development of Expanded Takayanagi Model for Tensile Modulus of Carbon Nanotubes Reinforced Nanocomposites Assuming Interphase Regions Surrounding the Dispersed and Networked Nanoparticles

In this paper, we consider the interphase regions surrounding the dispersed and networked carbon nanotubes (CNT) to develop and simplify the expanded Takayanagi model for tensile modulus of polymer CNT nanocomposites (PCNT). The moduli and volume fractions of dispersed and networked CNT and the surrounding interphase regions are considered. Since the modulus of interphase region around the dispersed CNT insignificantly changes the modulus of nanocomposites, this parameter is removed from the developed model. The developed model shows acceptable agreement with the experimental results of several samples. “E_R” as nanocomposite modulus per the modulus of neat matrix changes from 1.4 to 7.7 at dissimilar levels of “f” (CNT fraction in the network) and network modulus. Moreover, the lowest relative modulus of 2.2 is observed at the smallest levels of interphase volume fraction ( ${\varphi }_i$ < 0.017), while the highest “ ${\varphi }_i$ ” as 0.07 obtains the highest relative modulus of 11.8. Also, the variation of CNT size (radius and length) significantly changes the relative modulus from 2 to 20.