A model for tensile modulus of halloysite-nanotube-based samples assuming the distribution and networking of both nanoparticles and interphase zone after mechanical percolation

Abstract

There are few modeling papers on the mechanical behavior of halloysite nanotubes (HNT)-based system, which restrict the applications of these materials in advanced fields. In this paper, a model for tensile modulus of HNT-reinforced system is advanced based on Kolarik equation assuming the concentrations and moduli of dispersed HNT, networked HNT and interphase sections nearby the dispersed and networked HNT. The calculations of the advanced model at a number of levels of all factors are justified. Furthermore, numerous samples are used to confirm the forecasts of the established model by experimental data. The modulus of HNT-based system enhances by low HNT radius, high HNT length, high modulus of networked interphase section, high network modulus, low percolation onset, high modulus of interphase section around the dispersed HNT, great HNT modulus and high network percentage. The nonattendance of interphase section causes the nanocomposite’s modulus of 2.24 GPa, whereas the modulus of samples improves to 3.15 GPa by the interphase depth of 25 nm. Additionally, the experimental data of several samples containing different types of polymer media and HNT validate the predictability of the established model.