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To date, there have been a limited number of studies modeling the tensile modulus in the polymer halloysite nanotube (HNT) systems before or after percolation onset. In this paper, an equation for a composite's modulus post-percolation onset was developed for HNT-filled samples including the interphase and HNT network. The dispersed nanoparticles and adjoining interphase part were neglected, because they caused ineffective influences on the stiffness of the system after percolation onset. The developed model reflects the impacts of HNTs' size, interphase depth, percolation onset and the volume shares and moduli of the HNT network and its adjacent interphase on the modulus of HNT-based systems. The impacts of issues on the nanocomposite modulus are defendable, confirming the effectiveness of the developed model. HNT length, interphase depth, HNT concentration, net modulus and net portion directly influenced the stiffness, while the HNT radius and percolation onset had inverse effects. Results show that there was a 142% improvement in the modulus of samples at an interphase depth of 40 nm. Moreover, the stiffness improved by 60% at a net modulus of 200 GPa, but it later exhibited a 180% enhancement at a net modulus of 1000 GPa. In addition, the experimental data for the modulus of numerous composites display fine agreement to the predictions, confirming the validity of the developed model. [ABSTRACT FROM AUTHOR]

In the current article, Kolarik model is progressed for the tensile modulus of a polymeric system containing dispersed halloysite nanotubes (HNT) and adjacent interphase section. The progressive model correlates the nanocomposite's modulus to HNT concentration (volume fraction and weight percentage), the extents of HNT and nearby interphase section in addition to the densities of polymer medium and HNT. The productions of the progressive model are linked to the tentative results and the influences of all variables on the modulus of system are justified. The modulus of system reduces as HNT radius increases, but HNT weight percentage directly controls the nanocomposite's modulus. The modulus of samples maximizes by 47% by the deepest interphase section of 20 nm establishing a straight link among nanocomposite's modulus and interphase thickness. The increment of polymer matrix density improves the modulus of samples, but there is an opposite relation between the modulus of system and HNT density. Furthermore, the calculations exactly match to the experimental facts of numerous examples representing the accurateness of the progressed model. [ABSTRACT FROM AUTHOR]

To date, there have been a limited number of studies modeling the tensile modulus in the polymer halloysite nanotube (HNT) systems before or after percolation onset. In this paper, an equation for a composite’s modulus post-percolation onset was developed for HNT-filled samples including the interphase and HNT network. The dispersed nanoparticles and adjoining interphase part were neglected, because they caused ineffective influences on the stiffness of the system after percolation onset. The developed model reflects the impacts of HNTs’ size, interphase depth, percolation onset and the volume shares and moduli of the HNT network and its adjacent interphase on the modulus of HNT-based systems. The impacts of issues on the nanocomposite modulus are defendable, confirming the effectiveness of the developed model. HNT length, interphase depth, HNT concentration, net modulus and net portion directly influenced the stiffness, while the HNT radius and percolation onset had inverse effects. Results show that there was a 142% improvement in the modulus of samples at an interphase depth of 40 nm. Moreover, the stiffness improved by 60% at a net modulus of 200 GPa, but it later exhibited a 180% enhancement at a net modulus of 1000 GPa. In addition, the experimental data for the modulus of numerous composites display fine agreement to the predictions, confirming the validity of the developed model.