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A two-step methodology has been developed utilizing the models of Paul and Takayanagi to determine the modulus of polymer halloysite nanotube (HNT) products. Initially, HNTs and the adjacent interphase are considered as pseudoparticles, and their modulus is evaluated using the Paul model. Subsequently, the modulus of a nanocomposite, consisting of a polymer medium and pseudoparticles, is predicted by Takayanagi equation. The impacts of various factors on the modulus of the products are analyzed, and the results from the two-step method are compared with experimental data from different samples. It has been observed that the modulus of samples progressively increases with an increase in interphase depth. Also, a higher interphase modulus contributes to an enhanced modulus of samples. Nevertheless, excessively high interphase moduli (E i  > 60 GPa) result in only a marginal improvement in the modulus of nanocomposites. Additionally, narrower HNTs are advantageous for producing stronger samples, though the modulus of the nanocomposites slightly diminishes at very high HNT radii (R > 55 nm). The outputs of two-step method agree with the experimental moduli of various HNT-filled systems., (© 2024. The Author(s).)

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.