A novel technique including two steps for modulus prediction in polymer halloysite nanotube composites

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.