An applicable model for the modulus of polymer halloysite nanotubes samples by the characteristics of halloysite nanotubes, interphase zone and filler/interphase network

The simple and applicable models predicting the mechanical properties of halloysite nanotubes (HNT)-based samples are extremely limited despite the experimental characterizations. It is important to consider the HNT network and nearby interphase section in the models, because big and thin HNT produce the network after percolation onset reinforcing the samples. Additionally, Ji model as a multiphase equation does not reflect the networks of nanoparticles and interphase section for the modulus of samples above percolation onset. In this paper, Ji model is progressed for the modulus of polymer HNT system containing the networks of HNT and adjacent interphase zone. The moduli and volume portions of networked HNT and nearby interphase section are expressed by simple equations and meaningful factors. The outputs of the advanced model at numerous ranges of all factors are discussed and verified. Also, the calculations of the progressed model accurately follow the experimental values of numerous samples. The modulus of system improves by 350% at the smallest range of HNT radius (=25 nm) and the highest value of interphase depth (=35 nm), while thick HNT and thin interphase cause the slight reinforcing. The network modulus of 600 GPa and the interphase modulus of 100 GPa produce the maximum modulus improvement as 150%. Moreover, poor polymer media and large HNT are desirable for the modulus of samples, whereas a strong polymer medium and short HNT slightly improve the stiffness.