Development of a model for modulus of polymer halloysite nanotube nanocomposites by the interphase zones around dispersed and networked nanotubes

Theoretical studies on the mechanical properties of halloysite nanotube (HNT)-based nanocomposites have neglected the HNT network and interphase section, despite the fact that the network and interphase have significant stiffening efficiencies. In the present study, the advanced Takayanagi equation for determining the modulus of nanocomposites is further developed by considering the interphase zones around the dispersed and networked HNTs above percolation onset. Furthermore, simple equations are provided to determine the percolation onset of HNTs and the volume portions of HNTs and interphase section in the network. The experimental values obtained for many samples and the assessments of all relevant factors validate the proposed model. The high ranges of HNT concentration, interphase depth, HNT modulus, HNT length, network modulus, interphase modulus, interphase concentration, and network fraction enhance the system modulus. However, the low levels of HNT radius, percolation onset, and matrix modulus can intensify the reinforcing effect. Notably, the moduli of the dispersed HNTs and the surrounding interphase negligibly affect the modulus of the samples. Moreover, HNTs cannot reinforce the polymer medium when the HNT volume fraction is lower than 0.01 and the interphase depth is less than 5 nm.