Abstract
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.
Highlights
Theoretical studies on the mechanical properties of halloysite nanotube (HNT)-based nanocomposites have neglected the Halloysite nanotubes (HNTs) network and interphase section, despite the fact that the network and interphase have significant stiffening efficiencies
We focus on the Takayanagi model to approximate the modulus of HNT-filled nanocomposites by considering the interphase zones around dispersed and networked HNTs above the percolation onset
The cellulose/HNT sample exhibited the lowest percolation onset of 0.008, whereas polyamide 12 (PA12)/HNT system exhibited the highest percolation onset of 0.024. These results reveal that network formation in the cellulose/HNT sample is faster than that in the PA12/HNT system
Summary
Loos and Manas-Zloczower extended the Takayanagi system by considering networked and dispersed CNTs in the system above the percolation onset[47] as:. Eid and E iN denote the moduli of the interphase zones around dispersed and networked nanoparticles, respectively This equation adequately reflects the reinforcing effects of HNTs and the interphase regions in the system. Where “R” and “l” denote the radius and length of the nanoparticles, respectively, and “t” denotes the interphase depth This equation can be used for HNT-based systems because both CNTs and HNTs have the same shape, and the onset of percolation depends on the filler shape and the nearby interphase section. ΦiN (φi − φiN )EiN + (1 − φiN )2Eid (13) This expression reflects the influences of dispersed and networked HNTs and the adjacent interphase regions on the enhanced modulus of HNT-filled systems.
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