Development of Expanded Takayanagi Model for Tensile Modulus of Carbon Nanotubes Reinforced Nanocomposites Assuming Interphase Regions Surrounding the Dispersed and Networked Nanoparticles.

Yasser Zare,Kyong Yop Rhee

doi:10.3390/polym12010233

Abstract

In this paper, we consider the interphase regions surrounding the dispersed and networked carbon nanotubes (CNT) to develop and simplify the expanded Takayanagi model for tensile modulus of polymer CNT nanocomposites (PCNT). The moduli and volume fractions of dispersed and networked CNT and the surrounding interphase regions are considered. Since the modulus of interphase region around the dispersed CNT insignificantly changes the modulus of nanocomposites, this parameter is removed from the developed model. The developed model shows acceptable agreement with the experimental results of several samples. “ER” as nanocomposite modulus per the modulus of neat matrix changes from 1.4 to 7.7 at dissimilar levels of “f” (CNT fraction in the network) and network modulus. Moreover, the lowest relative modulus of 2.2 is observed at the smallest levels of interphase volume fraction ( < 0.017), while the highest “” as 0.07 obtains the highest relative modulus of 11.8. Also, the variation of CNT size (radius and length) significantly changes the relative modulus from 2 to 20.

Highlights

Carbon nanotubes (CNT) have involved significant interest in nanocomposites due to amazing mechanical behavior and good electrical conductivity, as well as nanometer size and high aspect ratio [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
In form 1, the percolation threshold causes a negative effect on the modulus of nanocomposites and the filler volume fractions above percolation threshold decrease the reinforcement of samples, because it assumes that the dispersed nanoparticles bear a higher load compared to the matrix
Equation (1) does not consider a particulate filler shape, but we develop it for the modulus of only polymer CNT nanocomposites in the current study

Summary

Introduction

Carbon nanotubes (CNT) have involved significant interest in nanocomposites due to amazing mechanical behavior and good electrical conductivity, as well as nanometer size and high aspect ratio [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. In form 1, the percolation threshold causes a negative effect on the modulus of nanocomposites and the filler volume fractions above percolation threshold decrease the reinforcement of samples, because it assumes that the dispersed nanoparticles bear a higher load compared to the matrix. The expanded model (form 2) does not consider the interphase regions around the dispersed and networked nanoparticles neglecting the important reinforcing and percolating effects of interphase zone in the modulus. The main novelty of this paper is the development of a simple and applicable model for modulus of PCNT considering the properties of all components such as the dispersed and networked CNT, as well as the surrounding interphase regions. The developed model includes the simple, meaningful, and applicable parameters for prediction of modulus, while the previous models usually disregarded the mechanical percolation, interphase region, and CNT network, or included the complex and baffling parameters

Equations

Evaluation of Model by Experimental Data

Parametric Analyses

Conclusions