Computational micromechanics analysis of electron-hopping-induced conductive paths and associated macroscale piezoresistive response in carbon nanotube–polymer nanocomposites

Abstract

In this study, a computational model is developed using finite-element techniques within a continuum micromechanics framework to capture the effect of electron-hopping-induced conductive paths at the nanoscale which contribute to the macroscale piezoresistive response of the nanocomposite. This is achieved by tracking the position of the nanotubes under applied deformations and modifying the conductivity of the intertube region depending on the relative proximity of individual pairs of nanotubes. The formation and disruption of the electron-hopping pathways are highly dependent on intertube distances and under deformations can result in microstructural rearrangements in terms of electrostatic properties leading to transitions in material symmetries and component magnitudes of the effective electrostatic properties. Thus, in order to capture the complexities of changing inhomogeneous nanoscale electrostatic behavior, where analytical Eshelby's approaches cannot be used, a computational micromechanics model is needed. The effective conductivity and piezoresistive strain tensor coefficients are evaluated using volume-averaged energy equivalencies for aligned CNT-polymer nanocomposites in the transverse direction exploring different volume fractions of CNTs in the polymer and the maximum electron-hopping range. The impact of the electron-hopping mechanism on the effective piezoresistive response is studied through the macroscale effective gauge factors under different loading conditions. The effective piezoresistive strain coefficients and macroscale effective gauge factors are observed to be nonlinear with applied macroscale strain and are highly dependent on the type of boundary conditions. The effective macroscale gauge factors observed in the current study have magnitudes comparable to experimental observations reported in the literature with higher gauge factors observed closer to the percolation threshold.

Electro-mechanical studies of multi-functional glass fiber/epoxy reinforced composites

“…In their findings, the determined gauge factors are much larger than the gauge factors of commonly used strain gauges. Using similar framework, recently, Chaurasia and Seidel 22 also captured the effect of electron-hopping-induced conductive paths at the nanoscale which contribute to the macro-scale piezoresistive response of the nanocomposite. In their approach, they tracked the position of the nanotubes under applied deformations and modified the conductivity of the intertube region depending on the relative proximity of individual pairs of nanotubes.…”

Computational Modeling and Experimental Characterization of Macroscale Piezoresistivity in Aligned Carbon Nanotube and Fuzzy Fiber Nanocomposites

“…8. In some of our earlier work, 38,39 it was shown that the uniform local macroscale strains applied to the nanoscale RVE as displacement boundary conditions lead to a change in the nanoscale intertube distances for the nanoscale RVE with perfectly bonded interface, resulting in an increased effective conductivity when subjected to compressive strains and a reduced effective conductivity for applied tensile strains. It was further observed that the change in effective conductivity was closely related to the formation of vertical and diagonal bands of increased/reduced conductivity in the polymer medium representative of electron hopping across the nanotubes.…”

“…38 The key idea is that the sides BC and AD are free to move in thex 1 direction while displacement boundary conditions, representative of macroscale uniform strain state, are applied in edges AB and CD of the nanoscale RVE (Fig. 1).…”

“…The details of the finite element implementation of electron hopping and inherent piezoresistivity are provided in some of our previous work. 38,39,48 Once the electromechanical BVP is solved at each time increment, micromechanics based energy equivalence principles are invoked to find the effective properties of the nanoscale RVE. The effective nanoscale or microscale conductivities, for the hexagonally packed CNTs in polymer matrix or for the fuzzy fibers in polymer matrix, are obtained from the volume averaged representation of Ohm's law.…”

“…26,[33][34][35][36][37] In this study, a finite element based computational continuum micromechanics method is developed to study the changing CNT-polymer morphology at the nanoscale, the subsequent changing electron hopping pathways in between nanotubes and their effect on the macroscale piezoresistive response of nanocomposites. 38,39 The interfacial damage of the CNT-polymer interphase is addressed through mechanical [40][41][42][43][44] and electrostatic cohesive zones in order to study the effect of interfacial damage on the effective piezoresistive response of CNT-polymer nanocomposites. In addition, the piezoresistive response of fuzzy fiber epoxy nanocomposite is studied through a 3-scale computational model allowing for electron hopping, inherent piezoresistivity and matrix damage at the nanoscale.…”