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

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.