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The introduction of carbon nanotubes (CNTs) into nonconducting polymers has been observed to yield orders of magnitude increases in conductivity at very low concentrations of CNTs. These low percolation concentrations have been attributed to both the formation of conductive networks of CNTs within the polymer and to a nanoscale effect associated with the ability of electrons to transfer from one CNT to another known as electron hopping. In the present work, a micromechanics model is developed to assess the impact of the effects of electron hopping and the formation of conductive networks on the electrical conductivity of CNT-polymer nanocomposites. The micromechanics model uses the composite cylinders model as a nanoscale representative volume element where the effects of electron hopping are introduced in the form of a continuum interphase layer, resulting in a distinct percolation concentration associated with electron hopping. Changes in the aspect ratio of the nanoscale representative volume element are used to reflect the changes in nanocomposite conductivity associated with the formation of conductive networks due to the formation of nanotube bundles. The model results are compared with experimental data in the literature for both single- and multi-walled CNT nanocomposites where it is observed that the model developed is able to qualitatively explain the relative impact of electron hopping and nanotube bundling on the nanocomposite conductivity and percolation concentrations.

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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.

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