Gary D. Seidel

A Micromechanics Model for the Electrical Conductivity of Nanotube-Polymer Nanocomposites

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.

Computational Micromechanics of Clustering and Interphase Effects in Carbon Nanotube Composites

Computational micromechanical analysis of high-stiffness hollow fiber nanocomposites is performed using the finite element method. The high-stiffness hollow fibers are modeled either directly as isotropic hollow tubes or equivalent transversely isotropic effective solid cylinders with properties computed using a micromechanics based composite cylinders method. Using a representative volume element for clustered high-stiffness hollow fibers embedded in a compliant matrix with the appropriate periodic boundary conditions, the effective elastic properties are obtained from the finite element results. These effective elastic properties are compared to approximate analytical results found using micromechanics methods. The effects of an interphase layer between the high-stiffness hollow fibers and matrix to simulate imperfect load transfer and/or functionalization of the hollow fibers is also investigated and compared to a multi-layer composite cylinders approach. Finally the combined effects of clustering with fiber-matrix interphase regions are studied. The parametric studies performed herein were motivated by and used properties for single-walled carbon nanotubes embedded in an epoxy matrix, and as such are intended to serve as a guide for continuum level representations of such nanocomposites in a multi-scale modelling approach.

Computational micromechanics modeling of inherent piezoresistivity in carbon nanotube–polymer nanocomposites

It has been observed that carbon nanotubes have a measurable inherent piezoresistive effect, that is to say that changes in carbon nanotube strain can induce changes in carbon nanotube resistivity, which may lead to observable macroscale piezoresistive response of carbon nanotube–polymer nanocomposites. In this article, the focus is on modeling the effect of inherent piezoresistivity of carbon nanotubes on the nanocomposite’s piezoresistive behavior using computational micromechanics techniques based on finite element analysis. Both in-plane and axial piezoresistive responses are being considered in an electromechanically coupled code. The computational results are used to estimate the magnitude of the piezoresistive coefficients of carbon nanotube needed for the piezoresistive response of macroscale nanocomposites to be comparable with experimental data in the literature. It is found that the current values for inherent piezoresistivity of the carbon nanotube are not sufficiently large enough to explain the observed macroscale piezoresistive response if inherent piezoresistive effect of carbon nanotubes is the only driving force for the piezoresistive response of the macroscale nanocomposites, and hence, additional mechanisms such as electron hopping and nanotube–nanotube contact may play important roles either individually or in a coupled fashion with inherent piezoresistivity of the carbon nanotube.

Self-sensing of elastic strain, matrix yielding and plasticity in multiwall carbon nanotube/vinyl ester composites

The piezoresistive response of multiwalled carbon nanotube/vinyl ester composites containing 0.3, 0.5 and 1% w/w carbon nanotubes (CNTs) loaded in tension and compression is investigated. The change in electrical resistance (ΔR) under tension loading was positive and showed a linear relationship with the applied strain up to failure, with slightly increased sensitivity for decreased CNT content. In compression, a nonlinear and non-monotonic piezoresistive behavior was observed, with ΔR initially decreasing in the elastic regime, leveling off at the onset of yielding and increasing after matrix yielding. The piezoresistive response of the composite is more sensitive to the CNT content for compression than for tension, and the calculated gage factors are higher in the compressive plastic regime. The results show that the piezoresistive signal is dependent on the CNT concentration, loading type and material elastoplastic behavior, and that recording ΔR during mechanical loading can allow self-identification of the elastic and plastic regimes of the composite.

A Micromechanics Model for the Thermal Conductivity of Nanotube-Polymer Nanocomposites

A micromechanics approach for assessing the impact of an interfacial thermal resistance, also known as the Kapitza resistance, on the effective thermal conductivity of carbon nanotube-polymer nanocomposites is applied, which includes both the effects of the presence of the hollow region of the carbon nanotube (CNT) and the effects of the interactions amongst the various orientations of CNTs in a random distribution. The interfacial thermal resistance is a nanoscale effect introduced in the form of an interphase layer between the CNT and the polymer matrix in a nanoscale composite cylinder representative volume element to account for the thermal resistance in the radial direction along the length of the nanotube. The end effects of the interfacial thermal resistance are accounted for in a similar manner through the use of an interphase layer between the polymer and the CNT ends. Resulting micromechanics predictions for the effective thermal conductivity of polymer nanocomposites with randomly oriented CNTs, which incorporate input from molecular dynamics for the interfacial thermal resistance, demonstrate the importance of including the hollow region in addition to the interfacial thermal resistance, and compare well with experimental data.

Computational micromechanics modeling of piezoresistivity in carbon nanotube–polymer nanocomposites

The macroscale piezoresistive response, i.e. the change in electrical resistivity under the application of strain, of carbon nanotube–polymer nanocomposites has been observed to lead to gauge factors which are much larger than the gauge factors of commonly used strain gauges. Whereas most strain gauges rely on geometric effects, the gauge factors of carbon nanotube–polymer nanocomposites are the result of a combination of nanoscale mechanisms, namely electrical tunneling (electron hopping) and carbon nanotube inherent piezoresistivity, which can lead to substantial differences between the nanocomposite resistivity at zero strain and the resistivity under an applied strain. This paper focuses on modeling the piezoresistive effect of carbon nanotube–polymer nanocomposites by using computational micromechanics techniques based on finite element analysis. For nanocomposites with aligned carbon nanotubes, an electromechanically coupled code is developed for nominal well-dispersed carbon nanotube representative volume elements (RVEs) and for non well-dispersed cases in the aligned and transverse directions. The microscale mechanisms that may have a substantial influence on the overall piezoresistivity of the nanocomposites, i.e. the electrical tunneling effect, and the coupled effect of the electrical tunneling effect and the inherent piezoresistivity of the carbon nanotube, are included in microscale RVEs in order to understand their influence on macroscale piezoresistive response in terms of both the normalized change in effective resistivity and the corresponding effective gauge factor under applied strain. It is found that in the transverse directions, the electrical tunneling effect is the dominant mechanism, and in order for the inherent carbon nanotube piezoresistivity to have a noticeable coupling effect or influence, the local volume fraction of the carbon nanotube should be sufficiently high or the height of barrier of the polymer matrix should be sufficiently low. It is also found that in the axial direction, although the electrical tunneling effect is still the dominant mechanism, the inherent piezoresistivity of the carbon nanotube may have a substantial contribution to the overall axial piezoresistive response.

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.

Damage-Induced Modeling of Elastic-Viscoelastic Randomly Oriented Particulate Composites

This paper presents a model for predicting the damage-induced mechanical response of particle-reinforced composites. The modeling includes the effects of matrix viscoelasticity and fracture, both within the matrix and along the boundaries between matrix and rigid particles. Because of these inhomogeneities, the analysis is performed using the finite element method. Interface fracture is predicted by using a nonlinear viscoelastic cohesive zone model. Rate-dependent viscoelastic behavior of the matrix material and cohesive zone is incorporated by utilizing a numerical time-incrementalized algorithm. The proposed modeling approach can be successfully employed for numerous types of solid media that exhibit matrix viscoelasticity and complex damage evolution characteristics within the matrix as well as along the matrix-particle boundaries. Computational results are given for various asphalt concrete mixtures. Simulation results demonstrate that each model parameter and design variable significantly influences the mechanical behavior of the mixture.

Modeling of mesoscale dispersion effect on the piezoresistivity of carbon nanotube-polymer nanocomposites via 3D computational multiscale micromechanics methods

In uniaxial tension and compression experiments, carbon nanotube (CNT)-polymer nanocomposites have demonstrated exceptional mechanical and coupled electrostatic properties in the form of piezoresistivity. In order to better understand the correlation of the piezoresistive response with the CNT dispersion at the mesoscale, a 3D computational multiscale micromechanics model based on finite element analysis is constructed to predict the effective macroscale piezoresistive response of CNT/polymer nanocomposites. The key factors that may contribute to the overall piezoresistive response, i.e. the nanoscale electrical tunneling effect, the inherent CNT piezoresistivity and the CNT mesoscale network effect are incorporated in the model based on a 3D multiscale mechanical–electrostatic coupled code. The results not only explain how different nanoscale mechanisms influence the overall macroscale piezoresistive response through the mesoscale CNT network, but also give reason and provide bounds for the wide range of gauge factors found in the literature offering insight regarding how control of the mesoscale CNT networks can be used to tailor nanocomposite piezoresistive response.

Computational micromechanics analysis of electron hopping and interfacial damage induced piezoresistive response in carbon nanotube-polymer nanocomposites

Carbon nanotube (CNT)-polymer nanocomposites have been observed to exhibit an effective macroscale piezoresistive response, i.e., change in macroscale resistivity when subjected to applied deformation. The macroscale piezoresistive response of CNT-polymer nanocomposites leads to deformation/strain sensing capabilities. It is believed that the nanoscale phenomenon of electron hopping is the major driving force behind the observed macroscale piezoresistivity of such nanocomposites. Additionally, CNT-polymer nanocomposites provide damage sensing capabilities because of local changes in electron hopping pathways at the nanoscale because of initiation/evolution of damage. The primary focus of the current work is to explore the effect of interfacial separation and damage at the nanoscale CNT-polymer interface on the effective macroscale piezoresistive response. Interfacial separation and damage are allowed to evolve at the CNT-polymer interface through coupled electromechanical cohesive zones, within a finite element based computational micromechanics framework, resulting in electron hopping based current density across the separated CNT-polymer interface. The macroscale effective material properties and gauge factors are evaluated using micromechanics techniques based on electrostatic energy equivalence. The impact of the electron hopping mechanism, nanoscale interface separation and damage evolution on the effective nanocomposite electrostatic and piezoresistive response is studied in comparison with the perfectly bonded interface. The effective electrostatic/piezoresistive response for the perfectly bonded interface is obtained based on a computational micromechanics model developed in the authors? earlier work. It is observed that the macroscale effective gauge factors are highly sensitive to strain induced formation/disruption of electron hopping pathways, interface separation and the initiation/evolution of interfacial damage.