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.