3D Monte Carlo simulation modeling for the electrical conductivity of carbon nanotube-incorporated polymer nanocomposite using resistance network formation

High electrical and thermal conductivity associated with high stiffness and strength offer tremendous opportunities to the development of a series of carbon nanotube incorporated composite materials for a variety of applications. In particular, a small amount of carbon fibers or carbon nanotubes in a non-conductive polymer will transform a composite into a conductive material, which reveals superb potential of their future application in electronic devices. The relation between the amount of carbon nanotubes in a polymer and the electrical conductivity of it can be studied experimentally as well as theoretically with various simulation models. A three-dimensional (3D) Monte Carlo simulation model using resistance network formation was developed to study the relation between the electrical conductivity of the polymer nanocomposite and the amount of carbon nanotubes dispersed in it. In this model, carbon nanotubes were modeled as curvy cylindrical nanotubes with various lengths and fixed tube diameter, all of which were randomly distributed in a non-conductive constrained volume, which represents polymer. The model can be used to find the volumetric electrical resistance of a constrained cubic structure by forming a comprehensive resistance network among all of the nanotubes in contact. As more and more nanotubes were added into the volume, the electrical conductivity of the volume increases exponentially. However, once the amount of carbon nanotubes reached about 0.1 % vt (volume percentage), electrical percolation was detected, which was consistent with the experimental results. This model can be used to estimate the electrical conductivity of the composite matrix as well as to acquire the electrical percolation threshold.