Polarizability tensors of Carbon Nanotubes and Graphene Sheets with realistic shapes

Carbon Nanotube (CNT) and Graphene Sheets (GS) dispersed in composites exhibit a variety of shapes that are controlled by many factors such as how the CNT/GS are fabricated, how they are dispersed, and the material in which the CNT/GS are embedded. The goal of this work is to study how the shape of the CNT and GS affects their electromagnetic properties. A large number of worm-like CNT and crumpled GS with realistic shapes were generated using a coarse-grained molecular dynamics model. The static electric and magnetic polarizability tensors of these worm-like CNT and crumpled GS were calculated. The electric polarizability tensor is defined as the polarizability tensor calculated when the ratio between the dielectric permittivity of the CNT/GS and the dielectric permittivity of the embedding environment is equal to infinity. The magnetic polarizability tensor is the polarizability tensor calculated when the ratio between the dielectric permittivity of the CNT/GS and the dielectric permittivity of the embedding environment is equal to zero. The electric polarizability tensors were calculated using ZENO, which is a Monte Carlo numerical path integration package, and the magnetic polarizability tensors were calculated using the commercial finite element package COMSOL.