Frequency and time domain analysis of carbon nanotubes with realistic shape and distribution

Abstract

Carbon nanotube (CNT) composites have been of significant research interest in a wide range of applications. For electromagnetic applications, simplifying assumptions regarding the distribution and shapes of the CNTs are typically made because the exact three-dimensional CNT distribution in the composite is unknown. The goal of this work is to use experimentally characterized 3D CNT maps to study the effect of distribution and shape of the CNTs on the electromagnetic properties of the composite. Recently, electron tomography techniques have advanced to the point that they are capable of generating 3D maps of Multi-Walled Carbon Nanotubes (MWCNTs) distributions with sub-nanometer resolutions. The electromagnetic responses of these maps were calculated using both full-wave electromagnetic solvers and dilute limit effective medium approximations for multiple CNT volume fractions with different conductivities. The results show that the electromagnetic response calculated using these two methods differs significantly especially at higher terahertz frequencies. By also studying the shapes of CNTs, we found several multi-branched shapes denoted Y-shaped, K-shaped, and T-shaped CNTs. These complex-shaped CNT junctions lead to unique properties that depend on the atomic structure of the carbon atoms in the vicinity of the junction, leading in some cases to a nonlinear conductivity. The electromagnetic scattering characteristics of these nonlinear CNT structures need to be quantified to predict their response to incident electromagnetic radiation. Time-domain electromagnetic codes facilitate the analysis of scatterers with non-linear loads. Therefore, we used the Time Domain Integral Equation (TDIE) formulation and Method of Moments (MoM) to calculate the electromagnetic scattering characteristics of these complex-shaped CNTs structures with nonlinear conductivities. The CNT analysis in this work has the potential to lead to a better understanding of the electromagnetic responses of CNT composites, which will facilitate the accurate nondestructive electromagnetic evaluation of the CNT shapes and distributions, which control the overall mechanical, thermal and electrical properties of these composites.