Rigorous Characterization of Carbon Nanotube Complex Permittivity Over a Broadband of RF Frequencies

Abstract

This study presents a comprehensive characterization of the frequency dependence of the effective complex permittivity of bundled carbon nanotubes (CNTs) considering different densities over a broadband of frequencies from 10 MHz to 50 GHz using only one measurement setup. The extraction technique is based on rigorous modeling of coaxial and circular discontinuities using a mode matching technique in conjunction with an inverse optimization method to map the simulated scattering parameters to those measured by a vector network analyzer. The dramatic values of complex permittivity obtained at low frequencies are physically explained by the percolation theory. The effective permittivity of a mixture of nanoparticles of alumina and CNTs versus frequency and packing density is studied to verify the previously obtained phenomenon.