Broadband characterization of carbon nanotube networks

In this paper, the complex permittivity of carbon nanotube networks is extracted over a broadband of frequencies using a non destructive, simple, and low-cost procedure. The structure holding the material under test is a hollow circular waveguide shorted at one end and connected through precision adapter to the 1.85 mm-50-Ω coaxial cable of performance network analyzer. In this testing configuration, discontinuities between different transmission lines are modeled based on the full-wave mode matching technique. In this modeling, all higher-order modes propagating and evanescent are considered in the computation which produces generalized scattering matrices (GSMs). A gradient-optimization method is used to solve the inverse problem and extract the complex permittivity of material under test from the measured magnitude and phase of reflection coefficient. The technique is general and requires only a small fraction of material under test which can be in liquid, pulverized or solid form.