Resonant and Broadband Microwave Characterization of Single-Walled Carbon Nanotubes

Abstract

We report on microwave measurements of the complex permittivity of single-walled carbon nanotubes (SWNT). The SWNT samples available for the study were a mixture of semiconducting and metallic nanotubes suspended with pluronic (F108) as a stabilizing surfactant agent, either in water or other (less lossy) liquid. Also powdered-form samples of SWNT and pluronic with varying conductivity were fully characterized. For broadband measurements, the shielded open-circuited transmission line technique was used. It is one of the variants of the coaxial transmission line based techniques, which have been used for dielectric properties measurements of solids and liquids for many years. Two different probes (7 mm and 3.5 mm with APC-7 and SMA connectors), both working in the frequency range of 50 MHz to 12 GHz, were utilized for the measurements. Inverse problem solving technique was employed to compute the complex permittivity from the measured Su complex reflection coefficient (labview controlled HP 8710 vector analyzer). The resonant technique measurements included the use of TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">011</sub> mode (3.4 GHz) and TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">011</sub> mode (6.5 GHz) dielectric resonators with cylindrical hole in the center of a dielectric disk. One of the modes should have electric energy concentrated predominantly in the direction perpendicular to the axis of static bias (z-axis) and the other one in the direction parallel to the axis of bias. For the TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">011</sub> mode, the electric field has only an azimuthal component, which is perpendicular to the z-axis, while for the TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">011</sub> mode the electric field has both the axial and radial components. The axial component approaches maximum at the resonator axis while the radial component vanishes there. If the radius of a sample (radius of the inner hole) is relatively small, then the electric energy filling factor in the sample has predominantly the axial component. By employing the dc-electric field along the z-axis of the resonator, two components of a permittivity tensor were calculated using frequency and Q-factor of both modes. Simultaneous measurements of the resonant frequencies and the unloaded Q-factors of the two modes allowed the determination of the two components (parallel and perpendicular) of the complex permittivity tensor. Real part of the permittivity tensor was found by solving characteristic transcendental equations for the specific modes with respect to the appropriate tensor components. An excellent agreement between the complex permittivity data measured with broadband and resonator techniques was achieved. Results of the measurements of the dielectric constant and dielectric loss tangents versus dc bias for two liquid crystals will be presented. In addition, the mechanism of SWNT response to the dc electric field and also their anisotropy properties will be discussed. Some examples of potential electronic and bio-medical application of SWNT will be also shown.