Microwave (8-50 GHz) characterization of multiwalled carbon nanotube papers using rectangular waveguides

Multiwalled carbon nanotubes (MWNTs) are characterized at X-, Ku-, Ka-, and Q-bands by rectangular waveguide measurements. The scattering parameters (S-parameters) of thin MWNT papers containing a large ensemble of randomly oriented nanotubes are measured by a vector network analyzer from 8 to 50 GHz. A rigorous extraction algorithm has been developed to compute the effective complex permittivity (ε = ε′ -jε″) and permeability (μ = μ′ -jμ″) of the nanotube papers from the measured S-parameters. The extracted effective medium parameters are verified by finite-element simulations using Ansoft's High Frequency Structure Simulator (HFSS). The uncertainties for this characterization method are analyzed. The systematic uncertainties are found larger at lower frequencies than at higher frequencies. The extracted conductivity of the nanotube papers is in the range of 810-1500 S/m and the dielectric constant is from 250 to 700. The extracted complex permittivity can be fitted with the Drude-Lorentz model for the 8-50-GHz frequency range. The effective medium theory is then applied to remove the impact of air in the nanotube paper.