Skin-effect modeling of carbon nanotube bundles: The high-frequency effective impedance

A bundle of single wall carbon nanotubes (SWCNTs) with circular cross-section is treated as a homogeneous material with a.c. effective conductivity σ(ω), which is evaluated by using the Drude´s complex expression. The effective d.c. conductivity of the homogeneous bundle is obtained from the total d.c. resistance. The frequency-domain distribution of current density along radial direction of the bundle is utilized to obtain the expressions of the skin depth and the effective impedance. Applications of the proposed formulation to SWCNT bundles of different configurations are carried out. The obtained results show the saturation behaviour of the effective resistance and inductance above a critical frequency, which depends on the momentum relaxation time of the CNTs.