Scattering properties of carbon nanotubes

Andrea G. Chiariello (Department of Industrial and Information Engineering, Seconda Università di Napoli, Aversa, Italy)
Carlo Forestiere (Department of Electrical Engineering and Information Technology, Università di Napoli Federico II, Napoli, Italy)
Giovanni Miano (Department of Electrical Engineering and Information Technology, Università di Napoli Federico II, Napoli, Italy)
Antonio Maffucci (Department of Electrical and Information Engineering, Università di Cassino e del Lazio Neridionale, Cassino, Italy)



Nowadays, nano-antennas or nanoscale absorbers made by innovative materials such as carbon nanotubes are gaining more and more interest, because of their outstanding features. The purpose of this paper is to investigate the scattering properties of carbon nanotubes, either isolated or arranged in arrays. The peculiar behaviour of such innovative materials is studied, taking also into account the finite length of the structure and the dependence of the scattering field from the operating temperature.


First a model is presented for the electrical transport along the carbon nanotubes, based on Boltzmann quasi-classical transport theory. The model includes quantistic and inertial phenomena observed in the carbon nanotube electrodynamics. The model also includes the effects of temperature. Using this electrodynamical model, the electromagnetic formulation of the scattering problem is cast in terms of a Pocklington-like equation. The numerical solution is obtained by means of the Galerkin method, with special care in handling the logarithmic singularity of the kernel. Case studies are carried out, either referred to isolated single-wall carbon nanotubes (SWCNTs) and array of SWCNTs.


The scattering properties of SWCNT are strongly influenced by the temperature and by the distance between the tubes. As temperature increases, the amplitude of the resonance peaks decreases, at a rate which is double the rate of changes of temperature. The resonance frequencies are insensitive to temperature. As for the distance between the tubes in an array, it influence the scattering resonance introducing a shift in the resonance frequencies which is appreciable for distances lower than the semi-length of the CNT. For higher distances the CNT scattered field may be regarded as the sum of the fields emitted by each CNT, as if they were isolated.

Research limitations/implications

As far as now only SWCNTs have been studied. The multi-wall carbon nanotubes would show a richer behaviour with temperature, due to the joint effect of reduction of the mean free path and increase of the number of conducting channels, as temperature increases.

Practical implications

Possible use of carbon nanotubes as absorbing material or scatterers.


The model presented here is based on a self-consistent and physically meaningful description of the CNT electrodynamics, which takes rigorously into account the effect of temperature, size and chirality of each CNT.



This work was supported in part by the EU FP7 CACOMEL Project FP7-247007.


G. Chiariello, A., Forestiere, C., Miano, G. and Maffucci, A. (2013), "Scattering properties of carbon nanotubes", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 6, pp. 1793-1808.

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