Elastic wave velocities in single-walled carbon nanotubes

This paper reports an atomistic simulation of single-walled carbon nanotubes subjected to harmonic waves, using the molecular structural mechanics method and normal mode superposition. The velocities of longitudinal, transverse, and torsional waves propagating in single walled carbon nanotubes are obtained. The results indicate that the longitudinal wave velocity is roughly twice as much as that of torsional wave. The velocity of the transverse wave in carbon nanotubes is dependent on wave frequency. The nanotube diameter and chirality also have some effects on wave propagation, especially on the torsional wave. The frequency of wave propagating in carbon nanotubes can reach the terahertz range.

Figure 1

(Color online) Three different incident waves: (a) Longitudinal incident wave; (b) transverse incident wave; and (c) torsional incident wave. (The arrows indicate the vibrational directions of incident waves).

Figure 2

(Color online) Standing waves formed in a SWCNTs: (a) Longitudinal wave; (b) transverse wave; and (c) torsional wave.

Figure 3

(Color online) Relationship between wavelength and wave frequency.

Figure 4

(Color online) Propagation velocity of longitudinal wave in SWCNTs.

Figure 5

(Color online) Propagation velocity of transverse wave in SWCNTs.

Figure 6

(Color online) The effect of nanotube diameter on the velocity of torsional wave.