Energy Dissipation Mechanisms in Carbon Nanotube Oscillators

Energy transfer from the translational degrees of freedom to phonon modes is studied for isolated systems of two coaxial carbon nanotubes, which may serve as a nearly frictionless nano-oscillator. It is found that for oscillators with short nanotubes (less than $30\mathrm{\AA }$) a rocking motion, occurring when the inner tube is pulled about $1/3$ out of the outer tube, is responsible for significant phonon energy acquisitions. For oscillators with long nanotubes translational energies are mainly dissipated via a wavy deformation in the outer tube undergoing radial vibrations. Frictional forces between ${10}^{-17}$ and ${10}^{-14}\mathrm{N}$ per atom are found for various dissipative mechanisms.

Figure 1

(a) Calculated $K_{\mathrm{r}\mathrm{e}\mathrm{l}}(t)$ for short-tube oscillators ($14.5/14.5\AA$): three values of $s=5$, 10, $12\AA$. Configurational graphs are drawn for (A) before the onset of the rocking motion (B) during the rocking motion (C) after the rocking motion. All except for $s=5\AA$, portions of translational energies are transferred into $K_{\mathrm{r}\mathrm{e}\mathrm{l}}(t)$ within 400 ps from the start of the simulation. (b) The center of mass displacements of two nanotubes for $s=12\AA$: solid line: inner tube; dashed line: outer tube. The frequency of translational oscillations long after the leap of acquired phonon kinetic energies is about 140 GHz.

Figure 2

(a) Calculated $K_{\mathrm{r}\mathrm{e}\mathrm{l}}(t)$ for long-tube oscillators ($70/55\AA$): two values of $s=7.5,27.5\AA$. Inset: a demonstration of the wavy deformation in the outer tube. The wavelength is $30\AA$. (b) Comparison of $K_{\mathrm{r}\mathrm{e}\mathrm{l}}(t)$ with and without freezing the atoms in the outer tube for $s=55.5\AA$. The frequency of the wavy deformation of the outer tube is found to be about 2 terahertz. The 40 GHz modulation in the $K_{\mathrm{r}\mathrm{e}\mathrm{l}}(t)$ corresponds to twice the frequency of the translational oscillation. A third curve near the bottom with a steplike jump near 300 ps is the calculated $K_{\mathrm{r}\mathrm{e}\mathrm{l}}(t)$ for a mixed-tube oscillator ($70/14.5\AA$) with an initial extrusion length $s=12.25\AA$.