**Observation of nonclassical scaling laws in the quality factors of
cantilevered carbon nanotube resonators**

AK Vallabhaneni and JF Rhoads and JY Murthy and XL Ruan, JOURNAL OF APPLIED PHYSICS, 110, 034312 (2011).

DOI: 10.1063/1.3611396

This work examines the quality factors (Q factors) of resonance
associated with the axial and transverse vibrations of single-wall
carbon nanotube (SWCNT) resonators through the use of molecular dynamics
(MD) simulation. Specifically, the work investigates the effect of
device length, diameter, and chirality, as well as temperature, on the
resonant frequency and quality factor of these devices and benchmarks
the results of MD simulations against classical theories of energy
dissipation. The quality factor (Q) associated with transverse vibration
is found to increase with increasing device length (Q similar to
L-theta, where 0.8 < theta < 1.4) and decrease with increasing device
diameter (Q similar to D-mu, where 1.4 < mu < 1.6), while the Q
associated with axial vibration is almost independent of length and
diameter. We show that to accurately predict temperature dependence of
Q, the external and internal energies need to be properly decomposed,
and temperature quantum correction should be performed. For both
vibrational modes, Q shows a temperature dependence Q similar to
T-alpha, where alpha > 1 when below Debye temperature due to quantum
effects, and Q gradually recovers the classical T-1 dependence when
above Debye temperature. Our temperature dependence is in contrast to
prior studies that suggested Q similar to T-beta, where 0 < beta < 1.
The observed size and temperature dependencies by us have many
deviations from existing classical theories of energy dissipation,
possibly due to phonon confinement effects in these nanostructures and
temperature quantum effects. (C) 2011 American Institute of Physics.
**doi:10.1063/1.3611396**

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