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

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 \u3c theta \u3c 1.4) and decrease with increasing device diameter (Q similar to D(-mu), where 1.4 \u3c mu \u3c 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 \u3e 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 \u3c beta \u3c 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