Energy Dissipation and Intrinsic Loss in Single Walled Carbon Nanotubes due to Anelastic Relaxation

Abstract

Based on the molecular dynamics simulation and an elastic shell model, we investigated the intrinsic loss under dynamic excitations in single walled carbon nanotube (SWCNT) due to the anelastic relaxation mechanism. We quantified the anelastic property of SWCNTs, i.e., the creep compliances, and showed them to be on the order of 1 (TPa-1) and sensitive to both the radius of SWCNT and the loading rate. Furthermore, our study showed that the time scale for a SWCNT to fully achieve its equilibrium elastic property through anelastic relaxation is on the order of nanosecond. This leads to significant intrinsic loss and damping for SWCNT resonators operating at the Gigahertz frequency range. Both the loss angle and quality (Q) factor of SWCNT were found to be strongly dependent on the load frequency. A dissipation peak and thus a low Q factor were observed in the Gigahertz frequency range. On the other hand, high Q factor and low dissipation were achieved in the range of low (< 0.001 GHz) excitation frequency. The predicted influence of load frequency on the Q factor is in good agreement with the recent experimental observations.

Energy Loss in Carbon Nanotube Beam Oscillators due to Anelastic Relaxation

“…Under dynamic excitation f{t) = Fo sin(a)i), it can be shown that (for details, see Refs. [14] and [15]) is phase shift angle between imposed loading and displacement response, which is also referred to as the loss angle and it is a fundamental measure of damping. We note that the quality factor Q is related to the phase shift angle through Q = l/tancp.…”

“…The effect of temperature on the Q factor was studied and the Q factor was found varying from 2 x 10^ at 0.05 K to 1.5 x 10^ at 293 K for a 3 nm long (5, 5) SWCNT. Recently, Zhou et al [14,15] investigated the anelastic relaxation in SWCNT under transverse loading through dynamic indentation. The energy dissipation was observed to depend significantly on the load frequency.…”