The first four flexural thermal vibrational modes of single-walled carbon nanotubes (SWCNTs) of various lengths and radii were studied using atomistic molecular dynamics within the framework of the Brenner interatomic potential and Fourier analysis. These simulations provide clear evidence for the failure of simplistic analytic models to accurately extract resonance frequencies as the ratio $R/L$ between the tube radius and the length increases. They are in excellent agreement with the Timoshenko beam model, which includes the effect of both rotary inertia and of shearing deformation. In addition, our results partially resolve Yakobson’s paradox and provide an upper cutoff estimate for the effective SWCNT thickness.

• Received 22 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.155410