Carbon nanotubes are long thin tubes made from rolled up single sheets of
graphene. Nanotube resonators have already reached the mass sensitivity
required to measure the mass of single molecules, but in order to detect
smaller (atomic) masses these devices must be further optimized. For this,
a deep understanding of their operational mechanism is required, but simple
analytic models and previous simulations have internal contradictions
leading to questions such as whether the Young's modulus of nanotubes is a
well defined concept.

We have made careful, extensive, atomistic Molecular Dynamics simulations
[1] of nanotubes using the Brenner potential. The nanotube vibrations were
recorded at selected points and decomposed into vibrational modes using a
Fourier Transform technique. The nanotubes were first slowly thermalized to
300 degrees K with periodic boundary conditions then clamped to retain its
at the mean length. Different lengths and radii were studied and we
developed protocols for dealing with the large quantity of data generated.
(Each nanotube is allowed to vibrate 1000 times more than the period of its
lowest frequency and we use a timestep of 0.5fm).

The simulations provide clear evidence for the failure of simplistic
analytic models to accurately extract resonance frequencies as a function
of the ratio between the tube's radius and length as the latter increases.
Our results agree with the Timoshenko beam model (which includes the effect
of both rotary inertia and of shearing deformation) and partially resolve
Yakobson's paradox concerning the Young's modulus, and provide an upper
cutoff estimate for the effective wall thickness. We have further [2] made
a comparison of the vibrational behavior of different types of nanotubes:
zigzag, armchair and two chiral types. This gives the surprising result
that nanotube structure/chirality does not affect the vibrational
frequencies under double clamping conditions. In the laboratory, nanotubes
are not fully clamped as in models and some simulations. Only atomistic
simulations can truly model partial clamping. Our latest simulations with
partial clamping [3] show that under such conditions the degeneracy lifts
and we can propose which type of nanotube would be  the best candidate to
progress towards weighing single atoms.

[1]  P. Pine, Y. Yaish and J. Adler, ``Simulational and vibrational
analysis of thermal oscillations of single-walled carbon nanotubes'', Phys. Rev. B (2011)83 155410.
[2]  P. Pine, Y. Yaish and J. Adler, ``Thermal oscillations of structurally
distinct nanotubes'', Phys. Rev. B, to appear.
[3] P. Pine, Y. Yaish and J. Adler,   ``The affect of boundary conditions on
the vibrations ofarmchair, zigzag and chiral single walled carbon nanotubesג'', JAP, to appear.