Atomistic simulations of vibration of carbon nanotubes: is it possible to measure the mass of a single atom?

Polina Pine, Yuval Yaish and Joan Adler

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 (2011)84, 245409.
[3] P. Pine, Y. Yaish and J. Adler,   ``The affect of boundary conditions on
the vibrations ofarmchair, zigzag and chiral single walled carbon nanotubes×’'', JAP, in proof

Visualization of Carbon, Boron, and Silicon single walled nanotubes

David Mazvovsky and Joan Adler

In recent years it has been observed that the classic folding model for single walled nanotubes by Dresselhaus and Dresselhaus fails to predict the correct radii for a given chiral vector. Simple molecular dynamics and ab initio calculations as well as physical measurements have discovered discrepancies with the current model predictions. A new polyhedral folding model has been proposed by Lee, Cox and Hill. In this talk we describe our realization of this model which incorporates the effects due to curvature that are observed in real nanotubes and produces a better approximation for the tube's radii. We developed a cross-platform code that outputs atomic coordinates for a given chiral vector.


Simulation of shear elastic moduli of copper near surfaces

Alex Kouniavsky, Emil Polturak and Joan Adler

We study elastic properties of copper both in bulk and near surfaces during
melting. The general melting process is not fully understood to date; many
aspects of this process remain open. According to the theoretical model of
melting, we expect that at the melting temperature the elastic shear modulus,
G', has to vanish. But experiments show that  G' has nonzero values at the
melting temperature. The reason for the discrepancy is the impossibility of
making shear modulus measurements for the surface alone. Therefore, the only
way to study elastic shear modulus behaviour on the surface is by using
simulations. These allow us to apply shear stress on a limited number of layers
near the surface only. Since we have to describe processes with time scales of
10-9 seconds and even more we cannot implement standard MD stress-
fluctuation and strain-fluctuation methods of calculation of elastic constants
which are only suitable for time scales of 10-15-10-12
seconds. Thus we have to use the direct method for the calculation of the
shear modulus where  one applies a constant stress,and determines the
average strain in the system and then obtains the elastic constants from the
stress-strain relation. This method is not  widely applied  due to the
required multiplicity of runs, but modern computer clusters, such as the
Technion's NANCO, and parallelization techniques allow us overcome this