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

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.

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

problem.