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(a) Setup of System
 Single-walled
nanotubes (SWNTs), double-walled nanotubes (DWNTs), and triple-walled
nanotube (TWNT) are considered. In particular, the SWNT is either a
(28,0) or (16,16) nanotube, the DWNT consists of a (19,0)@(28,0) or
(11,11)@(16,16) configuration, and the TWNT consists of a
(10,0)@(19,0)@(28,0) or (6,6)@(11,11)@(16,16). The nanotubes are open
at one end and capped at the other. The open ends are firmly fixed on
space to mimic the attachment of the nanotubes to a rigid surface.
Thermostats are applied to the atoms that are within 20 Å of the
open end to control the system temperature and maintain a temperature
of 300 K. This mimics the transfer of thermal energy from the nanotube
to the rigid surface to which it is attached. The length of nanotubes
is about 215 Å excluding the hemi-spherical caps. All the bonds
that connect the nanotubes and caps are sp2-hybridized,
and all defects at the cap-nanotube interface consist of pentagon and
heptagon rings.
Nine Ar atoms are located in an 8
Å × 8 Å plane 200 Å from the fixed points at
the end of the nanotube, and 20 Å above from the most upper atoms
of the outer nanotube wall. The Ar atoms are propelled once every 2 ps
multiple times (5 or 10) into the nanotubes. The kinetic energy of each
Ar atom is 10 eV, which corresponds to a velocity of 0.0694 Å/fs
(= 6.94 × 103 m/s). After each collision event, the nanotubes are
relaxed 100 ps - 140 ps prior to the deposition of the next group of Ar
atoms.
(b) Deformation of Nanotubes
As the Ar atoms
collide with the nanotube 10 times, the nanotube bends and "rumples"
form in the wall structure. After the Ar collision events have occurred
for 20 ps, the nanotubes are more deformed and remain so for a while.
The SWNT, which is more flexible than the DWNTs and TWNTs, even folds
over during the subsequent relaxation stage.
(c) Displacement of Nanotubes
They indicate that
the SWNTs displace more easily than the DWNTs and TWNTs after repeated
collision events. This is not surprising because of the larger number
of nanotube walls, which raise the mass and overall stiffness of the
nanotube as a whole. Most nanotube tips continue to move in the
direction of Ar flow for 10-30 ps after the last collision event. When
the nanotubes are folded, it takes longer for them to reach minimum
structures. Displacement after the collisions increases as the number
of collisions increase.
Since the
nanotubes flex in an oscillatory manner, the motion of the nanotubes
during the relaxation period can be described in terms of amplitude and
frequency as follows:
where A0 is the estimated amplitude
at the initial state of the relaxation process, f is frequency,
t is time in ps, φ is angular phase shift, and τ is
relaxation time. A0 is greater than the initial
downward-displacement if the oscillation of a nanotube is delayed by φ.
As the length of CNTs increases, A0 increases, φ
increases, τ increases, while f decreases. As the number of CNT
walls increases, A0 increases, φ and decreases.
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