INSTITUTE OF PHYSICS PUBLISHING NANOTECHNOLOGY
Nanotechnology 16 (2005) 583–589 doi:10.1088/0957-4484/16/4/041
Chaotic signature in the motion of
coupled carbon nanotube oscillators
V R Coluci
1
, S B Legoas
2
, M A M de Aguiar
1
and D S Galv ˜ ao
1
1
Instituto de F´ ısica ‘Gleb Wataghin’, Universidade Estadual de Campinas, CP 6165,
13083-970 Campinas SP, Brazil
2
Departamento de F´ ısica, Universidade Federal do Amazonas, 69077-000 Manaus AM,
Brazil
E-mail: coluci@ifi.unicamp.br
Received 17 November 2004, in final form 12 January 2005
Published 1 March 2005
Online at stacks.iop.org/Nano/16/583
Abstract
The motion of coupled oscillators based on multiwalled carbon nanotubes is
studied using rigid-body dynamics simulations. The results show the
existence of chaotic and regular behaviours for a given total energy,
indicating the manifestation of chaos in nanoscaled mechanical systems
based on carbon nanotube oscillators. Different regular motions are
observed for different total energies, and they can be obtained by
appropriately choosing the initial conditions. This possibility can allow the
construction of multi-functional nano-devices based on multiwalled carbon
nanotube oscillators.
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1. Introduction
It has become common knowledge that multiwalled carbon
nanotubes (MWNTs) [1] represented a breakthrough in
nanotechnology [2]. New and exciting phenomena have been
observed in these systems [3], including field emission [4],
quantum conductance [5], constant-force nanosprings [6],
as well as proposals for MWNT-based nano-devices [7].
High-resolution transmission electron microscopy (HRTEM)
experiments involving MWNTs have demonstrated an ultra-
low friction telescopic extension of MWNTs, opening up the
possibility of building new kinds of nano-devices such as linear
bearings [6] and nano-oscillators [7].
Analyzing a slightly modified configuration of the
HRTEM experiments of Cumings and Zettl [6], Zheng
and Jiang [7] have proposed an MWNT-based mechanical
oscillator which could oscillate at gigahertz range. The
oscillation mechanism is due to the excess of the van der Waals
potential energy which leads to a restoring force acting on
the MWNT core and causing its retraction to the equilibrium
position [8]. Several studies involving double-walled carbon
nanotubes have been carried out in order to investigate the
operation of such nanotube-based devices [9–16].
An application of carbon nanotube oscillators as building
blocks for nanoscale engines has been investigated by Kang
and Hwang using molecular dynamics simulations [17]. They
have analysed the integration of different nano-devices and
their respective functionalities to simulate the operation of a
nanoscale engine based on carbon nanotube oscillators. This
approach creates the possibility of using integrated carbon
nanostructures in the design of nano-engineering machines.
The goals of the present work are to propose and
study a modification of the carbon nanotube oscillator
configuration [7] in order to allow the movement of more
than one tube. This new configuration can be seen as two
coupled carbon nanotube oscillators and represents a new
building block type for nano-machines. We have demonstrated
that chaotic and regular movements can appear in such a
configuration.
It is well known that oscillator based configurations, such
as the Duffing oscillator and the double pendulum, can exhibit
chaotic behaviours. The irregular behaviour of many physical
systems has been the subject of intense experimental and
theoretical investigations [18, 19]. Chaotic manifestations
can appear in systems with different size scales, from the
quantum domain (the behaviour of a hydrogen atom in an
oscillating electric field [20–22]) to stellar dimensions with,
for instance, the motion of a relativistic three-body self-
gravitating system [23]. The system of two coupled carbon
nanotube oscillators investigated in this work is an example of a
nanoscaled configuration which can exhibit chaotic behaviour.
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