Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/65042
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Type: Journal article
Title: Mechanics of nanotubes oscillating in carbon nanotube bundles
Author: Cox, B.
Thamwattana, N.
Hill, J.
Citation: Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 2008; 464(2091):691-710
Publisher: Royal Soc London
Issue Date: 2008
ISSN: 1364-5021
1471-2946
Statement of
Responsibility: 
Barry J. Cox, Ngamta Thamwattana and James M. Hill
Abstract: Carbon nanotubes are nanostructures that promise much in the area of constructing nanoscale devices due to their enhanced mechanical, electrical and thermal properties. In this paper, we examine a gigahertz oscillator that comprises a carbon nanotube oscillating in a uniform concentric ring or bundle of carbon nanotubes. A number of existing results for nanotube oscillators are employed to analyse the design considerations of optimizing such a device, and significant new results are also derived. These include a new analytical expression for the interaction per unit length of two parallel carbon nanotubes involving the Appell hypergeometric functions. This expression is employed to precisely determine the relationship between the bundle radius and the radii of the nanotubes forming the bundle. Furthermore, several pragmatic approximations are also given, including the relationships between the bundle radius and the constituent nanotube radius and the oscillating tube radius and the bundle nanotube radius. We also present a simplified analysis of the force and energy for a nanotube oscillating in a nanotube bundle leading to an expression for the oscillating frequency and the maximum oscillating frequency, including constraints on configurations under which this maximum is possible.
Keywords: carbon nanotubes; gigahertz oscillators; Lennard-Jones potential; acceptance and suction energies
Rights: Copyright 2008 The Royal Society
RMID: 0020106852
DOI: 10.1098/rspa.2007.0247
Appears in Collections:Mathematical Sciences publications

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