Force distribution for double-walled carbon nanotubes and gigahertz oscillators |
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Authors: | Duangkamon Baowan James M Hill |
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Institution: | (1) Nanomechanics Group School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia |
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Abstract: | Advances in nanotechnology have led to the creation of many nano-scale devices and carbon nanotubes are representative materials
to construct these devices. Double-walled carbon nanotubes with the inner tube oscillating can be used as gigahertz oscillators
and form the basis of possible nano-electronic devices that might be instrumental in the micro-computer industry which are
predominantly based on electron transport phenomena. There are many experiments and molecular dynamical simulations which
show that a wave is generated on the outer cylinder as a result of the oscillation of the inner carbon nanotube and that the
frequency of this wave is also in the gigahertz range. As a preliminary to analyze and model such devices, it is necessary
to estimate accurately the resultant force distribution due to the inter-atomic interactions. Here we determine some new analytical
expressions for the van der Waals force using the Lennard–Jones potential for general lengths of the inner and outer tubes.
These expressions are utilized together with Newton’s second law to determine the motion of an oscillating inner tube, assuming
that any frictional effects may be neglected. An idealized and much simplified representation of the Lennard–Jones force is
used to determine a simple formula for the oscillation frequency resulting from an initial extrusion of the inner tube. This
simple formula is entirely consistent with the existing known behavior of the frequency and predicts a maximum oscillation
frequency occurring when the extrusion length is (L
2 – L
1)/2 where L
1 and L
2 are the respective half-lengths of the inner and outer tubes (L
1 < L
2). |
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Keywords: | 33C05 33C75 81V45 81V55 |
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