Force distribution for double-walled carbon nanotubes and gigahertz oscillators

被引:0
|
作者
Duangkamon Baowan
James M. Hill
机构
[1] University of Wollongong,Nanomechanics Group School of Mathematics and Applied Statistics
来源
Zeitschrift für angewandte Mathematik und Physik | 2007年 / 58卷
关键词
33C05; 33C75; 81V45; 81V55; Double-walled carbon nanotubes; hypergeometric functions; Appell’s hypergeometric functions; oscillatory behavior;
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学科分类号
摘要
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 (L2 – L1)/2 where L1 and L2 are the respective half-lengths of the inner and outer tubes (L1 < L2).
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页码:857 / 875
页数:18
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