Mechanics of nanotubes oscillating in carbon nanotube bundles

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.

Carbon molecules oscillating in carbon nanotube bundles

“…certain sections of this paper, it is convenient to assume 0 d z i < f or assume -f < z i < f. As derived in [1], the analytical expression E tt for the interaction potential per unit length of two parallel carbon nanotubes is given in terms of the Appell hypergeometric functions of two variables, thus 2 2 3 5 1 2 1 2 2 2 2 4 3 5 31 , , ,1,1; , 2 2 22…”

“…We refer to Cox et al [1] for a detailed analytical evaluation of (5). For a (5,5) carbon nanotube of length 30 Å entering a sixfold symmetry bundle of (5,5) nanotubes and of semiinfinite length, using (5) we plot the total energy E tot versus the position Z of the central tube, for different sizes of bundle radius R, as shown in Fig.…”

“…While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques which provides considerable insight into the underlying mechanisms. The paper presents a synopsis of the major results derived in detail by the present authors in [1,2]. Abstract-Fullerenes C 60 and carbon nanotubes are of considerable interest to researchers from many scientific areas due to their unique electronic and mechanical properties.…”

“…We note that the nanotube-bundle oscillators have previously been studied by Kang et al [11] using molecular dynamics simulations. However, here and in [1,2] a more general definition of a bundle is adopted than that of Kang et al [11]. Here we consider a bundle to comprise an integral number N of carbon nanotubes aligned parallel to and equidistant from a common axis, which is termed the bundle axis.…”

Restricted Three Body Problems at the Nanoscale

“…In addition, Cox et al [4,5] show that the gigahertz oscillatory behavior arises from the two peak-like forces operating at the nanotube's open ends. The analytical model of Cox et al [4,5] is also extended to examine some more complicated structures of the gigahertz oscillators, including the nanotube bundle oscillators, for which a single nanotube or a C 60 fullerene oscillates inside the bundle [6,7]. For other types of nanoscale oscillators, Hilder and Hill [13,14] find that the gigahertz frequencies can also be obtained from a sector of a nanotube orbiting inside a carbon nanotorus and an atom and a C 60 fullerene orbiting inside a nanotorus.…”