Mechanics of atoms and fullerenes in single-walled carbon nanotubes. I. Acceptance and suction energies

Abstract

Owing to their unusual properties, carbon nanostructures such as nanotubes and fullerenes have caused many new nanomechanical devices to be proposed. One such application is that of nanoscale oscillators which operate in the gigahertz range, the so-called gigahertz oscillators. Such devices have potential applications as ultrafast optical filters and nano-antennae. While there are difficulties in producing micromechanical oscillators which operate in the gigahertz range, molecular dynamical simulations indicate that nanoscale devices constructed of multi-walled carbon nanotubes or single-walled carbon nanotubes and C 60 fullerenes could feasibly operate at these high frequencies. This paper investigates the suction force experienced by either an atom or a C 60 fullerene molecule located in the vicinity of an open end of a single-walled carbon nanotube. The atom is modelled as a point mass, the fullerene as an averaged atomic mass distributed over the surface of a sphere. In both cases, the carbon nanotube is modelled as an averaged atomic mass distributed over the surface of an open semi-infinite cylinder. In both cases, the particle being introduced is assumed to be located on the axis of the cylinder. Using the Lennard-Jones potential, the van der Waals interaction force between the atom or C 60 fullerene and the carbon nanotube can be obtained analytically. Furthermore, by integrating the force, an explicit analytic expression for the work done by van der Waals forces is determined and used to derive an acceptance condition, that is whether the particle will be completely sucked into the carbon nanotube by virtue of van der Waals interactions alone, and a suction energy which is imparted to the introduced particle in the form of an increased velocity. The results of the acceptance condition and the calculated suction energy are shown to be in good agreement with the published molecular dynamical simulations. In part II of the paper, a new model is proposed to describe the oscillatory motion adopted by atoms and fullerenes that are sucked into carbon nanotubes.

Modelling interaction of atoms and ions with graphene

“…In this Letter, the authors adopt the 6-12 L-J potential together with the continuous approach employed by Cox et al [12,13] to evaluate such interactions and find that although the methodology provides only average values for the intermolecular spacing and the diffusion time, these results are comparable to those obtained from time-consuming molecular dynamics simulation. Although some subtle physical effects are ignored using the current methodology, it can be seen to provide reasonable predictions, for example the minimum possible battery size, the maximum battery capacity and better battery performance.…”

“…In this Letter, we adopt the approach employed by Cox et al [12,13] who employ the 6-12 Lennard-Jones (L-J) potential and further assume that carbon atoms are evenly distributed across the surface of carbon nanostructures so that the total potential energy between various non-bonded carbon nanomolecules can be determined analytically by performing a surface integral. Such total potential energy can be used to investigate the relative motions of quite complicated nanostructures, such as the oscillatory motion of a fullerene inside a single-walled carbon nanotube.…”

“…The authors comment that following the L-J description for atomic interaction by Jones [18], many theoretical efforts have been made to improve the accuracy of the results by taking into account dielectric properties of the surface [19]. Next, it is assumed that the carbon atoms are smeared across the surface of the graphene sheet and the continuous approach developed by Cox et al [12,13] is adopted to determine the total potential energy of the single atom/ion and the graphene sheet system, which is stated as…”

Modelling water molecules inside cyclic peptide nanotubes

“…The continuum approach using the Lennard-Jones potential was first introduced by Girifalco (1991) for the interaction between two C 60 molecules. Subsequently, the approach has been successfully adopted in other studies, such as and Cox et al (2007aCox et al ( , b, 2008) to obtain explicit analytical criteria for the interaction potentials involving carbon nanostructures. Furthermore, studies of interactions involving biological materials, such as lipid bilayers, lipid nanotubes and liposomes (Baowan et al 2012;Baowan and Thamwattana 2014;Baowan et al 2013), have also indicated that this approach produces results in good agreement with intensive computational studies.…”

A carbon atom orbiting around the outside of a carbon nanotube

“…Here, in this paper, we investigate a related dynamical system that has potential to produce an orbiting motion with a gigahertz frequency. In particular, we examine a carbon atom orbiting around the outside of a (6,6) carbon nanotube, where the circular orbiting frequency is found to be in the gigahertz range, which is comparable to the oscillating frequencies of gigahertz oscillators. The van der Waals force is modeled by the Lennard-Jones potential, which is assumed to be the only interaction between the carbon atom and the atoms of the molecule.…”