The discovery of carbon nanotubes and C 60 fullerenes has created an enormous impact on possible new nanomechanical devices. Owing to their unique mechanical and electronic properties, such as low weight, high strength, flexibility and thermal stability, carbon nanotubes and C 60 fullerenes are of considerable interest to researchers from many scientific areas. One aspect that has attracted much attention is the creation of high-frequency nanoscale oscillators, or the so-called gigahertz oscillators, for applications such as ultrafast optical filters and nano-antennae. While there are difficulties for micromechanical oscillators, or resonators, to reach a frequency in the gigahertz range, it is possible for nanomechanical systems to achieve this. This study focuses on C 60 –single-walled carbon nanotube oscillators, which generate high frequencies owing to the oscillatory motion of the C 60 molecule inside the single-walled carbon nanotube. Using the Lennard-Jones potential, the interaction energy of an offset C 60 molecule inside a carbon nanotube is determined, so as to predict its position with reference to the cross-section of the carbon nanotube. By considering the interaction force between the C 60 fullerene and the carbon nanotube, this paper provides a simple mathematical model, involving two Dirac delta functions, which can be used to capture the essential mechanisms underlying such gigahertz oscillators. As a preliminary to the calculation, the oscillatory behaviour of an isolated atom is examined. The new element of this study is the use of elementary mechanics and applied mathematical modelling in a scientific context previously dominated by molecular dynamical simulation.

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.

A porous treasure: Porous aromatic framework PAF‐1 (see picture, blue structure) has been lithiated, giving a reduced framework with an increased gas storage capacity compared to native PAF‐1 (by 22, 71, and 320 % for H2, CH4, and CO2, respectively). The reduced framework was examined spectroscopically, and the potential hydrogen storage capacity was calculated.

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We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving rise to the Einstein special theory of relativity that applies to relative velocities less than the speed of light. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but, most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions. Making use of the dependence on relative velocity of the Lorentz transformation, the paper provides an elementary derivation of the new transformations between inertial frames for relative velocities v in excess of the speed of light c, and further we suggest two possible criteria from which one might infer one set of transformations as physically more likely than the other. If the energy-momentum equations are to be invariant under the new transformations, then the mass and energy are given, respectively, by the formulae m = (p ∞ /c) [(v/c) 2 − 1] −1/2 and E = mc 2 , where p ∞ denotes the limiting momentum for infinite relative velocity. If, however, the requirement of invariance is removed, then we may propose new mass and energy equations, and an example having finite non-zero mass in the limit of infinite relative velocity is given. In this highly controversial topic, our particular purpose is not to enter into the merits of existing theories, but rather to present a succinct and carefully reasoned account of a new aspect of Einstein's theory of special relativity, which properly allows for faster than light motion.

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