Ngamta Thamwattana

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

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 C60 fullerenes could feasibly operate at these high frequencies. This paper investigates the suction force experienced by either an atom or a C60 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 C60 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.

Mechanics of atoms and fullerenes in single-walled carbon nanotubes. II. Oscillatory behaviour

The discovery of carbon nanotubes and C60 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 C60 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 C60–single-walled carbon nanotube oscillators, which generate high frequencies owing to the oscillatory motion of the C60 molecule inside the single-walled carbon nanotube. Using the Lennard-Jones potential, the interaction energy of an offset C60 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 C60 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.

Mechanics of nanotubes oscillating in carbon nanotube bundles

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.

Orientation of spheroidal fullerenes inside carbon nanotubes with potential applications as memory devices in nano-computing

A spheroid is an ellipsoid for which two of the axes are equal, and here the interaction between spheroidal fullerenes and carbon nanotubes is modeled using the Lennard–Jones potential and the continuum approximation. The resulting surface integrals are evaluated analytically for a number of configurations, including lying and standing as well as spheroids with an arbitrary tilt angle, and centered on the nanotube axis. Analytical expressions for off-axis spheroids in all three orientations are also given, and the findings are shown to agree well with previously published work. However, the major contribution of this work is the derivation of new exact analytical formulae to calculate the van der Waals interaction energy for these configurations, and in particular the results for the tilting and off-axis configurations which are far more general than those which have appeared in the literature previously. From these exact expressions, five primary regimes are identified: lying on-axis, tilting on-axis, standing on-axis, standing off-axis and finally lying off-axis. Also identified in this study is a precisely prescribed radius, for the transition between regimes four and five, for which two equally energetically favorable orientations exist and for which these two configurations are separated by a known energy barrier. The notion arises that such configurations may be exploited for nano-scaled memory devices used in nano-computing.

Mechanics of fullerenes oscillating in carbon nanotube bundles

In this paper, we examine the mechanics of a nano-scaled gigahertz oscillator comprising a fullerene that is moving within the center of a bundle of carbon nanotubes. Although numerical results specifically for a C60 fullerene are presented, the method is equally valid for any fullerene which can be modeled as a spherical molecule. A general definition of a nanotube bundle is employed which can comprise any number of parallel carbon nanotubes encircling the oscillating fullerene. Results are presented which prescribe the dimension of the bundle for any nanotube radius and the optimal configurations which give rise to the maximum suction energy for the fullerene. Prior results for fullerene single-walled nanotube oscillators are employed, and new results are also derived. These include a calculation of optimum nanotube bundle size to be employed for a C60-nanotube bundle oscillator, as well as new analytical expressions for the force and energy for a semi-infinite nanotube and a fullerene not located on the axis of the cylinder.

Electric field-induced force between two identical uncharged spheres

The problem of electric field-induced force between spheres is fundamental to electrorheological fluids. Previously published experimental results indicate that the interaction force between two spheres under an external field is not adequately explained by the existing approximate and numerical methods. The specific models compared were dipole, dipole with local field corrections and a finite-element analysis. This letter employs an exact solution (via the equivalent multipole-moment method) to the electrostatic problem which accurately predicts the low-frequency experimental results at all measured interstices. The solution presented later is self-contained and addresses specifically the geometry of the previously mentioned experimental results. While more general solutions have been published previously, they are more complex than is required by this problem. The solution presented here is accurate for all sphere spacings, but in particular could apply to nano-spheres in close proximity.

Modelling peptide nanotubes for artificial ion channels

We investigate the van der Waals interaction of D,L-Ala cyclopeptide nanotubes and various ions, ion-water clusters and C(60) fullerenes, using the Lennard-Jones potential and a continuum approach which assumes that the atoms are smeared over the peptide nanotube providing an average atomic density. Our results predict that Li(+), Na(+), Rb(+) and Cl(-) ions and ion-water clusters are accepted into peptide nanotubes of 8.5 Å internal diameter whereas the C(60) molecule is rejected. The model indicates that the C(60) molecule is accepted into peptide nanotubes of 13 Å internal diameter, suggesting that the interaction energy depends on the size of the molecule and the internal diameter of the peptide nanotube. This result may be useful for the design of peptide nanotubes for drug delivery applications. Further, we also find that the ions prefer a position inside the peptide ring where the energy is minimum. In contrast, Li(+)-water clusters prefer to be in the space between each peptide ring.

Continuum modelling for carbon and boron nitride nanostructures

Continuum based models are presented here for certain boron nitride and carbon nanostructures. In particular, certain fullerene interactions, C(60)-C(60), B(36)N(36)-B(36)N(36) and C(60)-B(36)N(36), and fullerene-nanotube oscillator interactions, C(60)-boron nitride nanotube, C(60)-carbon nanotube, B(36)N(36)-boron nitride nanotube and B(36)N(36)-carbon nanotube, are studied using the Lennard-Jones potential and the continuum approach, which assumes a uniform distribution of atoms on the surface of each molecule. Issues regarding the encapsulation of a fullerene into a nanotube are also addressed, including acceptance and suction energies of the fullerenes, preferred position of the fullerenes inside the nanotube and the gigahertz frequency oscillation of the inner molecule inside the outer nanotube. Our primary purpose here is to extend a number of established results for carbon to the boron nitride nanostructures.

Oscillation of carbon molecules inside carbon nanotube bundles

In this paper, we investigate the mechanics of a nanoscaled gigahertz oscillator comprising a carbon molecule oscillating within the centre of a uniform concentric ring or bundle of carbon nanotubes. Two kinds of oscillating molecules are considered, which are a carbon nanotube and a C(60) fullerene. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the nanotube-bundle and the C(60)-bundle oscillators. 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 of the nanoscaled oscillators. The paper presents a synopsis of the major results derived in detail by the present authors (Cox et al 2007 Proc. R. Soc. A 464 691-710 and Cox et al 2007 J. Phys. A: Math. Theor. 40 13197-208).

Zigzag and spiral configurations for fullerenes in carbon nanotubes

The success or otherwise of nanoscale devices hinges on a correct understanding of the physical effects at this scale. Research in nanotechnology is predominantly through either experimentation using electron and atomic force microscopy or through large-scale computation using molecular dynamics simulation. In this paper, we employ elementary mechanical principles and classical modelling procedures to investigate the packing of C60 fullerene chains inside a single-walled carbon nanotube by utilizing the Lennard–Jones potential function and the continuum approximation. Such assemblies are often referred to as nanopeapods. We examine both zigzag and spiral chain configurations inside (10, 10), (16, 16) and (20, 20) carbon nanotubes and we obtain analytical expressions in terms of hypergeometric functions for the potential energy for such configurations. We find that for a (10, 10) tube, the C60 fullerene chain is formed linearly along the tube axis. In the case of both (16, 16) and (20, 20) tubes, both zigzag and spiral configurations are more clearly evident along the tube. In particular, the resulting pattern obtained for the zigzag chain is entirely consistent with a specific angular spacing for the spiral pattern.