Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration

In this work we investigate the rainbows appearing in channeling of 1 GeV protons through the long (11,9) single-wall carbon nanotubes. The nanotube length is varied from 10 to 500 μm. The angular distributions of channeled protons are computed using the numerical solution of the proton equations of motion in the transverse plane and the Monte Carlo method. The rainbows are identified as the rings in the angular distributions, which correspond to the extrema of the proton deflection functions. Each rainbow is characterized by a sharp decrease of the proton yield on its large angle side. As the nanotube length increases, the number of rainbows increases and the average distance between them decreases in an easily predictable way. When the average distance between the rainbows becomes smaller than the resolution of the angular distribution, one cannot distinguish between the adjacent rainbows, and the angular distribution becomes equilibrated. We call this route to equilibration the rainbow route to equilibration. This work is a demonstration of how a simple one-dimensional bound dynamic system can exhibit a complex collective behavior.     

Atomic particle channeling simulation in carbon nanotubes

The ion distributions of vibration and rotation energies, as well as of the degree of torsion at the nanotube outlet, have been calculated via mathematical simulation of molecular hydrogen ion channeling in a carbon nanotube. The observed resonance effects have been analyzed. It is found that the probability of ion detection increases near the axis of a chiral carbon nanotube.     

The effect of crystal atomic chain discontinuity upon channeling

It is shown that diffusion of transversal energy due to discontinuity of atomic chains decreases exponentially, when the transversal energy decreases.     

Diffraction and channeling in nanotubes

A theory of the interaction of fast charged particles and gamma rays with nanotubes with different helicity is developed. Analytical expressions are obtained for the potential and the electron density of a nanotube taking account of the anisotropic thermal vibrations of the atoms. A system of equations determining the quantum states of the transverse motion of relativistic electrons, positrons, and x-ray photons in a superlattice consisting of nanotubes is formulated, and methods for solving this system are developed. Calculations of the soft x-ray Bragg reflection coefficients of a superlattice are performed in the two-wave approximation of the dynamical theory of diffraction.     

Chemisorption of atomic hydrogen in graphite and carbon nanotubes

An orthogonal tight-binding model of the carbon-hydrogen interaction was modified to deal with the different hybridization states of atomic hydrogen on carbon surfaces, without explicitly including charge self-consistency. The resulting model has great flexibility and computational efficiency, generally with a good quantitative accuracy. The non-self-consistent C-H model was tested by calculating structural properties of small hydrocarbons and simple polymers, and against ab initio results of H binding to both perfect and defective graphite. The model was employed to study the chemisorption properties and dynamics of atomic hydrogen on perfect and defective surfaces of graphite and carbon nanotubes.     

A hybrid continuum and molecular mechanics model for the axial buckling of chiral single-walled carbon nanotubes

The purpose of this study is to describe the axial buckling behavior of chiral single-walled carbon nanotubes (SWCNTs) using a combined continuum-atomistic approach. To this end, the nonlocal Flugge shell theory is implemented into which the nonlocal elasticity of Eringen incorporated. Molecular mechanics is used in conjunction with density functional theory (DFT) to precisely extract the effective in-plane and bending stiffnesses and Poisson's ratio used in the developed nonlocal Flugge shell model. The Rayleigh-Ritz procedure is employed to analytically solve the problem in the context of calculus of variation. The results generated from the present hybrid model are compared with those from molecular dynamics simulations as a benchmark of good accuracy and excellent agreement is achieved. The influences of small scale factor, commonly used boundary conditions and chirality on the critical buckling load are fully explored. It is indicated that the importance of the small length scale is affected by the type of boundary conditions considered.     

Nanoscale atomic waveguides with suspended carbon nanotubes

We propose an experimentally viable setup for the realization of one-dimensional ultracold atom gases in a nanoscale magnetic waveguide formed by single doubly-clamped suspended carbon nanotubes. We show that all common decoherence and atom loss mechanisms are small, guaranteeing a stable operation of the trap. Since the extremely large current densities in carbon nanotubes are spatially homogeneous, our proposed architecture allows for creation of a very regular trapping potential for the atom cloud. Adding a second nanowire allows creation of a double-well potential with a moderate tunneling barrier which is desired for tunneling and interference experiments with the advantage of tunneling distances being in the nanometer regime. PACS 03.75.Gg; 03.75.Dg; 73.63.Fg     

Focusing of atomic and molecular beams in electric fields of various configuration

The properties of an axisymmetric electrostatic lens used for focusing atomic or molecular beams were studied. The lens was formed by a dip in an electric field in the axial direction. Two types of interaction between the particles and the electric field were studied: quadratic and linear in field. An analytical approximation of the dependence of the focal distance of the lens on the beam energy and the parameters of the electric field was obtained. Chromatic and spherical aberrations of the lens were determined.     

Role of vacancies and adsorbed atoms in the channeling of molecular particles in CNTs

The channeling of atomic and molecular particles in carbon nanotubes is considered in the presence of vacancies on the walls and of adsorbed atoms inside them. It is shown that the significant influence of the indicated disturbance of nanotube structures greatly affects channeling, which makes it possible to use beams of atomic and molecular particles to probe nanotubes.     

On the role of structural defects during particle channeling through carbon nanotubes

The formation of structural defects during particle-flux channeling in an array of nanotubes is studied by the molecular dynamic method. The approach accounts for the formation of defects by means of the AIREBO potential. The characteristic dependences of the energy of the channeling particles on time are considered. Data are obtained on the types of effects formed and the energy of their formation.     

Linking chiral indices and transport properties of double-walled carbon nanotubes

We performed in situ transport measurements in a transmission-electron microscope (TEM) on individual double-walled carbon nanotubes (DWNT). Using selected-area electron diffraction, the chiral indices of the two tubes constituting the DWNTs were determined through careful comparison with theory. We discuss the case of a DWNT whose two tubes have a gap at half filling and show a finite density of delocalized state at the Fermi level. The exact determination of chiral indices should be reachable in any transport-measurement experiment with samples that allow TEM characterization.     

Dynamics of ultimately short electromagnetic pulses in chiral carbon nanotubes

The wave equation for the electromagnetic field propagating in chiral carbon nanotubes has been analyzed. The phenomenological equation similar to the sine-Gordon equation has been derived. The dynamics of the electromagnetic pulse has been investigated.     

Single-shell carbon nanotubes imaged by atomic force microscopy

Single-shell carbon nanotubes, approximately 1 nm in diameter, have been imaged for the first time by atomic force microscopy operating in both the contact and tapping modes. For the contact mode, the height of the imaged nanotubes has been calibrated using the atomic steps of the silicon substrate on which the nanotubes were deposited. For the tapping mode, the calibration was performed using an industry-standard grating. The paper discusses substrate and sample preparation methods for the characterization by scanning probe microscopy of nanotubes deposited on a substrate.     

Manipulation and soldering of carbon nanotubes using atomic force microscope

Manipulation of carbon nanotubes (CNTs) by an atomic force microscope (AFM) and soldering of CNTs using Fe oxide nanoparticles are described. We succeeded to separate a CNT bundle into two CNTs or CNT bundles, to move the separated CNT to a desirable position, and to bind it to another bundle. For the accurate manipulation, load of the AFM cantilever and frequency of the scan were carefully selected. We soldered two CNTs using an Fe oxide nanoparticle prepared from a ferritin molecule. The adhesion forces between the soldered CNTs were examined by an AFM and it was found that the CNTs were bound, though the binding force was not strong.     

Chaotic behavior of channeling particles

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E(0) and incident angle psi(0), the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles' chaotic motion.     

Identity of molecular and macroscopic pressure on carbon nanotubes

Abstract

Raman spectroscopy was used to compare the structural effects on single-walled carbon nanotubes of pressures due to the cohesive energy of liquid media with the effects of an externally applied macroscopic pressure. Results were very similar, showing that the interpretation of the cohesive energy density as an internal pressure is physically realistic.