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2008, Optics Communications
We have studied the interaction of charged particles with single-walled metallic nanotubes by solving Poisson's equation with appropriate boundary conditions. Numerical results for the energy dispersion relations as a function of the wave vector are presented when the charged particle is inside or outside the nanotube.
Chemphyschem, 2007
While the electronic structure of metallic single-walled carbon nanotubes, SWCNTs, is well-understood, only a few, perhaps too rare, steps have been taken to investigate the metallic contribution to their interactions with charged species. This is not to say that interactions between SWCNTs and molecules have not been studied, but rather that the additional metallic contribution to the interaction with a (partial) charge has often been left unquantified or even neglected. And yet, this is not a trivial issue because prior to many of the practical applications advocated for SWCNTs there is the separation of metallic from semiconducting tubes that could be based on the larger adsorption energy of charged molecules when bound to metallic nanotubes. It was, for instance, noticed that for DNAnanotube hybrids, the negative charge of DNA induces a positive charge on the tube so that the overall charge is smaller to that of pure DNA and, although not quantified, this effect was used to separate metallic from semiconducting nanotubes. Moreover, if the additional metallic contribution is neglected, results of interactions/simulations with tubes of similar radius, such as (10,10) and (17,0), become equivalent, although the former is metallic and the latter semiconducting. Quantum chemical calculations can differentiate between the interaction of a metallic, or a semiconducting, nanotube with a charged species in a way analogous to that of Lu and co-workers who used first-principles calculations to show that the larger electronic polarizability of metallic SWCNTs makes them interact more strongly with adsorbates via p interactions. Quantum chemical calculations, however, routinely handle only a limited number of atoms and may have difficulties with weakly binding van der Waals interactions. If extensive systems of thousands of atoms must be considered and non-bonding interactions play a major role, classical potentials must be applied and they usually do not include this metallic contribution. Quantum chemical calculations, however, routinely handle only a limited number of atoms and if proper periodic boundary conditions are not implemented, that is, a cluster approach is employed, the metallic nature of the SWCNT may disappear.
Physical Review B, 2008
We calculate the plasma excitations in a bundle as well as a two-dimensional (2D) periodic array of aligned parallel multishell nanotubes on a substrate. The carbon nanotubes are oriented perpendicular to the substrate. The model we use for the system is an electron gas confined to the surface of an infinitely long cylinder embedded in a background dielectric medium. Electron tunneling between individual tubules is neglected. We include the Coulomb interaction between electrons on the same tubule and on different tubules for the same nanotube and neighboring nanotubes. We present a self-consistent field theory for the dispersion equation for intrasubband and intersubband plasmon excitations. For both the bundle and 2D array of aligned parallel nanotubes, the dispersion relation of the collective modes is determined by a three-dimensional wave vector with components in the direction of the nanotube axes and in the transverse directions. The dispersion equation is solved numerically for a singlewall nanotube 2D array as well as a bundle, and the plasmon excitation energies are obtained as a function of wave vector. The intertube Coulomb interaction couples plasmons with different angular momenta m in individual nanotubes, lifting the ±m degeneracy of the single-nanotube modes. This effect is analyzed numerically as a function of the separation between the tubules. We show that the translational symmetry of the lattice is maintained in the plasmon spectrum for the periodic array, and the plasmon energies have a periodic dependence on the transverse wave vector q ⊥ . For the bundle, the Coulomb interaction between nanotubes gives rise to optical plasmon excitations.
Journal of Nanophotonics, 2010
Journal of Materials Science, 2008
In this work, we describe the excitation of plasmons in nano-systems of cylindrical symmetry when charged particles impinge on them. In particular, we calculate the average number of plasmons excited by electrons in hollow, metallic tubules, using a Drude model to describe the dielectric function of the material. Based on previous results, which show the equivalence between quantum and classical descriptions of the phenomenon, we are able to evaluate in a simple manner the integrals along penetrating trajectories, perpendicular to the cylinder axis. We study the influence of various parameters on the excitation of the different modes available for such geometry, including the variation of the inner radius of the tube, and the impact parameter of the electron beam. We obtain similarities and differences with the already studied cases of solid wires, and hollow capillaries.
Physical Review B, 2002
We have analytically computed the energy-loss probability of a fast electron passing near a locally anisotropic hollow nanotube, in the nonretarded approximation. Numerical simulations have been performed in the low loss ͑below 50 eV͒ region, and a good agreement with experimental spatially resolved electron energy-loss spectroscopy results is reported. We also show the importance of the surface coupling effect and of the local anisotropy of the tubes for the plasmonic response, extending the conclusions previously reported for spherical nano-objects.
Physical Review A, 2004
We propose a simple, parameter-free two-fluid model for the collective electron response of a single-walled carbon nanotube, which treats the and electrons as separate two-dimensional fluids constrained to the same cylindrical surface. The electrostatic interaction between the fluids gives rise to splitting of the plasmon frequencies into two groups closely following the experimentally determined longitudinal dispersions of the + and plasmons. The model is used to calculate the induced electron density on the nanotube, as well as the stopping power for a charged particle moving parallel to the axis of the nanotube. It is found that these quantities exhibit novel features when the particle speed matches the phase velocity of the quasiacoustic plasmon.
Physical Review B, 2006
We extend the two-fluid, two-dimensional hydrodynamic model, describing the collective response of a multiwalled carbon nanotube, to include solid dielectric media embedded inside, or surrounding the nanotube. In the case of aluminum, we study plasmon hybridization in the UV range and find that the nanotube's low-energy, quasiacoustic plasmons are remarkably stable, whereas the shift of the high-energy + plasmons strongly depends on the gap between the nanotube and the aluminum boundary. Moreover, we study the stopping force on fast ions moving inside nanotubes encapsulated in channels of insulating, amorphous carbon, and metallic materials, with special attention paid to nickel. Finally, our study of the dynamical image potential for fast ions shows that a nanotube will effectively shield the influence of an embedded nickel wire.
Journal of Experimental and Theoretical Physics Letters, 2002
A microscopic model is developed for calculating electrostatic properties of nanotube devices. It is shown that the quantum-mechanical approach yields the same results as the statistical calculation in the limit of a thin tube suspended over a conducting gate at a distance exceeding the nanotube radius. A closed analytic expression is obtained for the atomistic capacitance of a straight nanotube and for a nanotube with a modest curvature. This method allows the fast and exact calculation of device parameters for the nanotube electromechanical systems and nanotube electronic devices. © 2002 MAIK "Nauka/Interperiodica".
Physical Review B, 2002
A theory of collective plasma excitations in a linear periodic array of multishell nanotubes is presented. The electron system in the nanotubes is modeled by a quasifree electron gas confined to the surface of an infinitely long cylinder. The plasmon dispersion equation is derived in the random-phase approximation neglecting the electron tunneling between the individual cylindrical tubules. The dispersion equation is solved numerically for a single-wall nanotube array, and the plasmon excitation energies are obtained as a function of the wave vector in the direction of the nanotube axes and in the transverse direction. It is found that the intertube Coulomb interaction couples the modes with different angular momenta m in individual nanotubes and, in particular, lifts the Ϯm degeneracy of the single-nanotube modes. This effect is analyzed numerically as a function of the separation between the tubules. We show that the translational symmetry of the lattice is maintained in the plasmon spectrum, and the plasmon energies have a periodic dependence on the transverse wave vector.
Physical Review B, 2001
Electron energy loss spectroscopy is a well adapted tool for the investigation of the valence excitations of individual nanometer-size particles. The interpretation of the loss spectra of such small particles, however, relies in most cases on a quantitative comparison with simulated excitation probabilities. Here we present a formalism developed for the interpretation of the energy loss data of single-wall carbon nanotubes based on the hydrodynamic theory of plasmon excitations by high-energy electrons. The nanotubes are modeled as a twodimensional electron gas confined on the circumference of a cylinder. The plasmon excitation probabilities, directly comparable to measurements, are discussed for various parameters.
Physical Review B, 2010
We present a quantization of the hydrodynamic model to describe the excitation of plasmons in a singlewalled carbon nanotube by a fast point charge moving near its surface at an arbitrary angle of incidence.
2017
To investigate the wake effects in the transport of charged particles through single-walled (SWCNT) and double-walled (DWCNTs) carbon nanotubes, by using a semiclassical kinetic model, with the introduction of electron band structure effect. The analytical expressions of the induced electron density at nanotube surface and the induced potential around the nanotube walls are obtained. The results indicate that a bell-like distribution appears for the induced electron density when the incident particle speed is below a threshold value, otherwise wake-like oscillation can be seen behind the particle in the axial distribution. Dependencies of the amplitude and frequency of oscillations on the incident particle speed are. Meanwhile, it is noted that the valence electrons in the outer wall of DWCNTs tend to be easily excited by the polarized electrons on the inner wall, compared with that by the incident particle without the inner wall in SWCNTs. Finally, the induced potential trailing th...
2007
The discovery of carbon nanotubes by Iijima in 1991 has created a torrent of new research activities. Research on carbon nanotubes ranges from studying their fundamental properties, such as their electron band structure and plasma frequencies, to developing new applications, such as self-assembled nano-circuits and field emission displays. Robust models are now needed to enable a better understanding of the electronic response of carbon nanotubes. We use timedependent density functional theory to derive a two-fluid two-dimensional (2D) hydrodynamic model describing the collective response of a multiwalled carbon nanotube with dielectric media embedded inside or surrounding the nanotube. We study plasmon hybridization of the nanotube system in the UV range, the stopping force for ion channelling, the dynamical image potential for fast ions, channelled diclusters and point dipoles, and the energy loss for ions with oblique trajectories. Comparisons are made of results obtained from th...
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2005
We used the hydrodynamic model to describe the dielectric response of a multi-walled carbon nanotube to a fast point charge moving paraxially, either inside or outside the nanotube. Calculations are performed for a two-walled nanotube, giving rise to a splitting of the plasmon frequencies due to the interaction between the electron fluids on the two cylinders. The dependences of the projectile stopping power and the self-energy (image potential) on the velocity and the distance from the nanotube axis show interesting features when the projectile velocity matches the phase velocity of the plasmon mode with a quasi-linear dispersion.
2017
By developing a semiclassical kinetic model to simulate the plasmon excitation of carbon nanotubes and the transport of charged particles moving through nanotubes. The analytical expressions of the dielectric function and the energy loss function are obtained for zigzag and armchair nanotubes of metallic properties, respectively. Numerical results display several very distinct peaks in the curves of loss function, showing effects from the collective excitation. As well, the stopping power and selfenergy are calculated while charged particles move along the axis of nanotubes with different geometries, under the influence of friction coefficients. The results had been achieved by using the programs are written in FORTRAN 90 using software Computer Visual FORTRANV6.6, which performed for the numerical calculation, showing the influence of the damping factor, the nanotube radius, and the particle position on its self-energy, loss function and the stopping power. Keywords—carbon nanotube...
Physical Review B, 2005
We computationally study the electrostatic potential profile and current carrying capacity of carbon nanotubes as a function of length and diameter. Our study is based on solving the non equilibrium Green's function and Poisson equations self-consistently, including the effect of electron-phonon scattering. A transition from ballistic to diffusive regime of electron transport with increase of applied bias is manifested by qualitative changes in potential profiles, differential conductance and electric field in a nanotube. In the low bias ballistic limit, most of the applied voltage drop occurs near the contacts. In addition, the electric field at the tube center increases proportionally with diameter. In contrast, at high biases, most of the applied voltage drops across the nanotube, and the electric field at the tube center decreases with increase in diameter. We find that the differential conductance can increase or decrease with bias as a result of an interplay of nanotube length, diameter and a quality factor of the contacts. From an application view point, we find that the current carrying capacity of nanotubes increases with increase in diameter. Finally, we investigate the role of inner tubes in affecting the current carried by the outermost tube of a multiwalled nanotube.
Nanotechnology, 2005
Dielectrophoresis has appeared recently as a non-destructive means to manipulate and sort carbon nanotubes. In order to compute the electrostatic forces that act on carbon nanotubes when subjected to an external field and placed in the vicinity of metallic protrusions, we develop a technique that relies on a monopole-dipole description of the nanotubes and on a dielectric-function model of the metallic elements. The technique proceeds iteratively between these two descriptions in order to determine the nanotube polarization and the resulting counter-polarization of the metallic elements. Specific differentiation schemes as well as a finite-difference formulation of Poisson's equation are given in cartesian and cylindrical coordinates. As an application, we compute the polarization and forces that act on a metallic (5, 5) and a semiconducting (10, 0) nanotube, when placed in the vicinity of a flat metallic support with either a conical or semi-elliptical protrusion. The results quantify the relevant electrostatic forces as well as the contribution of the image interaction to these forces. It is shown that the nanotubes get more polarized and attracted to the protrusion when the latter has a semi-elliptical shape. The differences in the polarization and forces that act on the metallic (5, 5) and semiconducting (10, 0) nanotubes support the idea that dielectrophoresis may be used to separate them.
Optics Communications, 2010
Propagation of surface plasma waves in a metallic single-walled carbon nanotube that either is encapsulated in a solid metallic channel or encapsulates a metallic nanowire are studied within the framework of the classical electrodynamics. The linearized ...
Nano Letters, 2004
Electron scattering rates in metallic single-walled carbon nanotubes are studied using an atomic force microscope as an electrical probe. From the scaling of the resistance of the same nanotube with length in the low-and high-bias regimes, the mean-free paths for both regimes are inferred. The observed scattering rates are consistent with calculations for acoustic-phonon scattering at low biases and zone boundary/ optical phonon scattering at high biases.
Journal of Mathematical Chemistry, 2010
In this paper, a study on the electromagnetic behaviour of a single wall carbon nanotube model is described. The electrons available for conduction are treated as a thin cylindrical layer fluid and their motion is described by means of classical hydrodynamics equations in linearized form. These equations are solved in time domain using the Smoothed Particle Hydrodynamics method. The method suitably handled runs on GRID environment.
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