Zigzag Tubes Research Articles

カーボンナノチューブを用いたナノベアリング(S09-1 計算ナノ・マイクロテクノロジーの新展開(1),S09 計算ナノ・マクロテクノロジーの新展開)

The paper describes a nano-bearing that is composed of carbon nanotubes analyzed by molecular dynamics simulation. To describe multiwall carbon nanotubes, Tersoff potential is applied for atoms in a basal plane of tubes and the Morse potential is for interlayer tubes, whose parameters are newly developed based on the equilibrium interlayer distance, the interlayer cohesive energy and the Young's modulus in the interlayer direction of graphite. The research shows the excellent possibility and properties of the nano-bearing composed of zigzag tubes It works on the wide range of temperature from 0K to 3000K, with high rotation speed and accuracy and in an ultra-high vacuum without any lubricant.

Tuning chirality of single-wall carbon nanotubes by selective etching with carbon dioxide.

CO2 molecule chemisorbs selectively on the zigzag tube edge without an activation barrier, whereas it physisorbs on the armchair edge of nanotubes. In addition, carbon nanotubes can be etched by an adsorbed oxygen atom of CO2 molecule. From our results, we suggest a selective etching mechanism for tuning the chirality of the mass-produced carbon nanotubes.

Electron transmission through atom-contacted carbon nanotubes

The transmission through side-contacted single-wall carbon nanotubes is investigated within the Landauer-B\"utikker formalism for arbitrary tubes, geometries of contacts, and energies of transmission (E) for the case of monoatomic contacts. An efficient method to calculate transmission within the tight-binding approach including curvature effects is devised allowing, in particular, for an analytical treatment of zigzag, armchair, and some chiral tubes. The transmission function is described as a superposition of the contributions from one-dimensional bands of all nanotube lines, each of them oscillating or/and decaying with the distance between the leads. We find five different types of antiresonances. Two of them arise from a destructive interference of the contributions from different nanotube lines when E is in the gap of semiconducting nanotubes and either are due to symmetry reasons or are accidental. A further two can show up at energies of Van Hove singularities originating from isolated singular points in 1D bands of nanotubes and can lead either to split or completely missing transmission peaks. The fifth one is related to the flat band in zigzag nanotubes at the energy of Van Hove singularity in graphene and results in zero transmission between carbon atoms belonging to different translational units in these tubes. A strong anisotropy of transmission in two opposite directions along the tube's axis is found in the middle of the energy gap of semiconducting nanotubes, which reaches several orders of magnitude in zigzag tubes. The transmission at Van Hove singularities (when nonzero) is of the order of unity and decays at a large axial distance R between the leads as ${R}^{\ensuremath{-}2},$ similarly to monoatomic chains. The transmission in the band region of nanotubes shows two types of behavior depending on the divisibility by three of the difference between corresponding reduced nanotube indices ${n}^{\ensuremath{'}}\ensuremath{-}{m}^{\ensuremath{'}}.$ Close to the Fermi level the amplitude of the transmission function is independent from the chiral angle of the nanotubes and scales as an inverse square of their diameter.

Electron–optical phonon interaction in carbon nanotubes

The electron-phonon interaction is calculated for electrons states in single wall carbon nanotubes. Explicit results are presented for armchair and zig-zag tubes. The scattering by acoustical phonons confirm earlier results, while the scattering by optical phonons is new.

Effect of Elliptical Deformation on Molecular Polarizabilities of Model Carbon Nanotubes from Atomic Increments

The interacting induced dipole polarization model implemented in our program POLAR is used for the calculation of the dipole-dipole polarizability alpha. The method is tested with single-wall carbon nanotube models as a function of nanotube radius and elliptical deformation. The results for polarizability follow the same trend as reference calculations performed with our version of the program PAPID. For the zigzag tubes, the polarizability is found to follow a remarkably simple law, that is, it varies as the inverse of the radius. A dramatic effect is also found with elliptical deformation. It is found that the polarizability and related properties can be modified continuously and reversibly by the external radial deformation. These results suggest an interesting technology in which mechanical deformation can control chemical properties of the carbon nanotubes. POLAR calculations differentiate more effectively than PAPID computations among single-wall nanotube models with increasing radial deformation. Different effective polarizabilities are calculated for the atoms at the highest and lowest curvature sites. POLAR calculations discriminate more efficiently than PAPID computations between the effective polarizabilities of the highest and lowest curvature sites. This remarkable and significant tunable polarizability can have important implications for metal coverage of metals on nanotubes and selective adsorption and desorption of foreign atoms and molecules on nanotubes and can lead to a wide variety of technological applications, such as catalysts, hydrogen storage, magnetic tubes, etc.

Atomic and electronic structures of fluorinated single-walled carbon nanotubes

We have investigated stable adsorption geometries of fluorine atoms on a single-walled carbon nanotube (SWNT) using density-functional calculations. Chemisorption of fluorine atoms induces heavy strain on the tube wall, giving rise to one of the C-C back bonds of 1.54 \AA{}, single bonded similar to that of diamond. We find that at coverage of 0.5, the most stable isomer is a ladder-type on an armchair nanotube, whereas it is a helical-type on a zigzag tube, both revealing a semiconducting behavior. This is in good agreement with the experimental observations that the fluorinated SWNT's increase the resistivity by decreasing the electronic density of states near the Fermi level. We also demonstrate that the electron-beam-induced structural deformation of the fluorinated SWNT's could be explained by a selective desorption of fluorine atoms. Various types of isomers, relative stability, and electronic properties at different coverages will be further discussed.

Ab initiocalculations of the lattice dynamics of boron nitride nanotubes

We present an extensive first-principles study of the phonons in boron nitride nanotubes using density functional perturbation theory in the local density approximation. Based on the nonsymmorphic rod-group symmetry of the tubes, the Raman- and infrared-active modes at the G point of the one-dimensional Brillouin zone are evaluated. For zigzag and chiral nanotubes, the set of infrared-active modes is a subset of the Raman-active modes. In particular, the radial breathing mode is not only Raman but also infrared active. However, for armchair tubes, the sets of infrared- and Raman-active modes are disjoint. This may serve to spectroscopically distinguish between macroscopic samples of zigzag-chiral and armchair nanotubes. We present the frequencies of the active modes of zigzag, chiral, and armchair tubes as a function of the tube diameter and compare the results with the frequencies obtained by the zone-folding method, i.e., the rolling of a single hexagonal BN sheet into a tube. Except for the high-frequency tangential modes, the zone-folding results are in very good agreement with the ab initio calculations. The radial breathing mode frequency can be derived by folding a sheet of finite width. Finally, we show that the effects of bundling on the phonon frequencies are small. This demonstrates that the obtained results for isolated BN tubes may serve as a basis for an accurate assignment of phonon modes in spectroscopic measurements.

Eigenstates and transmission coefficients of finite-sized carbon nanotubes

The tight-binding eigenstates of isolated finite-sized zigzag and armchair nanotubes are obtained analytically using the transfer matrix method. Edge states are encountered for zigzag tubes but not for armchair tubes. Inclusion of curvature leads to a decaying-oscillating behavior of the highest occupied and lowest unoccupied molecular orbital gap in armchair tubes as a function of length. For zigzag tubes the inclusion of curvature induces the conversion of an extended state at nonbonding energy to an edge state. In addition the transmission coefficient of zigzag and armchair tubes with featureless leads is analytically obtained. The existence of a transmission peak at the Fermi level that decays exponentially with nanotube length for zigzag tubes is explained.

Electronic transport through bent carbon nanotubes: Nanoelectromechanical sensors and switches

We theoretically investigate the mechanical deformations of armchair, zigzag, and zigzag-armchair kink nanotube structures, under severe bendings, within a tight-binding model. It is shown that the zigzag tube is stiffer than the armchair tube with the same diameter. The kink structure is found to be quite stable under severe bendings. Calculating the I-Vcharacteristics, we show that, at the same bias, the current of metallic tube decreases with increased bending, while that of semiconducting tube increases. Such a universal behavior is not observed for the kink structure due to two competing effects. Possible application to nanoelectromechanical sensors and switches is discussed.

Energetics and stability within the microscopic, empirical model for finite, open-ended, single-walled carbon nanotubes

We demonstrate that the total energy of finite, open-ended, single-walled carbon nanotubes is determined by a balance between the elastic energy due to the curvature of a tube and the chemical energy due to the dangling bonds at the open ends of a tube. The differences in total energy and radius between the most energetically stable zig-zag and armchair tubes, increases with increasing number of atoms in the tubes.

Theoretical Analysis of Ether-Group Derivatization at Carbon Nanotube Ends

Electronic structure theory methods have been used to study oxygen−alkyl bond strengths of ether-bonded carbon nanotube−alkyl systems where the alkyl groups are attached to the carbon nanotube ends. The results show that these bonds are exothermic and that they are stronger for armchair nanotubes than for zigzag tubes. This has potential applications in nanotube manipulation and separation, where large polymers can be used to separate and arrange nanotubes.

Observation of a logarithmic temperature dependence of thermoelectric power in multiwall carbon nanotubes

The energetics of small zigzag carbon nanotubes at high temperature regime (T = 2500 K) is investigated via k-space tight-binding molecular dynamics (TBMD) simulations. It is found that the n dangling atoms at the end of a zigzag tube with 5 < n < 12 can automatically transform into an (n - 1)-member ring at the top, accompanied by the release of a C, dimer and the formation of (n - 1) pentagons and a hexagon-pentagon pair involving up to five layers of atoms. For tubes larger than (11, 0) or smaller than (6, 0), it is found that energetically it is more favorable for the tube to remain open. (C) 2002 Elsevier Science B.V. All rights reserved.

Electronic Response and Bandstructure Modulation of Carbon Nanotubes in a Transverse Electrical Field

The electronic properties of carbon nanotubes (NTs) in a uniform transverse field are investigated within a single orbital tight-binding (TB) model. For doped nanotubes, the dielectric function is found to depend not only on symmetry of the tube, but also on radius and Fermi level position. Band gap opening/closing is predicted for zigzag tubes, while it is found that armchair tubes always remain metallic, which is explained by the symmetry in their configuration. The bandstructures for both types are considerably modified when the field strength is large enough to mix neighboring subbands.

Structural and equivalent continuum properties of single-walled carbon nanotubes

Single-walled carbon nanotubes are treated as cylindrical structures of which their extensional, torsional, and bending rigidities are investigated. Using the potential energy for interatomic forces of the molecular mechanics model, pin-jointed truss models for single-walled carbon nanotubes were created. These truss models were then used to determine the extensional, torsional, and bending rigidities for both armchair and zigzag tubes. New stiffness parameters were introduced that are independent of the cross sectional area of the nanotube. Subsequently, by treating a single-walled nanotube as an equivalent thin-walled continuum hollow cylinder, and, in addition, requiring the structural rigidities of the continuum cylinder to be equal to that of the truss model, the effective Young's modulus of the nanotube is determined after choosing the wall thickness to be 0.34 nm.

Phonon spectrum of single-walled carbon nanotubes

The phonon spectra are calculated within the frame of force constant model. By virtue of five rotation operations determined by the coordinates of carbon atoms, it is convenient for us to obtain the force matrix. The calculations show that there are only 12 non-degenerate phonon branches and 6(n-1) degenerate branc hes for armchair (n, n) tube and zigzag (n, 0) tube.

Energetics of high temperature dimer desorption and reconstruction at the end of small zigzag carbon nanotubes

The energetics of small zigzag carbon nanotubes at high temperature regime ( T=2500 K) is investigated via k-space tight-binding molecular dynamics (TBMD) simulations. It is found that the n dangling atoms at the end of a zigzag tube with 5< n<12 can automatically transform into an ( n−1)-member ring at the top, accompanied by the release of a C 2 dimer and the formation of ( n−1) pentagons and a hexagon–pentagon pair involving up to five layers of atoms. For tubes larger than (11, 0) or smaller than (6, 0), it is found that energetically it is more favorable for the tube to remain open.

Carbon-nanotube-based quantum pump in the presence of a superconducting lead

Parametric electron pump through superconductor-carbon-nanotube based molecular devices was investigated. It is found that a dc current, which is assisted by resonant Andreev reflection, can be pumped out from such molecular device by a cyclic variation of two gate voltages near the nanotube. The pumped current can be either positive or negative under different system parameters. Due to the Andreev reflection, the pumped current has the double peak structure around the resonant point. The ratio of pumped current of N-SWNT-S system to that of N-SWNT-N system (I^{NS}/I^N) is found to approach four in the weak pumping regime near the resonance when there is exactly one resonant level at Fermi energy inside the energy gap. Numerical results confirm that in the weak pumping regime the pumped current is proportional to the square of the pumping amplitude V_p, but in the strong pumping regime the pumped current has the linear relation with V_p. Our numerical results also predict that pumped current can be obtained more easily by using zigzag tube than by using armchair tube.

Luttinger parametergfor metallic carbon nanotubes and related systems

The random phase approximation (RPA) theory is used to derive the Luttinger parameter g for metallic carbon nanotubes. The results are consistent with the Tomonaga-Luttinger models. All metallic carbon nanotubes, regardless if they are armchair tubes, zigzag tubes, or chiral tubes, should have the same Luttinger parameter g. However, a (10,10) carbon peapod should have a smaller g value than a (10,10) carbon nanotube. Changing the Fermi level by applying a gate voltage has only a second order effect on the g value. RPA theory is a valid approach to calculate plasmon energy in carbon nanotube systems, regardless if the ground state is a Luttinger liquid or Fermi liquid. (This paper was published in PRB 66, 193405 (2002). However, Eqs. (6), (9), and (19) were misprinted there.)

Bend-induced insulating gap in carbon nanotubes

The effect of uniform bend on the electronic structure of single wall carbon nanotubes is investigated as function of diameter, chirality, and plane of bend. This deformation can only mix states with the same projection of $\mathbf{k}$ on the tube's axis and belonging either to one nanotube line or to nearest neighbor and next nearest neighbor lines. The bend-induced insulating gap opens in chiral and zigzag tubes, scales as the square of the bend curvature and is strongly dependent on the chirality of the tube. For large diameters of the tubes, the bend-induced gap scales as the square of the tube's diameter and is strongly determined by the changes of the bond lengths. The observation of these gaps should become possible with current experimental techniques.

Localization length in deformed metallic carbon nanotubes

Based upon the metallic band model, and including the disorder perturbation, we have studied the band structure and localization length ξ of deformed carbon nanotubes. It is found that the ξ becomes shorter for deformed tubes. Also, the ξ of deformed armchair tubes decreases faster than that of deformed metallic zigzag tubes.