A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

Aharonov-Bohm oscillation and chirality effect in optical activity of single-wall carbon nanotubes

We study the Aharonov-Bohm effect in the optical phenomena of single-wall carbon nanotubes (SWCN) and also their chirality dependence. Especially, we consider the natural optical activity as a proper observable and derive its general expression based on a comprehensive symmetry analysis, which reveals the interplay between the enclosed magnetic flux and the tubule chirality for arbitrary chiral SWCN. A quantitative result for this optical property is given by a gauge invariant tight-binding approximation calculation to stimulate experimental measurements.

Growth of aligned single-walled carbon nanotubes under ac electric fields through floating catalyst chemical vapour deposition

Through floating catalyst chemical vapour deposition(CVD) method, well-aligned isolated single-walled carbon nanotubes (SWCNTs) and their bundles were deposited on the metal electrodes patterned on the SiO2/Si surface under ac electric fields at relatively low temperature(280 degrees C). It was indicated that SWCNTs were effectively aligned under ac electric fields after they had just grown in the furnace. The time for a SWCNT to be aligned in the electric field and the effect of gas flow were estimated. Polarized Raman scattering was performed to characterize the aligned structure of SWCNTs. This method would be very useful for the controlled fabrication and preparation of SWCNTs in practical applications.

Surface-enhanced resonant Raman spectroscopy (SERRS) of single-walled carbon nanotubes absorbed on the Ag-coated anodic aluminum oxide (AAO) surface

In this paper, we developed a new kind of substrate, the silver-coated anodic aluminum oxide (AAO), to investigate the characters of surface-enhanced resonant Raman scattering (SERRS) of the dilute single-walled carbon nanotubes. Homogeneous Ag-coated AAO substrate was obtained by decomposing the AgNO3 on the surface of AAO. single-walled carbon nanotubes (SWNTs) were directly grown onto this substrate through floating catalyst chemical vapor deposition method (CVD). SERRS of SWNTs was carried out using several different wavelength lasers. The bands coming from metallic SWNTs were significantly enhanced. The two SERRS mechanisms, the "electromagnetic" and "chemical" mechanism, were mainly responsible for the experiment results. (c) 2005 Elsevier B.V. All rights reserved.

Pressure-induced Raman-active radial breathing mode transition in single-wall carbon nanotubes

Using classical constant-pressure molecular dynamics simulations and the force constants model, radial breathing mode (RBM) transition of single-wall carbon nanotubes under hydrostatic pressure is reported. With the pressure increased, the RBM shifts linearly toward higher frequency, and the RBM transition occurs at the same critical pressure as the structural transition. The group theory indicates that the RBMs are all Raman-active; however, due to the effect of the frequency transition and the electronic structure change for tube radial deformation, the Raman intensity of the modes becomes so weak as not to be experimentally detected, which is in agreement with a recent experiment by S. Lebedkin [Phys. Rev. B 73, 094109 (2006)]. Furthermore, the calculated RBM transition pressure is well fitted to the cube of diameter (similar to 1/d(3)).

Chiral symmetry analysis and rigid rotational invariance for the lattice dynamics of single-wall carbon nanotubes

We provide a detailed expression of the vibrational potential for the lattice dynamics of single-wall carbon nanotubes (SWCNT's) satisfying the requirements of the exact rigid translational as well as rotational symmetries, which is a nontrivial generalization of the valence force model for the planar graphene sheet. With the model, the low-frequency behavior of the dispersion of the acoustic modes as well as the flexure mode can be precisely calculated. Based upon a comprehensive chiral symmetry analysis, the calculated mode frequencies (including all the Raman- and infrared-active modes), velocities of acoustic modes, and the polarization vectors are systematically fitted in terms of the chiral angle and radius, where the restrictions of various symmetry operations of SWCNT's are fulfilled.

Raman evidence for atomic correlation between the two constituent tubes in double-walled carbon nanotubes

Four well-resolved peaks with very narrow linewidths were found in the D-band and G'-band features of double-walled carbon nanotubes (DWNTs). This fact implies the occurrence of additional van Hove singularities (vHSs) in the joint density of states (JDOS) of DWNTs, which is consistent with theoretical calculations. According to their peak frequencies and theoretical analysis, the two outer peaks can be deduced to originate from a strong coupling between the two constituent tubes of commensurate DWNTs and the two inner peaks were curvature-related and assigned to originate from the two tubes with a weak coupling. This observation and elucidation constitute the first Raman evidence for atomic correlation and the resulting electronic structure change of the two constituent tubes in DWNTs. This result opens the possibility of predicting and modifying the electronic properties of DWNTs for their electronic applications.

Correlation effects for semiconducting single-wall carbon nanotubes: A density matrix renormalization group study

In this paper we report the applicability of the density matrix renormalization group (DMRG) approach to the cylindrical single wall carbon nanotube (SWCN) for the purpose of its correlation effect. By applying the DMRG approach to the t+U+V model, with t and V being the hopping and Coulomb energies between the nearest neighboring sites, respectively, and U the on-site Coulomb energy, we calculate the phase diagram for the SWCN with chiral numbers (n(1)=3, n(2)=2), which reflects the competition between the correlation energy U and V. Within reasonable parameter ranges, we investigate possible correlated ground states, the lowest excitations, and the corresponding correlation functions in which the connection with the excitonic insulator is particularly addressed.

Purification of single-walled carbon nanotubes synthesized by the catalytic decomposition of hydrocarbons

A procedure for purifying single-walled carbon nanotubes (SWNTs) synthesized by the catalytic decomposition of hydrocarbons has been developed. Based on the results from SEM observations, EDS analysis and Raman measurements, it was found that amorphous carbon, catalyst particles, vapor-grown carbon nanofibers and multi-walled carbon nanotubes were removed from the ropes of SWNTs without damaging the SWNT bundles, and a 40% yield of the SWNTs with a purity of about 95% was achieved after purification. (C) 2000 Elsevier Science Ltd. All rights reserved.

Low potential detection of glutamate based on the electrocatalytic oxidation of NADH at thionine/single-walled carbon nanotubes composite modified electrode

A glutamate biosensor based on the electrocatalytic oxidation of reduced nicotinamide adenine dinucleotide (NADH), which was generated by the enzymatic reaction, was developed via employing a single-walled carbon nanotubes/thionine (Th-SWNTs) nanocomposite as a mediator and an enzyme immobilization matrix. The biosensor, which was fabricated by immobilizing glutamate dehydrogenase (GIDH) on the surface of Th-SWNTs, exhibited a rapid response (ca. 5 s), a low detection limit (0.1 mu M), a wide and useful linear range (0.5-400 mu M), high sensitivity (137.3 +/- 15.7) mu A mM(-1) cm(-2), higher biological affinity, as well as good stability and repeatability. In addition, the common interfering species, such as ascorbic acid, uric acid, and 4-acetamidophenol, did not cause any interference due to the use of a low operating potential (190 mV vs. NHE). The biosensor can be used to quantify the concentration of glutamate in the physiological level. The Th-SWNTs system represents a simple and effective approach to the integration of dehydrogenase and electrodes, which can provide analytical access to a large group of enzymes for wide range of bioelectrochemical applications including biosensors and biofuel cells.

Accurate determination of electronic transition energy of carbon nanotubes from the resonant behavior of radial breathing modes and their overtones

The resonant Raman behavior of the radial breathing modes are very useful to analyze the electronic property of carbon nanotubes. We investigated the resonant behaviors of Stokes and anti-Stokes radial breathing mode and its overtone of a metallic nanotube, and show how to accurately determine the electronic transition energy of carbon nanotubes from radial breathing modes and their overtones. Based on the present results, the previously reported resonant Raman behavior of the radial breathing modes of SWINT bundles can be interpreted very well.

Photoluminescence from carbon nanotubes

We observed yellow colored light emission bands from multiwalled carbon nanotubes in photo-luminescence (PL) experiments. The light emission band features indicate that the PL bands are associated with the electronic properties inherent to the carbon nanotube (CNT) structures.

Observation of the resonant Raman behavior of individual single-walled carbon nanotubes

The different resonant Raman scattering process of single-walled carbon nanotubes (SWNTs) has been found between the Stokes and anti-Stokes sides of the radial breathing modes (RBMs), and this provides strong evidence that Raman spectra of some special diametric SWNTs are in resonance with their electronic transitions between the singularities in the one-dimensional electronic density of states in the valence and conduction bands, and other SWNTs axe beyond the resonant condition. Because of the coexistence of resonant and non-resonant Raman scattering processes for different diametric SWNTs, the relative intensity of each RBM does not reflect the proportion of a particular SWNT.