On the size of small single-walled carbon nanotubes

We derive a formula relative to the diameter/length ratio of a small single-walled carbon nanotube by means of calculations referring to Fermi energy. These calculations arise from the consideration of the Fermi's velocity for a multiwalled carbon nanotube.     

Low-frequency linear vibrations of single-walled carbon nanotubes: Analytical and numerical models

Low-frequency vibrations of single-walled carbon nanotubes with various boundary conditions are considered in the framework of the Sanders–Koiter thin shell theory. Two methods of analysis are proposed. The first approach is based on the Rayleigh–Ritz method, a double series expansion in terms of Chebyshev polynomials and harmonic functions is considered for the displacement fields; free and clamped edges are analysed. This approach is partially numerical. The second approach is based on the same thin shell theory, but the goal is to obtain an analytical solution useful for future developments in nonlinear fields; the Sanders–Koiter equations are strongly simplified neglecting in-plane circumferential normal strains and tangential shear strains. The model is fully validated by means of comparisons with experiments, molecular dynamics data and finite element analyses obtained from the literature. Several types of nanotubes are considered in detail by varying aspect ratio, chirality and boundary conditions. The analyses are carried out for a wide range of frequency spectrum. The strength and weakness of the proposed approaches are shown; in particular, the model shows great accuracy even though it requires minimal computational effort.     

On the electronic band structure of zigzag-type single-walled carbon nanotubes

The electronic band structure of a zigzag-type carbon nanotube has been computed by using the tight-binding approximation method in the framework of SSH Model Hamiltonian modified by the inclusion of two Lagrange multipliers instead of one. This modification yielded an electronic band structure consistent with the experimental reports that an infinite (3,0) zigzag-type single-walled carbon nanotubes displays a metallic behaviour.     

Conductivity of single-walled carbon nanotubes

In a system of N interacting single-level quantum dots (QDs), we study the relaxation dynamics and the current–voltage characteristics determined by symmetry properties of the QD arrangement. Different numbers of dots, initial charge configurations, and various coupling regimes to reservoirs are considered. We reveal that effective charge trapping occurs for particular regimes of coupling to the reservoir when more than two dots form a ring structure with the C_N spatial symmetry. We reveal that the effective charge trapping caused by the C_N spatial symmetry of N coupled QDs depends on the number of dots and the way of coupling to the reservoirs. We demonstrate that the charge trapping effect is directly connected with the formation of dark states, which are not coupled to reservoirs due to the system spatial symmetry C_N. We also reveal the symmetry blockade of the tunneling current caused by the presence of dark states.     

Hydrogenation of single-walled carbon nanotubes

Towards the development of a useful mechanism for hydrogen storage, we have studied the hydrogenation of single-walled carbon nanotubes with atomic hydrogen using core-level photoelectron spectroscopy and x-ray absorption spectroscopy. We find that atomic hydrogen creates C-H bonds with the carbon atoms in the nanotube walls, and such C-H bonds can be completely broken by heating to 600 degrees C. We demonstrate approximately 65 +/- 15 at % hydrogenation of carbon atoms in the single-walled carbon nanotubes, which is equivalent to 5.1 +/- 1.2 wt % hydrogen capacity. We also show that the hydrogenation is a reversible process.     

Nucleation of single-walled carbon nanotubes

The nucleation pathway for single-wall carbon nanotubes on a metal surface is demonstrated by a series of total energy calculations using density functional theory. Incorporation of pentagons at an early stage of nucleation is energetically favorable as they reduce the number of dangling bonds and facilitate curvature of the structure and bonding to the metal. In the presence of the metal surface, nucleation of a closed cap or a capped single-wall carbon nanotube is overwhelmingly favored compared to any structure with dangling bonds or to a fullerene.     

Ester-functionalized soluble single-walled carbon nanotubes

We report the preparation of soluble ester- functionalized single-wall carbon nanotubes (sSWNT-COO(CH₂)₁₇CH₃). By use of solution phase IR spectroscopy we are able to compare the ratio of the carbon atoms in the SWNT backbone to the carbon atoms in the ester and amide functionalities of s-SWNTs. Received: 16 July 2001 / Accepted: 3 December 2001 / Published online: 4 March 2002     

On the characterization of the elastic properties of asymmetric single-walled carbon nanotubes

In order to characterize asymmetric single-walled carbon nanotubes, an algorithm has been developed based on numerical simulation to relate the physical geometry to the elastic properties of asymmetric single-walled carbon nanotubes (SWCNTs). A large number of finite element results for the stiffness of asymmetric SWCNTs has been used to develop a best surface fitting function to define the relationship between the geometry of SWCNTs and their stiffness. However, since the stiffness of asymmetric nanotubes depends upon the configuration parameters, n and m, it was impossible to define any diameter dependency. Based on the maximum reaction force concept and in order to account for the hidden mechanical behavior of asymmetric SWCNTs, the chiral factor (CF) has been employed in this study. The proposed CF converts any asymmetric geometry (n and m) into a value between 0 and 1. A group of the SWCNTs with the same applied boundary condition (n+m=30) and different range of the CF was also used for studying of the shear contribution. The chiral factor dependency, which is developed in this study, is applicable for characterising and selecting asymmetric SWCNTs in the design of advanced nanomaterials. Furthermore, the equation which is calculated in this study can be useful for finding the best criteria for selecting asymmetric SWCNTs.     

Longitudinal,transverse, and torsional vibrations and stabilities of axially moving single-walled carbon nanotubes

Thanks to the brilliant mechanical properties of single-walled carbon nanotubes (SWCNTs), they are suggested as high speed nanoscale vehicles. To date, various aspects of vibrations of SWCNTs have been addressed; however, vibrations and instabilities of moving SWCNTs have not been thoroughly assessed. Herein, vibrational properties of an axially moving SWCNT with simply supported ends are studied using nonlocal Rayleigh beam theory. Employing assumed mode and Galerkin methods, the discrete governing equations pertinent to longitudinal, transverse, and torsional motions of the moving SWCNT are obtained. The resulting eigenvalue equations are then numerically solved. The speeds corresponding to the initiation of the instability within the moving nanostructure are calculated. The roles of the speed of the moving SWCNT, small-scale parameter, and aspect ratio on the characteristics of longitudinal, transverse, and torsional vibrations of axially moving SWCNTs are scrutinized. The obtained results show that the appearance of the small-scale parameter would result in the occurrence of both divergence and flutter instabilities at lower levels of the speed.     

Photophysics of polymer-wrapped single-walled carbon nanotubes

Single-walled carbon nanotubes (SWNTs) are successfully dispersed in two conjugated polymer poly(9,9-dioctylfluorenyl-2,7-diyl) (PFO) and poly[2-methoxy-5- (2’-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEHPPV) solutions. Steady-state and time-resolved photoluminescence spectroscopy in the near-infrared and visible spectral regions are used to study the interaction of the dispersed carbon nanotube and the wrapped polymer in the nano-hybrids. The SWNTs infrared emission is the signatures of the separation of single semiconducting tubes, the lifetime of the photoluminescence of these tubes is bi-exponential with the first component varying from 6 ps (in MEHPPV wrapped SWNTs) to 14 ps (in PFO wrapped SWNTs), while the second component of the decay for all samples is in the range of 30-40 ps, revealing the intrinsic lifetime of the SWNTs. The study of the photoluminescence of the nano-hybrids in the visible spectral range shows, in the case of the PFO, a relatively strong quenching, the photoluminescence lifetime for the hybrid is more than 100 ps shorter than the one of the pristine polyfluorene solution. For the MEHPPV-SWNT hybrid an opposite behavior is revealed with the photoluminescence lifetime surprisingly longer than the polymer solution. The possible mechanism for the interaction of the two conjugated polymers and the SWNTs is discussed in terms of their electronic band structure.     

Bactericidal action of single-walled carbon nanotubes

The action of single-walled carbon nanotubes (SWCNTs) on cells of the genetically engineered K12 TG1 strain of Escherichia coli, which have a luminescent phenotype generated by the cloning of the lux operon of the native luminescent marine bacterium Photobacterium leiognathi into the strain, is studied in this work. The survival rate of the bacterial cells and their morphological changes are studied by means of atomic force microscopy as a function of their exposure to SWCNTs.     

单壁纳米碳管的声子谱研究

通过五步旋转操作方便地得到了不同位置原子间的力常数矩阵，从而可以使对各种不同类型管的声子谱的计算变得简便. 计算表明，非螺旋的扶手椅型（n, n）管与锯齿型(n, 0)管的非简并和二重简并模式数分别为12和6(n-1)，这与从群论等方法所得结果相符. 关键词： 纳米碳管 声子谱 振动模式密度 动力学矩阵     

Flame synthesis of single-walled carbon nanotubes

Flames offer potential for synthesis of carbon nanotubes in large quantities at considerably lower costs than that of other methods currently available. This study aims to examine conditions for carbon nanotube formation in premixed flames and to characterize the morphology of solid carbon deposits and their primary formation mechanisms in the combustion environment. Single-walled nanotubes have been observed in the post-flame region of a premixed acetylene/oxygen/15 mol% argon flame operated at 6.7 kPa with Fe(CO)₅ vapor used as a source of metallic catalyst necessary for nanotube growth. Thermophoretic sampling and transmission electron microscopy were used to characterize the solid material present in the flame at various heights above burner (HAB), giving a resolution of formation dynamics within the flame system. Catalyst particle formation and growth is observed to dominate the immediate post-flame region (10–40 mm HAB). Nanotubes were observed to be present after 40 mm HAB with nanotube inception occurring as early as 30 mm HAB. Between 40 and 70 mm HAB, nanotubes are observed to coalesce into clusters. A nanotube formation ‘window’ is evident with formation limited to fuel equivalence ratios between 1.5 and 1.9. A continuum of morphologies ranging from relatively clean clusters of nanotubes to amorphous material is observed between these lower and upper limits. High-resolution TEM and Raman spectroscopy revealed nanotube bundles with each nanotube being single-walled with diameters between 0.9 and 1.5 nm.     

Piezoresistive effect in single-walled carbon nanotubes

This paper reports on the results of the theoretical investigation of the piezoresistive effect in single-walled carbon nanotubes of two structural modifications: arm-chair type and zig-zag type. The variation in the band gap of semiconducting nanotubes under the influence of the compressive and tensile deformations has been analyzed. The main quantitative characteristic of the piezoresistive effect—the longitudinal component of the elastic conductivity tensor—has been calculated, and its dependence on the diameter of semiconducting nanotubes has been shown. The variants of practical implementation of the effect under study have been proposed.     

Axial-strain-induced torsion in single-walled carbon nanotubes

Using classical molecular dynamics and empirical potentials, we show that the axial deformation of single-walled carbon nanotubes is coupled to their torsion. The axial-strain-induced torsion is limited to chiral nanotubes-graphite sheets rolled around an axis that breaks its symmetry. Small strain behavior is consistent with chirality and curvature-induced elastic anisotropy (CCIEA)-carbon nanotube rotation is equal and opposite in tension and compression, and decreases with curvature and chirality. The large-strain compressive response is remarkably different. The coupling progressively decreases, in contrast to the tensile case, and changes its sign at a critical compressive strain. Thereafter, it untwists with increasing axial strain and then rotates in the opposite direction, i.e., the same sense as under tension. This suggests that the response is now dictated by a combination of nonlinear elasticity and CCIEA.     

Parametric instabilities in single-walled carbon nanotubes

Parametric instabilities induced by the coupling excitation between the high frequency quantum Langmuir waves and the low frequency quantum ion-acoustic waves in single-walled carbon nanotubes are studied with a quantum Zakharov model. By linearizing the quantum hydrodynamic equations, we get the dispersion relations for the high frequency quantum Langmuir wave and the low frequency quantum ion-acoustic wave. Using two-time scale method, we obtain the quantum Zaharov model in the cylindrical coordinates. Decay instability and four-wave instability are discussed in detail. It is shown that the carbon nanotube＇s radius, the equilibrium discrete azimuthal quantum number, the perturbed discrete azimuthal quantum number, and the quantum parameter all play a crucial role in the instabilities.     

Interband magneto-optics in single-walled carbon nanotubes

We have carried out magneto-absorption and magneto-photoluminescence experiments on micelle-suspended single-walled carbon nanotubes in magnetic fields up to 45 T. Chirality-assigned spectral peaks exhibit significant changes with increasing magnetic field, which can be quantitatively explained in terms of the theoretically predicted splittings and redshifts of the band edge due to the Aharonov–Bohm effect combined with the magnetic-field-induced alignment of the nanotubes.     

Optical anisotropy in single-walled carbon nanotubes

Optical anistropy at optical communication wavelength was observed in films of vertically aligned single-walled carbon nanotubes (SWNTs). We report the control of both the polarization state and transmission of incoming light at 1550 nm by azimuthal and axial tilting of SWNT film about its aligned axis. The experiments reveal that the polarization state of light is susceptible to the azimuthal angle of the aligned direction of a SWNT having semiconductor characteristics and the intensity of the output beam after SWNT film shows cosine function dependence on the axial tilting angle.     

Investigation of superconductivity in the single-walled carbon nanotubes

Superconductivity in the single-walled carbon nanotubes is investigated. First, effect of diameter increasing on the clean systems critical temperature, T_c, is calculated. Then effect of impurity doping on the reduction of critical temperature T_c, of single-walled carbon nanotubes, is discussed. Our calculations illustrate that metallic zigzag single-walled carbon nanotubes have higher T_c than armchair single-walled carbon nanotubes with approximately same diameters and T_c decreases by increasing diameter. This can explain why superconductivity could be found in the small diameter single-walled carbon nanotubes. We found for the impurity doped systems, impurity in the strong scattering regime can decrease T_c significantly while in the weak scattering regime T_c is not affected by impurity doping.