利用径向呼吸模及其倍频模的共振特性精确测定单壁碳纳米管的电子跃迁能量

提出一个根据拉曼基频模及其倍频模的斯托克斯和反斯托克斯拉曼成分的不同共振行为来探测样品与激光共振的系统能级的方法.此方法被应用到不均匀单壁碳纳米管束样品中某一径向呼吸模频率为219波数的金属型碳纳米管.通过分析呼吸模及其倍频模和切向模的共振行为,获得了该碳纳米管的电子跃迁能量,并获得纳米管C-C最近邻重叠积分因子为2.80 eV.此数值可以很好的解释单壁碳纳米管径向呼吸模的共振行为. 关键词： 单壁碳纳米管 呼吸模 共振拉曼散射 电子跃迁能     

Phonon and thermal properties of achiral single wall carbon nanotubes

A detailed theoretical study of the phonon and thermal properties of achiral single wall carbon nanotubes has been carried out using force constant model considering up to third nearest-neighbor interactions. We have calculated the phonon dispersions, density of states, radial breathing modes (RBM) and the specific heats for various zigzag and armchair nanotubes, with radii ranging from 2.8 Å to 11.0 Å. A comparative study of phonon spectrum with measured Raman data reveals that the number of Raman active modes for a tube does not depend on the number of atoms present in the unit cell but on its chirality. Calculated phonon modes at the zone center more or less accurately predicted the Raman active modes. The radial breathing mode is of particular interest as for a specific radius of a nanotube it is found to be independent of its chirality. We have also calculated the variation of RBM and G-band modes for tubes of different radii. RBM shows an inverse dependence on the radius of the tube. Finally, the values of specific heat are calculated for various nanotubes at room temperature and it was found that the specific heat shows an exponential dependence on the diameter of the tube.     

Resonant Raman excitation profiles of individually dispersed single walled carbon nanotubes in solution

Raman excitation profiles were generated between 695 and 985 nm for individual carbon nanotubes dispersed in aqueous solution. We confirmed that previously published spectral assignments for semi-conducting and metallic carbon nanotubes are able to predict the location and resonant maxima of radial breathing mode features in the Raman spectrum. Three large diameter features were observed within the excitation space over the scan range and accurately predicted as metallic species. There was significant agreement between predicted and observed Raman modes. However, one discrepancy is noted with the (6,4) nanotubes. This species is not observed when excited at or near its absorption transition. We find that the Raman cross-sections in general, assuming a diameter-based distribution of nanotubes, are disproportionately smaller for mod(n-m,3)=1 semi-conducting nanotubes than their counterparts by at least an order of magnitude. These results have important implications for the use of Raman spectroscopy to effectively characterize the chirality distribution of carbon nanotube samples. PACS 61.46.+w; 73.22.-f; 78.30.-j     

Anti‐Stokes Raman spectroscopy as a method to identify the metallic and semiconducting configurations of double‐walled carbon nanotubes

Although Raman spectra reveal, as a signature of double‐walled carbon nanotubes (DWCNTs), two radial breathing mode (RBM) lines associated with the inner and outer tubes, the specification of their nature as metallic or semiconducting remains a topic for debate. Investigating the spectral range of the RBM lines, we present a new procedure of the indexing of the semiconducting or metallic nature of the inner and outer shell that forms the DWCNT. The procedure exploits the difference between the intensities of recorded anti‐Stokes Raman spectrum and the anti‐Stokes spectrum calculated by applying the Boltzmann formulae to the recorded Stokes spectrum. The results indicate that the two spectra do not coincide with what should happen in a normal Raman process, namely, that there are RBM lines of the same intensity in both spectra, as well as RBM lines of higher intensity that are observed in the calculated spectrum. This discrepancy results from the surface‐enhanced Raman scattering mechanism that operates differently on metallic or semiconducting nanotubes. In this context, the analysis of the RBM spectrum can reveal pairs of lines associated with the inner/outer shell structure of DWCNT, and when the intensities between the recorded and calculated spectra coincide, the nanotube is metallic; otherwise, the nanotube is semiconducting. Copyright © 2014 John Wiley & Sons, Ltd.     

Raman and SERS studies of carbon nanotube systems

In this paper, we report on Raman studies carried out on different carbon nanotube systems, namely single-walled and multi-walled carbon nanotubes and polymer/nanotube composites. We focus on different types of interactions which can take place in these materials. In single-walled nanotubes, the introduction of van der Waals interactions between tubes when arranged in bundles leads to an upshift of the radial breathing mode (RBM) ranging from 11 to 16 cm⁻¹ depending on the size of the bundle. In multi-walled carbon nanotubes, similar interactions between concentric tubes permit to interpret the low frequency Raman modes. In composites, PMMA/nanotubes, an upshift of the RBM is also observed, explained by the dynamical strain applied by the polymer on the bundles, in response to the breathing vibration. In addition, surface enhanced Raman scattering experiments have demonstrated the occurrence of interfacial reactions between the nanotubes and the metallic support. This is put in evidence by the degradation of tubes, especially metallic ones, and reconstruction of C₆₀-like molecules are in some cases observed.     

Resonance Raman spectroscopic study for radial vibrational modes in ultra‐thin walled TiO2 nanotubes

The study reports the observation of radial vibrational modes in ultra‐thin walled anatase TiO₂ nanotube powders grown by rapid breakdown anodization technique using resonant Raman spectroscopic study. The as‐grown tubes in the anatase phase are around 2–5 nm in wall thickness, 15–18 nm in diameter and few microns in length. The E_{g(ν1,ν5,ν6)} phonon modes with molecular vibrations in the radial direction are predominant in the resonance Raman spectroscopy using 325 nm He–Cd excitation. Multi‐phonons including overtones and combinational modes of E_{g(ν1,ν5,ν6)} are abundantly observed. Fröhlich interaction owing to electron–phonon coupling in the resonance Raman spectroscopy of ultra‐thin wall nanotubes is responsible for the observation of radial vibrational modes. Finite size with large surface energy in these nanotubes energetically favor only one mode, B_1g(ν4) with unidirectional molecular vibrations in the parallel configuration out of the three Raman modes with molecular vibration normal to the radial modes. Enhanced specific heat with increasing temperatures in these nanotubes as compared to that reported for nanoparticles of similar diameter may possibly be related to the presence of the prominent radial mode along with other energetic phonon mode. The findings elucidate the understanding of total energy landscape for TiO₂ nanotubes. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling and simulation of vibrational breathing-like modes in individual multiwalled carbon nanotubes

We study the collective vibrational breathing modes in the Raman spectrum of multiwalled carbon nanotubes (MCNTs). First, a bond polarization theory and the spectral moment's method (SMM) are used to calculate the non-resonant Raman frequencies of the breathing-like modes (BLMs) and the tangential-like ones (TLMs). Second, the Raman active modes of MCNTs are computed for different diameters and numbers of layers. The obtained low frequency modes in MCNTs can be identified to each single-walled carbon nanotubes. These modes that originate from the radial breathing ones of the individual walls are strongly coupled through the concentric tube–tube van der Waals interaction. The calculated BLMs in the low-frequency region are compared with the experimental Raman data obtained from other studies. Finally, special attention is given to the comparison with Raman data on MCNTs composed of six layers.     

Variable electron-phonon coupling in isolated metallic carbon nanotubes observed by Raman scattering

We report the existence of broad and weakly asymmetric features in the high-energy (G) Raman modes of freely suspended metallic carbon nanotubes of defined chiral index. A significant variation in peak width (from 12 cm(-1) to 110 cm(-1)) is observed as a function of the nanotube's chiral structure. When the nanotubes are electrostatically gated, the peak widths decrease. The broadness of the Raman features is understood as the consequence of coupling of the phonon to electron-hole pairs, the strength of which varies with the nanotube chiral index and the position of the Fermi energy.     

Detection of invisible phonon modes in individual defect-free carbon nanotubes by gradient-field Raman scattering

We provide an effective method to investigate the field gradient effect in nanoconfined plasmon-matter interaction.Aligned ultralong SWNTs without defects were grown on marked substrates, followed by assembling gold nanoparticle clusters around individual nanotubes. The Raman scattering behavior of a nanotube placed in an atomic scale nanogap between adjacent nanoparticles was studied. In addition to the expected plasmon-induced Raman enhancement up to 103,the defect-free D-mode of an individual SWNT induced by gradient field is found for the first time. When the light is confined at atomic scale, gradient field Raman scattering becomes significant and dipole-forbidden phonon modes can be activated by quadrupole Raman tensor variation, indicating breakdown of the Raman selection rules.     

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.     

Fabrication and characterization of suspended single-walled carbon nanotubes

Suspended single-walled carbon nanotubes (SWCNTs) between SiO₂ pillars via a direct lithographic route using a simple mixture of catalyst precursor [Co(III) acetylacetonate, Co(acac)₃] and conventional electron beam resist (ma-N2403) were fabricated. The catalytic electron beam resist (Cat-ER) layer plays dual roles as a catalyst and a resist layer for the growth and alignment of CNTs, respectively. The structure of the grown nanotube was characterized by Raman spectroscopy (633 nm laser excitation). Nanotubes grown from Cat-ER with Co(acac)₃ show the typical Raman spectra of SWCNTs which are characterized by the strong tangential bands near to 1590 cm⁻¹ and radial breathing modes (RBMs) in the low frequency region (<300 cm⁻¹). The calculated diameter of the probed nanotubes individually corresponds to the range 0.86-1.77 nm.     

Surface‐enhanced Raman scattering studies of carbon nanotubes using Ag‐core Au‐shell nanoparticles

Surface‐enhanced Raman scattering from carbon nanotube bundles adsorbed with plasmon‐tunable Ag‐core Au‐shell nanoparticles (Ag@Au nps) was carried out for the first time. By utilizing nanoparticles whose plasmon resonance peak (541, 642 nm) closely matches the commonly used Raman excitation sources (532, 632.81 nm), we can observe a large enhancement in the Raman signatures of carbon nanotubes. We obtain greater enhancement in the Raman signal for the above case when compared to nanotubes adsorbed with conventional Ag, Au or other ‘off resonant’ Ag@Au nps. The power‐dependent SERS experiment on single‐walled nanotubes (SWNTs) with resonant Ag@Au nps reveals a linear behavior between the G‐band intensity and the photon flux density, which is in agreement with the vibrational pumping model of SERS. The observed enhancement by resonance matching is pronounced for carbon nanotubes and may lead to insights into understanding nanotube–nanoparticle interaction. Copyright © 2009 John Wiley & Sons, Ltd.     

Anisotropic packing and one-dimensional fluctuations of C60 molecules in carbon nanotubes

The confinement of a C60 molecule encapsulated in a cylindrical nanotube depends on the tube radius. In small tubes with radius RT approximately < 7 A, a fivefold axis of the molecule coincides with the tube axis. The interaction between C60 molecules in the nanotube is then described by a O2-rotor model on a 1D liquid chain with coupling between orientational and displacive correlations. This coupling leads to chain contraction. The structure factor of the 1D liquid is derived. In tubes with a larger radius the molecular centers of mass are displaced off the tube axis. The distinction of two groups of peapods with on- and off-axis molecules suggests an explanation of the apparent splitting of Ag modes of C60 in nanotubes measured by resonant Raman scattering.     

High-energy phonon branches of an individual metallic carbon nanotube

We present excitation-energy dependent Raman measurements between 2.05 and 2.41 eV on the same individual carbon nanotube. We find a change in the Raman frequencies of both the D mode (63 cm(-1)/eV) and the high-energy modes. The observed frequencies of the modes at approximately 1600 cm(-1) as a function of laser-energy map the phonon dispersion relation of a metallic tube near the Gamma point of the Brillouin zone. Our results prove the entire first-order Raman spectrum in single-wall carbon nanotubes to originate from double-resonant scattering. Moreover, we confirm experimentally the phonon softening in metallic tubes by a Peierls-like mechanism.     

Measuring the uniaxial strain of individual single-wall carbon nanotubes: resonance Raman spectra of atomic-force-microscope modified single-wall nanotubes

Raman spectroscopy is used to measure the strain in individual single-wall carbon nanotubes, strained by manipulation with an atomic-force-microscope tip. Under strains varying from 0.06%-1.65%, the in-plane vibrational mode frequencies are lowered by as much as 1.5% (40 cm(-1)), while the radial breathing mode (RBM) remains unchanged. The RBM Stokes/anti-Stokes intensity ratio remains unchanged under strain. The elasticity of these strain deformations is demonstrated as the down-shifted Raman modes resume their prestrain frequencies after a nanotube is broken under excessive strain.     

Temperature dependence of the raman spectra of carbon nanotubes with 1064 nm excitation

In this report, the near infrared 1064 nm line of an Nd:YAG laser, which has strong thermal effect, was used as the excitation. A temperature dependence of the Raman spectra of carbon nanotubes was observed at different temperatures by varying the incident laser power. The results show that the relative Raman intensities to the tangential stretching mode (G mode) of the higher-order Raman modes within 2500–3500 cm⁻¹ increase with increasing excitation laser power at the sample and the changes in the relative Raman intensities are linear in the excitation laser power. This has not been reported elsewhere. Thorough analysis shows that this is a temperature dependence of double-phonon Raman scattering and maybe provide important information for the studying of CNTs and double-phonon Raman scattering.     

The effect of a large SWNT diameter distribution on cesium intercalation

Vapor-phase intercalation of a single-walled carbon nanotube sample with Cs was carried out and monitored in situ by Raman spectroscopy. Results indicate that the endpoint of the intercalation was limited by small interstitial gaps in the nanotube bundles. These small-diameter gaps are present because of the significant number of small-diameter nanotubes (0.9-1.0 nm, as calculated from Raman radial breathing mode frequencies) present in the sample. It is not possible to determine from our Raman spectra whether the early endpoint is the result of diffusion limitation or the equilibrium energetics at the endpoint, although some diffusion limitation is observed near the beginning of the reaction. A simple geometric model for expansion of the nanotube bundles under intercalation is presented; this model reproduces, reasonably well, measured expansions reported by others and explains both diffusion- and equilibrium-limited mechanisms in terms of the larger lattice expansion required for smaller-diameter nanotubes. Staging of the intercalation process, in analogy with the staged intercalation of graphite intercalation compounds, is not observed. Instead, the transverse mode peaks undergo a gradual decrease in intensity and a gradual charge transfer- and electronic coupling-induced downshift.     

Phonons in carbon nanotubes

A broad review of the unusual one-dimensional properties of phonons in carbon nanotubes is presented, including phonons in isolated nanotubes and in crystalline arrays of nanotubes in nanotube bundles. The main technique for probing the phonon spectra has been Raman spectroscopy and the many unique and unusual features of the Raman spectra of carbon nanotubes are reviewed. Also included is a brief review of the thermal properties of carbon nanotubes in relation to their unusual phonon dispersion relations and density of states.     

Phonon spectrum and interaction between nanotubes in single-walled carbon nanotube bundles at high pressures and temperatures

The Raman spectra of single-walled carbon nanotubes at temperatures up to 730 K and pressures up to 7 GPa have been measured. The behavior of phonon modes and the interaction between nanotubes in bundles have been studied. It has been found that the temperature shift of the vibrational G mode is completely reversible, whereas the temperature shift of radial breathing modes is partially irreversible and the softening of the modes and narrowing of phonon bands are observed. The temperature shift and softening of radial breathing modes are also observed when samples are irradiated by laser radiation with a power density of 6.5 kW/mm². The dependence of the relative frequency Ω/Ω₀ for G ⁺ and G ^? phonon modes on the relative change A ₀/A in the triangular lattice constant of bundles of nanotubes calculated using the thermal expansion coefficient and compressibility coefficient of nanotube bundles shows that the temperature shift of the G mode is determined by the softening of the C-C bond in nanotubes. An increase in the equilibrium distances between nanotubes at the breaking of random covalent C-C bonds between nanotubes in bundles of nanotubes is in my opinion the main reason for the softening of the radial breathing modes.     

Vibrational analysis of double-walled carbon nanotubes with inner and outer nanotubes of different lengths

In this study, the Euler-Bernoulli beam model is used to analyze the resonant vibration of double-walled carbon nanotubes (DWCNTs) with inner and outer nanotubes of different lengths. The resonant properties of DWCNTs with different inner and outer nanotube lengths are investigated in detail using this theoretical approach. The resonant vibration is significantly affected by the vibrational modes of the DWCNTs, and by the lengths of the inner and outer nanotubes. For an inner or outer nanotube of constant length, the vibrational frequencies of the DWCNTs increase initially and then decrease as the length of another nanotube increases. A design for nanoelectromechanical devices that operate at various frequencies can be realized by controlling the length of the inner and outer nanotubes of DWCNTs. This investigation may be helpful in applications of carbon nanotubes such as high frequency oscillators, dynamic mechanical analysis and mechanical sensors.