A symmetry-adapted force-constant lattice-dynamical model for single-walled carbon nanotubes

We develop a lattice-dynamical model based on the screw symmetry of single-walled carbon nanotubes that allows for reducing the size of the dynamical matrix to six, for all tube chiralities. The model uses force constants derived from fitting to the phonon dispersion of 2D graphite. We present the calculation procedure in a clear and transparent way, making the model easier to follow. We calculate the phonon dispersions of a number of nanotubes of different chiralities. The splitting of two highest Raman active modes and the radial breathing mode frequency are studied by changing the tube diameter and chirality.     

Raman spectroscopy on single- and multi-walled nanotubes under high pressure

The pressure dependence of the high-energy Raman modes in single- and multi-walled carbon nanotubes was measured in the range 0–10 GPa. We found the pressure coefficient to be linear in both materials but 25% smaller in MWNT. Given that the curvature effects on vibrational properties of the rolled-up graphene sheets are small, we can explain this difference simply with elasticity theory. Received: 17 May 1999 / Accepted 18 May 1999 / Published online: 4 August 1999     

Intermediate frequency modes in Raman spectra of Ar+‐irradiated single‐wall carbon nanotubes

We study the effect of Ar⁺ irradiation on the intermediate frequency modes (IFM) in Raman spectra of single‐wall carbon nanotubes. We observe new features in the intermediate frequency region from 386 to 635 cm^–1 as the defect concentration increases, whereas at the same time there is a decrease of other IFM modes. After annealing in vacuum, the IFM modes recover and become similar to those of the nanotubes before irradiation. We interpret the new features in the Raman spectra as originating from the phonon density of states that becomes visible in the Raman process due to the presence of defects. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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     

The origin of polarized blackbody radiation from resistively heated multiwalled carbon nanotubes

We observed very pronounced polarization of light emitted by highly aligned free-standing multiwall carbon nanotube (MWNT) sheet in axial direction which is turned to the perpendicular polarization when a number of layers are increased. The radiation spectrum of resistively heated MWNT sheet closely follows to the Plank's blackbody radiation distribution. The obtained polarization features can be described by a classical dielectric cylindrical shell model, taking into consideration the contribution of delocalized π-electrons (π surface plasmons). In absorption (emission) the optical transverse polarizability, which is much smaller than longitudinal one, is substantially suppressed by depolarization effect due to screening by induced charges. This phenomenon suggests very simple and precise method to estimate the alignment of nanotubes in bundles or large assemblies.     

Raman spectroscopy and field-emission properties of CVD-grown carbon-nanotube films

Carbon-nanotube films are very efficient cathodes for field-emission devices. This study presents a comprehensive comparison between structural, spectroscopic and field-emission properties of films of aligned and non-aligned multi-wall nanotubes (MWNTs) which are grown by thermal chemical vapour deposition. Three types of films are investigated: vertically aligned MWNTs with clean and coated nanotube side walls as well as non-aligned MWNT films. Raman spectra taken on the aligned MWNT films consist of many lines of first-, second- and third-order signals. Several lines are reported here for the first time for MWNTs. The presence of the surface coating leads to a decrease and broadening of the higher-order signals as well as an increase in the disorder-induced contributions in the first-order regime. The aligned MWNT films have excellent field-emission properties with very high emission current densities and low turn-on and threshold fields. The presence of a surface coating has no impact on the efficiency of the field-emission process. Films of non-aligned MWNTs show considerably reduced electron-emission current densities and larger critical fields. Received: 25 April 2001 / Accepted: 30 May 2001 / Published online: 25 July 2001     

Laser heating method for estimation of carbon nanotube purity

A new method of a carbon nanotube purity estimation has been developed on the basis of Raman spectroscopy. The spectra of carbon soot containing different amounts of nanotubes were registered under heating from a probing laser beam with a step-by-step increased power density. The material temperature in the laser spot was estimated from a position of the tangential Raman mode demonstrating a linear thermal shift (-0.012 cm^-1/K) from the position 1592 cm^-1 (at room temperature). The rate of the material temperature rise versus the laser power density (determining the slope of a corresponding graph) appeared to correlate strongly with the nanotube content in the soot. The influence of the experimental conditions on the slope value has been excluded via a simultaneous measurement of a reference sample with a high nanotube content (95 vol. %). After the calibration (done by a comparison of the Raman and the transmission electron microscopy data for the nanotube percentage in the same samples) the Raman-based method is able to provide a quantitative purity estimation for any nanotube-containing material. Received: 11 December 2001 / Accepted: 12 December 2001 / Published online: 4 March 2002     

Charge-carrier dynamics in single-wall carbon nanotube bundles: a time-domain study

We present a real-time investigation of ultra-fast carrier dynamics in single-wall carbon nanotube bundles using femtosecond time-resolved photoelectron spectroscopy. The experiments allow us to study the processes governing the sub-picosecond and the picosecond dynamics of non-equilibrium charge carriers. On the sub-picosecond time scale the dynamics are dominated by ultra-fast electron–electron scattering processes, which lead to internal thermalization of the laser-excited electron gas. We find that quasiparticle lifetimes decrease strongly as a function of their energy up to 2.38 eV above the Fermi level – the highest energy studied experimentally. The subsequent cooling of the laser-heated electron gas to the lattice temperature by electron–phonon interaction occurs on the picosecond time scale and allows us to determine the electron–phonon mass-enhancement parameter λ. The latter is found to be over an order of magnitude smaller if compared, for example, with that of a good conductor such as copper. Received: 4 March 2002 / Accepted: 7 March 2002 / Published online: 3 June 2002     

Conductance of a Quantum Dot in the Presence of a Phonon Field

We theoretically investigate the electrical transport property of a quantum dot with longitudinal optical phonons. The conductance through the dot connected to two leads is calculated by the nonequilibrium Green function within the Landauer-Büttiker framework. The numerical examples of the conductance with different electron-phonon coupling strengths show that the presence of a phonon field typically results in the suppression of the main peak accompanied by some phonon side peaks. Both the main peak and the side peaks axe sensitive to the electron-phonon coupling strength, which is related to temperature. Our results for this system are consistent with some related previous works but the calculation is comparatively simple.     

Are deformed modes still Raman active for single-wall carbon nanotubes?

Using group theory calculations combined with the force-constant model and molecular-dynamics simulations, whether the deformed modes are Raman active or not for (10,10) and (10,0) single-wall carbon nanotubes under hydrostatic pressure is discussed. With increasing pressure, the tube symmetry lowers from D_20h to D_2h then to C_2h point group. For D_20h, A_1g is changed to A_g, while E_1g and E_2g are split: E_1g→B_2g+B_3g→2B_g and E_2g→A_g+B_1g→2A_g. On the basis of the correlation between D_20h, D_2h, and C_2h point groups, the deformed modes should be still Raman active. The result can help us clarify the essence of the experimental observations.     

Effect of ZnS shell on the Raman spectra from CdSe nanorods

We investigated the influence of an epitaxially grown ZnS shell on the phonon spectra of CdSe nanorods of different sizes. The CdSe related Raman peaks shift with addition of a ZnS shell. The longitudinal optical phonon shifts slightly due to strain and the low‐energy shoulder shifts stronger, which can be explained within a model for surface optical phonons. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Surface acoustic phonon modes of Ge nanocrystals embedded in SiO2

Ge nanocrystals (NCs) embedded in SiO₂ are synthesized by ion implantation, and the surface vibrational modes of the Ge NCs are investigated using the low-frequency Raman scattering (LFRS) technique. LFRS studies show distinct low-frequency Raman modes in the range 6.5-21.2 cm⁻¹ for the Ge NCs depending on the implant dose and annealing temperature. These low-frequency Raman modes are attributed to the confined surface acoustic phonon modes of Ge NCs with (0,0) spheroidal mode and (0,3) torsional modes. Our results are in excellent agreement with the recent theoretical predictions of surface vibrational modes in Ge NCs.     

Investigation of size-driven phase transition in bismuth titanate nanocrystals by Raman spectroscopy

Raman spectroscopy was used to investigate the lattice dynamics and structural transformations in bismuth titanate (Bi₄Ti₃O₁₂) nanocrystals prepared by a chemical coprecipitation technique. The crystal structure of the samples of different grain sizes was determined by X-ray-diffraction analysis. The evolution of the Raman spectrum with grain size was characterized by an intensity decrease, a broadening of the line width, a frequency shift, and the disappearance of the Raman mode. The results revealed the appearance of a size-driven phase transition from orthorhombic to tetragonal phases at a critical size of 44 nm. This result is quite consistent with the X-ray-diffraction measurement and differential thermal analysis. The origin was attributed to the grain-size effect and explained by the surface-energy mechanism. Received: 26 June 2002 / Accepted: 18 August 2002 / Published online: 15 January 2003 RID="*" ID="*"Corresponding author. Fax: +86-25/3595535, E-mail: msz@nju.edu.cn     

Two modes of electroluminescence from single‐walled carbon nanotubes

The electroluminescence from single‐walled carbon nanotube field effect transistors is spectrally resolved, and shows two distinct modes of light emission. The vast majority of nanotubes have spectrally broad emission consistent with the spectrum of blackbody radiation. Much more rarely, superposed on the broad emission is a single narrow (<50 meV) peak which is consistent with expectation for electron–hole recombination. The narrow emission is strong even at lower biases and in general has greater peak intensity than the broadband emission. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radial breathing-like mode of wide carbon nanoribbon

The radial breathing-like mode (RBLM), an interesting Raman mode, of the carbon nanoribbons (CNRs) with different widths have been calculated by the empirical Brenner potential. It is found that the RBLM frequencies of CNRs whose widths are larger than 25 Å follow a new 1/w rule, which is different from the rule, obtained for the narrow CNRs [J. Zhou, J. Dong, Appl. Phys. Lett. 91 (2007) 173108]. A continuum rod model is proposed to explain the new 1/w rule, which is also different from the previous simple one-dimensional oscillator model, suitable only for the narrow CNRs. Based upon the CNR's RBLMs, we have proposed a practical experimental method to determine the widths of CNRs by their Raman spectra.     

Analysis of the concentration of C60 fullerenes in single wall carbon nanotubes

Single wall carbon nanotubes filled with C₆₀ were analyzed using resonance Raman scattering and electron energy loss spectroscopy. In order to obtain concentrations of the fullerene molecules inside the tubes, the scattering intensity from the fullerenes relative to that from the tubes was used. Since the scattering intensity from the tubes is subject to strong fluctuations, the determination of the concentrations is shown to require averaging of results from different lasers and from all observable Raman lines. The fluctuations are shown to be intrinsic and a consequence of photoselective resonance scattering. Calibration of absolute concentrations can be obtained from electron energy loss spectroscopy performed on the same samples. Samples with three different diameters were analyzed and good agreement between the fullerene concentrations measured by the two methods was obtained. Received: 20 September 2002 / Accepted: 4 November 2002 / Published online: 10 March 2003 RID="*" ID="*"Corresponding author. Fax: +43-1/4277-51375, E-mail: kuzman@ap.univie.ac.at     

Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration

In this work we investigate the rainbows appearing in channeling of 1 GeV protons through the long (11,9) single-wall carbon nanotubes. The nanotube length is varied from 10 to 500 μm. The angular distributions of channeled protons are computed using the numerical solution of the proton equations of motion in the transverse plane and the Monte Carlo method. The rainbows are identified as the rings in the angular distributions, which correspond to the extrema of the proton deflection functions. Each rainbow is characterized by a sharp decrease of the proton yield on its large angle side. As the nanotube length increases, the number of rainbows increases and the average distance between them decreases in an easily predictable way. When the average distance between the rainbows becomes smaller than the resolution of the angular distribution, one cannot distinguish between the adjacent rainbows, and the angular distribution becomes equilibrated. We call this route to equilibration the rainbow route to equilibration. This work is a demonstration of how a simple one-dimensional bound dynamic system can exhibit a complex collective behavior.     

Raman spectroscopy of graphene and carbon nanotubes

This paper reviews progress that has been made in the use of Raman spectroscopy to study graphene and carbon nanotubes. These are two nanostructured forms of sp² carbon materials that are of major current interest. These nanostructured materials have attracted particular attention because of their simplicity, small physical size and the exciting new science they have introduced. This review focuses on each of these materials systems individually and comparatively as prototype examples of nanostructured materials. In particular, this paper discusses the power of Raman spectroscopy as a probe and a characterization tool for sp² carbon materials, with particular emphasis given to the field of photophysics. Some coverage is also given to the close relatives of these sp² carbon materials, namely graphite, a three-dimensional (3D) material based on the AB stacking of individual graphene layers, and carbon nanoribbons, which are one-dimensional (1D) planar structures, where the width of the ribbon is on the nanometer length scale. Carbon nanoribbons differ from carbon nanotubes is that nanoribbons have edges, whereas nanotubes have terminations only at their two ends.     

Probing disorder and charged impurities in graphene by Raman spectroscopy

Disorder and doping can strongly affect the properties of graphene. Here we analyze these effects on several samples by Raman spectroscopy. In particular, we show that pristine and unprocessed graphene samples deposited on silicon, covered with a thin silicon oxide layer, show strong variations in their Raman spectra, even in absence of disorder. The variation in the Raman parameters is assigned to charged impurities. This shows that as‐deposited graphene is unintentionally doped, reaching charge concentrations up to 10¹³ cm^–2 under ambient conditions. The doping varies from sample to sample and the charges are inhomogeneously distributed on a submicron scale. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)