Raman-Active modes in Homogeneous and Inhomogeneous Bundle of Single-Walled Carbon Nanotubes

In the present work, the non-resonant Raman active modes were calculated for several diameters, chiralities and sizes for homogeneous and inhomogeneous bundles of single-walled carbon nanotubes (BSWCNT's), using the spectral moment’s method (SMM). Additional intense Raman active modes are present in the breathing-like modes (BLM) spectra of these systems in comparison with a single fully symmetric A1g mode characteristic of isolated nanotubes (SWCNT's). The dependence of the frequency of these modes in terms of diameters, lengths and number of tubes is investigated. We find that for finite bundle, additional breathing-like modes (BLM's) appear as a specific signature. Finally, the effects of the inhomogeneous bundles on the Raman spectra were studied.In the present work, the non-resonant Raman active modes were calculated for several diameters, chiralities and sizes for homogeneous and inhomogeneous bundles of single-walled carbon nanotubes (BSWCNT's), using the spectral moment’s method (SMM). Additional intense Raman active modes are present in the breathing-like modes (BLM) spectra of these systems in comparison with a single fully symmetric A1g mode characteristic of isolated nanotubes (SWCNT's). The dependence of the frequency of these modes in terms of diameters, lengths and number of tubes is investigated. We find that for finite bundle, additional breathing-like modes (BLM's) appear as a specific signature. Finally, the effects of the inhomogeneous bundles on the Raman spectra were studied

Size And Chirality Effects On Raman Spectrum Of Double-Wall Carbon Nanotube Bundle

We study the tube size and bundling effects on Raman active breathing-like phonon modes (BLM) and tangential-like phonon mode (TLM) of double-walled carbon nanotubes (DWCNT) in the framework of the bond polarization theory, and use the spectral moment’s method. The Raman active modes are calculated for different diameter and chirality of the inner and outer DWCNT tubes. The dependence of the Raman spectrum of bundles of identical DWCNTs as a function of the size of the bundle is analysed and additional breathing-like modes are predicted in DWCNT bundle of finite size.We study the tube size and bundling effects on Raman active breathing-like phonon modes (BLM) and tangential-like phonon mode (TLM) of double-walled carbon nanotubes (DWCNT) in the framework of the bond polarization theory, and use the spectral moment’s method. The Raman active modes are calculated for different diameter and chirality of the inner and outer DWCNT tubes. The dependence of the Raman spectrum of bundles of identical DWCNTs as a function of the size of the bundle is analysed and additional breathing-like modes are predicted in DWCNT bundle of finite size

Modelling and simulation of vibrationnal properties of carbon nanotubes and derivatives

The aim of the present paper is to identify the main Raman vibrational features of carbon nanotubes and derivatives. In this goal, Raman active mode calculations have been performed on different single-walled carbon nanotubes (SWCNTs) and double-walled carbon nanotubes (DWCNTs) as well as peapods. The comparison between the calculations performed on these different systems allows us to identify the Raman-active modes of each carbon nanomaterials. In SWCNTs, the tangential modes are located around 1590 cm-1 and the radial breathing mode follows A/D law. This latter law is modified in bundle of SWCNTs, DWCNTs or peapods.The aim of the present paper is to identify the main Raman vibrational features of carbon nanotubes and derivatives. In this goal, Raman active mode calculations have been performed on different single-walled carbon nanotubes (SWCNTs) and double-walled carbon nanotubes (DWCNTs) as well as peapods. The comparison between the calculations performed on these different systems allows us to identify the Raman-active modes of each carbon nanomaterials. In SWCNTs, the tangential modes are located around 1590 cm-1 and the radial breathing mode follows A/D law. This latter law is modified in bundle of SWCNTs, DWCNTs or peapods

Nonresonant Raman spectrum of C60 nanopeapod: C60 polymerization effects

We present a force constants model for the vibrational modes in C60 dimer and polymer phases. The results of this model are used to calculate the nonresonant Raman spectra of infinitely long isolated C60 dimer and polymer peapod in the framework of bond-polarization theory by using the spectral moment’s method. The changes of the Raman spectrum in terms of the structure of the C60 molecules inside the nanotubes are identified. We show that the lowest Raman frequency region of the nanotube is more affected by the C60 chain insertion in comparison with the higher one.We present a force constants model for the vibrational modes in C60 dimer and polymer phases. The results of this model are used to calculate the nonresonant Raman spectra of infinitely long isolated C60 dimer and polymer peapod in the framework of bond-polarization theory by using the spectral moment’s method. The changes of the Raman spectrum in terms of the structure of the C60 molecules inside the nanotubes are identified. We show that the lowest Raman frequency region of the nanotube is more affected by the C60 chain insertion in comparison with the higher one

Finite size effects on Raman spectrum of single-walled boron nitride nanotube

Using the spectral moments method, we present calculations of Raman active modes of Single Walled Boron Nitride Nanotube (SW-BNNT). The Spectra are computed for chiral and achiral nanotubes in terms of their diameter and length. The behaviors of low frequency Raman active modes characteristic, in terms of the tube diameter revealed that these frequencies are diameter dependent. We show that the number of Raman active modes, their frequencies, and intensities depend on the length and chirality of the nanotubes. These predictions are useful to interpret the experimental Raman spectra of BNNTs.Using the spectral moments method, we present calculations of Raman active modes of Single Walled Boron Nitride Nanotube (SW-BNNT). The Spectra are computed for chiral and achiral nanotubes in terms of their diameter and length. The behaviors of low frequency Raman active modes characteristic, in terms of the tube diameter revealed that these frequencies are diameter dependent. We show that the number of Raman active modes, their frequencies, and intensities depend on the length and chirality of the nanotubes. These predictions are useful to interpret the experimental Raman spectra of BNNTs

Interlayer Dependence of G-Modes in Semiconducting Double-Walled Carbon Nanotubes

A double-walled carbon nanotube (DWNT), a coaxial composite of two single-walled carbon nanotubes (SWNT), provides a unique model to study interactions between the two constituent SWNTs. Combining high resolution transmission electron microscopy (HRTEM), electron diffraction (ED), and resonant Raman scattering (RRS) experiments on the same individual suspended DWNT is the ultimate way to relate unambiguously its atomic structure, defined by the chiral indices of the coaxial outer/inner SWNTs, and its Raman-active vibration modes. This approach is used to investigate the intertube distance dependence of the G-modes of individual index-identified DWNTs composed of two semiconducting SWNTs. We state the main features of the dependence of the G-mode frequencies on the distance between the inner and outer layers: (i) When the interlayer distance is larger than the nominal van der Waals distance (close to 0.34 nm), a downshift of the inner-layer G-modes with respect to the G-modes in the equivalent SWNTs is measured. (ii) The amplitude of the downshift depends on the interlayer distance, or in other words, on the negative pressure felt by the inner layer in DWNT. (iii) No shift is observed for an intertube distance close to 0.34 nm

Study of collective radial breathing-like modes in double-walled carbon nanotubes: Combination of continuous two-dimensional membrane theory and Raman spectroscopy

Radial breathing modes (RBMs) are widely used for the atomic structure characterization and index assignment of single-walled carbon nanotubes (SWNTs) from resonant Raman spectroscopy. However, for double-walled carbon nanotubes (DWNTs), the use of conventional ¿RBM(d) formulas is complicated due to the van der Waals interaction between the layers, which strongly affects the frequencies of radial modes and leads to new collective vibrations. This paper presents an alternative way to theoretically study the collective radial breathing-like modes (RBLMs) of DWNTs and to account for interlayer interaction, namely the continuous two-dimensional membrane theory. We obtain an analytical ¿RBLM(do, di) relation, being the equivalent of the conventional ¿RBM(d) expressions, established for SWNTs. We compare our theoretical predictions with Raman data, measured on individual index-identified suspended DWNTs, and find a good agreement between experiment and theory. Moreover, we show that the interlayer coupling in individual DWNTs strongly depends on the interlayer distance, which is manifested in the frequency shifts of the RBLMs with respect to the RBMs of the individual inner and outer tubes. In terms of characterization, this means that the combination of Raman spectroscopy data and predictions of continuous membrane theory may give additional criteria for the index identification of DWNTs, namely the interlayer distance

Excitonic optical transitions characterized by Raman excitation profiles in single-walled carbon nanotubes

We examine the excitonic nature of the E33 optical transition of the individual free-standing index-identified (23, 7) single-walled carbon nanotube by means of the measurements of its radial-breathing-mode and G-mode Raman excitation profiles. We confirm that it is impossible to determine unambiguously the nature of its E33 optical transition (excitonic vs band to band) based only on the excitation profiles. Nevertheless, by combining Raman scattering, Rayleigh scattering, and optical absorption measurements on strictly the same individual (23, 7) single-walled carbon nanotube, we show that the absorption, Rayleigh spectra, and Raman excitation profiles of the longitudinal and transverse G modes are best fitted by considering the nature of the E33 transition as excitonic. The fit of the three sets of data gives close values of the transition energy E33 and damping parameter G33. This comparison shows that the fit of the Raman excitation profiles provides with good accuracy the energy and damping parameter of the excitonic optical transitions in single-walled carbon nanotubes

Low frequency raman scattering in plastic crystals

In this paper we were concerned with the informations provided by the analysis of the low frequency Raman scattering in plastic crystals involving two aspects of the rotational dynamics : The librational dynamics and the reorientational dynamics. Three typical behaviours of low frequency Raman spectra are given. A comparison with neutron scattering data is made

Etude par diffusion Raman de la dynamique réorientationnelle monomoléculaire dans une phase plastique : l'exemple du Bicyclo (222) octane

In this paper we use a model of instantaneous rotational jumps to calculate the reorientational contribution to the broadening of bands related to internal modes active in Raman scattering in a plastic phase. We apply our results to the Bicyclo (222) octane plastic phase (molecular symmetry D3h). We show that in this case the measurements of the bandwidths of the E' and E" internal modes allow us to estimate a characteristic time of the jump model : τC4 (τC4 residence time of the molecule along the direction of the face centred cubic lattice). The temperature dependence of τC4 is coherent with the same variation derived from quasi elastic incoherent neutron scattering data.Dans cet article nous utilisons un modèle de sauts à deux mouvements distincts pour évaluer la contribution réorientationnelle à l'élargissement des bandes relatives à des modes internes actifs en diffusion Raman dans une phase plastique. Nous appliquons nos résultats au cas du Bicyclo (222) octane (symétrie moléculaire D3h). Nous montrons que dans cet exemple la mesure des largeurs des bandes relatives aux modes de symétrie E' et E" permet d'évaluer le temps τ C4 du modèle (τC4 temps de résidence de la molécule le long d'une direction du réseau cristallin cubique à faces centrées). La variation avec la température de τC4 est cohérente avec celle dérivée de données de diffusion incohérente neutronique