Breathing-like Modes Research Articles

Infrared-active modes in finite and infinite double-walled boron nitride nanotubes

The calculation of the infrared spectrum of double-walled boron nitride nanotubes (DBNNT's) is performed in the framework of the force constants model, using the spectral moment's method. The calculation of the DBNNT infrared active modes as a function of the diameter and chirality of the inner and outer tubes allows us to derive the diameter dependence of the wave number of the breathing-like modes, intermediate-like modes and tangential-like modes in a large diameter range. In particular, the diameter dependence of the wave numbers of the two radial breathing-like modes resulting from the in-phase and counterphase coupled motions of the totally symmetric radial breathing mode (the so-called RBM) of the inner and outer tubes is discussed. Depending on the relative lengths of the inner and outer tubes, additional modes are evidenced in the RBM region. These modes must be considered in the analysis of the experimental data.

Vibrational properties and Raman spectra of different edge graphene nanoribbons, studied by first-principles calculations

Abstract The vibrational properties and Raman spectra of graphene nanoribbons with six different edges have been studied by using the first-principles calculations. It is found that edge reconstruction leads to the emergence of localized vibrational modes and new topological defect modes, making the different edges identified by polarized Raman spectra. The radial breathing-like modes are found to be independent of the edge structures, while the G-band-related modes are affected by different edge structures. Our results suggest that the polarized Raman spectrum could be a powerful experimental tool for distinguishing the GNRs with different edge structures due to their different vibrational properties.

Raman Spectroscopy of Folded and Scrolled Graphene

Here we examine the effects of folding and scrolling on the Raman spectra of mechanically exfoliated single- and bilayer graphene prepared on SiO(2) substrates. We find that incommensurate folding in bilayer graphene results in a shift of the second-order G' band frequency, similar to that observed in folded single-layer graphene due to fold-induced changes in the phonon/electronic energy dispersion. Importantly, we show that the contrasting Raman shifts reported for the G' band frequency in folded graphene can be rationalized by taking into account the relative strength of fold-induced electron/phonon renormalization. More interestingly, we find that curvature in scrolled graphene lifts the degeneracy of the G band and results in a splitting of the G band and the appearance of low-frequency radial breathing-like (RBLM) modes. This study highlights a variety of Raman signatures for fold-induced and curvature-induced graphene and sets the stage for further theoretical and experimental studies of these novel structures.

Experimental observation of radial breathing-like mode of graphene nanoribbons

We report that single-walled carbon nanotubes (SWNTs) can be etched into graphene nanoribbons (GNRs) by iron etching, which is confirmed by Raman spectroscopy and transmission electron microscopy. Compared with SWNTs, there are some unique features in Raman spectra of GNRs: symmetric G peak with no splitting, larger Raman intensity of 2D peak than G peak, and lower frequency and narrower full width at half maximum for 2D peak. Similar to radial breathing modes in SWNTs, theoretically predicted radial breathing-like mode of GNRs is also observed: a clear and prominent peak around 223 cm−1 in the low frequency regions. This work paves the way for future studies of nanodevices based on SWNT-GNR heterojunction.

Raman Spectroscopy on Individual Identified Carbon Nanotubes

ABSTRACTIn this paper, we discuss the low-frequency range of the Raman spectrum of individual suspended index-identified single-walled (SWCNTs) and double-walled carbon nanotubes (DWCNTs). In SWCNTs, the role of environment on the radial breathing mode (RBM) frequency is discussed. We show that the interaction between the surrounding air and the nanotube does not induce a RBM upshift. In several DWCNTs, we evidence that the low-frequency modes cannot be connected to the RBM of each related layer. We discuss this result in terms of mechanical coupling between the layers which results in collective radial breathing-like modes. The mechanical coupling qualitatively explains the observation of Raman lines of radial breathing-like modes, whenever only one of the layers is in resonance with the incident laser energy.

Experimental Evidence of a Mechanical Coupling between Layers in an Individual Double-Walled Carbon Nanotube

We perform transmission electron microscopy, electron diffraction, and Raman scattering experiments on an individual suspended double-walled carbon nanotube (DWCNT). The first two techniques allow the unambiguous determination of the DWCNT structure: (12,8)@(16,14). However, the low-frequency features in the Raman spectra cannot be connected to the derived layer diameters d by means of the 1/d power law, widely used for the diameter dependence of the radial-breathing mode of single-walled nanotubes. We discuss this disagreement in terms of mechanical coupling between the layers of the DWCNT, which results in collective vibrational modes. Theoretical predictions for the breathing-like modes of the DWCNT, originating from the radial-breathing modes of the layers, are in a very good agreement with the observed Raman spectra. Moreover, the mechanical coupling qualitatively explains the observation of Raman lines of breathing-like modes, whenever only one of the layers is in resonance with the laser energy.

Observation of Breathing-like Modes in an Individual Multiwalled Carbon Nanotube

We study collective vibrational breathing modes in the Raman spectrum of a multiwalled carbon nanotube. In correlation with high-resolution transmission electron microscopy, we find that these modes have energies differing by more than 23% from the radial breathing modes of the corresponding single-walled nanotubes. This shift in energy is explained with intershell interactions using a model of coupled harmonic oscillators. The strength of this interaction is related to the coupling strength expected for few-layer graphene.

MgO-Supported Gold Cages Identified by Their Vibrational Modes: First-Principles Simulations

The structural and vibrational properties of the MgO-supported gold clusters, AuN (N = 25−41), have been investigated by using the first-principles calculations. It is found that they indeed prefer the open pyramidal hollow (OPH) cages in this size range, showing distinctly different vibrational spectra from other adsorbed isomers. The spectra can provide a fingerprint signal to accurately identify their characteristic OPH structures. More interestingly, it is found that each of these OPH cages has its own breathing-like mode, whose frequency depends on cluster size, following approximately a linear variation with its inverse effective radius, which may be tested by the future Raman measurements.

Symmetry properties of vibrational modes in graphene nanoribbons

We present symmetry properties of the lattice vibrations of graphene nanoribbons with pure armchair (AGNRs) and zigzag edges (ZGNRs). In nonsymmorphic nanoribbons, the phonon modes at the edge of the Brillouin zone are twofold degenerate whereas the phonon modes in symmorphic nanoribbons are nondegenerate. We identified the Raman-active and infrared-active modes. We predict $3N$ and $3(N+1)$ Raman-active modes for $N$-ZGNRs and $N$-AGNRs, respectively ($N$ is the number of dimers per unit cell). These modes can be used for the experimental characterization of graphene nanoribbons. Calculations based on density-functional theory suggest that the frequency splitting of the LO and TO modes in AGNRs (corresponding to the ${E}_{2g}$ mode in graphene) exhibits characteristic width and family dependence. Further, all graphene nanoribbons have a Raman-active breathinglike mode, the frequency of which is inversely proportional to the nanoribbon width and thus might be used for experimental determination of the width of graphene nanoribbons.

Acousto-plasmonic Hot Spots in Metallic Nano-Objects

We investigate the acousto-plasmonic dynamics of metallic nano-objects by means of resonant Raman scattering and time-resolved femtosecond transient absorption. We observe an unexpectedly strong acoustic vibration band in the Raman scattering of silver nanocolumns, usually not found in isolated nano-objects. The frequency and the polarization of this unexpected Raman band allow us to assign it to breathing-like acoustic vibration modes. On the basis of full electromagnetic near-field calculations coupled to the elasticity theory, we introduce a new concept of "acousto-plasmonic hot spots" which arise here because of the indented shape of the nanocolumns. These hot spots combine both highly localized surface plasmons and strong shape deformation by the acoustic vibrations at specific sites of the nano-objects. We show that the coupling between breathing-like acoustic vibrations and surface plasmons at the "acousto-plasmonic hot spots" is strongly enhanced, turning almost silent vibration modes into efficient Raman scatterers.

Raman-active modes in homogeneous and inhomogeneous bundles of single-walled carbonnanotubes

In the present work, the non-resonant Raman-active modes are calculated for severaldiameters, chiralities and sizes for homogeneous and inhomogeneous bundles ofsingle-walled carbon nanotubes (BWCNTs), using the spectral moment’s method(SMM). Additional intense Raman-active modes are present in the breathing-likemodes (BLM) spectra of these systems in comparison with a single fully symmetricA1g mode characteristic of isolated nanotubes (SWCNTs). The dependence of the wavenumberof these modes in terms of diameters, lengths and number of tubes was investigated. Wefound that, for a finite (in)homogeneous bundle, additional breathing-like modes appear asa specific signature.

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 1 / w 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.

Finite-size effect on the Raman-active modes of double-walled carbon nanotubes

The dependence of the breathing-like phonon modes (BLM) and tangential-likephonon modes (TLM) of individual, finite and infinite bundles of double-walledcarbon nanotubes (DWCNTs) as a function of the relative lengths of the inner(Li) andouter (Lo) tubes is calculated by using the spectral moments method in the frameworkof the bond-polarization theory. Depending on the relative lengths of the inner(Li) andouter (Lo) tubes, additional modes are evidenced in the BLM region. These modes must beconsidered in the analysis of the experimental data.

Radial breathinglike mode of the collapsed single-walled carbon nanotube bundle under hydrostatic pressure

Using the first-principles calculations we have studied the vibrational modes and Raman spectra of a (10, 10) single-walled carbon nanotube (SWNT) bundle under hydrostatic pressure. Detailed analysis shows that the original radial breathing mode (RBM) of the SWNT bundle disappears after the structural phase transition (SPT). And significantly a RBM-like mode appears at about 509cm−1, which could be considered as a fingerprint of the SPT happened in the SWNT bundle, and further used to determine the microscopic structure of the bundle after the SPT.

Raman spectra of commensurate double-walled carbon nanotubes

Using nonresonant bond-polarization theory, Raman spectra of periodicdouble-walled carbon nanotubes are calculated. Although the symmetry ofthese tubes is highly reduced in comparison with the symmetry of the layers,the intensities of Raman active modes do not show significant changes. InZZ polarization, modes related to radial breathing and high energy modes of individual layersremain the most intensive ones, even though the number of totally symmetric modes couldbe quite high. The shift of all Raman active modes with notable intensity is discussed andspecial attention is given to the possibility of tube identification from Raman data. In thecase of breathing-like modes, the frequency of the out of phase mode is found to bechirality dependent, while the in phase one remains only diameter dependent as in the caseof individual layers.

Raman-active modes in finite and infinite double-walled carbon nanotubes

The calculation of the nonresonant Raman spectrum of double-walled carbon nanotubes (DWCNT's) is performed in the framework of the bond polarization theory, using the spectral moment method. The calculation of the Raman spectrum of DWCNT's as a function of the diameter and chirality of the inner and outer tubes allows us to derive the diameter dependence of the frequencies of the breathing-like modes (BLM's) and tangential-like modes (TLM's) in a large diameter range. In particular, the diameter dependence of the frequencies of the two radial breathing-like modes (RBLM's) resulting from the in-phase and counterphase coupled motions of the totally symmetric radial breathing mode (the so-called RBM) of the inner and outer tubes is discussed. The Raman spectrum of a bundle of identical DWCNT's is also calculated. The dependence of the spectrum with the size of the bundle is analyzed. Additional breathing-like modes are predicted in DWCNT bundles of finite size. The majority of these peaks rapidly vanish when the tube length increases, except a totally symmetric mode that subsists in the DWCNT crystal.

Structure and spectrum of classical two-dimensional clusters with a logarithmic interaction potential

We present a numerical study of the effect of the repulsive logarithmic inter-particle interaction on the ground state configuration and the frequency spectrum of a confined classical two-dimensional cluster containing a finite number of particles. In the case of a hard wall confinement all particles form one ring situated at the boundary of the potential. For a general ${r}^{n}$ confinement potential, also inner rings can form and we find that all frequencies lie below the frequency of a particular mode, namely the breathing-like mode. An interesting situation arises for the parabolic confined system (i.e., $n=2$). In this case the frequency of the breathing mode is independent of the number of particles leading to an upper bound for all frequencies. All results can be understood from Earnshaw's theorem in two dimensions. In order to check the sensitivity of these results, the spectrum of vortices in a type II superconductor which, in the limit of large penetration depths, interact through a logarithmic potential, is investigated.

Breathinglike phonon modes of multiwalled carbon nanotubes

The breathinglike phonon modes of multiwalled carbon nanotubes are studied within a valence force field model for nanotubes with two and three layers of armchair type and within a continuum model for nanotubes with a large number of layers. A bond-polarizability model is used to calculate the nonresonant Raman intensity of the breathinglike modes. It is obtained that among all breathinglike modes of a given multiwalled tube, the in-phase one has a maximal intensity. The predicted intensity of the breathinglike modes is compared to available low-frequency experimental Raman data. Special attention is given to the comparison with Raman data on double-walled carbon nanotubes.

Influence of packing on the vibrational properties of infinite and finite bundles of carbon nanotubes

The quantitative analysis of the vibrational properties of carbon nanotubes is a key issue for the interpretation of Raman experiments. In particular, a reliable characterization of the atomic structure of single-wall carbon nanotubes produced under various conditions is mainly based on the interpretation of low-frequency $(100--300 {\mathrm{cm}}^{\ensuremath{-}1})$ Raman spectra. In the present work, we analyze the influence of the packing of the tubes on these low-frequency modes. We find that the low-frequency spectra of crystals of single-wall carbon nanotubes present two intense Raman modes instead of a single fully symmetric ${A}_{1g}$ mode characteristic of isolated tubes. The second mode has a non-negligible intensity for crystals formed with nanotubes of radii larger than $7 \AA{}.$ For finite number of tubes in a bundle, two breathinglike intense modes appear as a specific signature. Finally, our simulation for inhomogenous bundles made of a large number of tubes does not reveal any specific signature of the individual tubes in the low-frequency Raman spectra.

Evidence for the existence of two breathinglike phonon modes in infinite bundles of single-walled carbon nanotubes

We study the low-frequency region of the Raman spectra of infinite bundles of identical single-walled carbon nanotubes within a valence force field model of the lattice dynamics and a bond-polarizability model for the Raman intensity. It is obtained that two breathinglike phonon modes are present in such bundles for each tube type. Based on this prediction, an alternative interpretation of the experimental Raman spectra is proposed. In particular, an explanation is given for the appearence of resonant Raman lines that are predicted as nonresonant within the noninteracting tube picture.