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Register a new userUnderstanding double-resonant Raman scattering in chiral carbon nanotubes: Diameter and energy dependence of the $D$ mode
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We present a theoretical model to describe the double-resonant scattering process in arbitrary carbon nanotubes. We use this approach to investigate the defect-induced $D$ mode in CNTs and unravel the dependence of the $D$-mode frequency on the CNT diameter and on the energy of the resonant optical transition. Our approach is based on the symmetry of the hexagonal lattice and geometric considerations, hence the method is independent of the exact model that is chosen to describe the electronic band structure or the phonon dispersion. We finally clarify the diameter dependence of this Raman mode that was controversely discussed in the past and demonstrate that, depending on the experimental conditions, in general two different dependencies can be measured. We also prove that carbon nanotubes with arbitrary chiral index can exhibit a $D$ mode in their Raman spectrum, in contrast to previous symmetry-based arguments. Furthermore, we give a direct quantification of the curvature-induced phonon frequency corrections of the $D$-mode in carbon nanotubes with respect to graphite.
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We present measurements of the $D$ Raman mode in graphene and carbon nanotubes at different laser excitation energies. The Raman mode around 1050 - 1150,cm$^{-1}$ originates from a double-resonant scattering process of longitudinal acoustic (LA) phonons with defects. We investigate its dependence on laser excitation energy, on the number of graphene layers and on the carbon nanotube diameter. We assign this Raman mode to so-called inner processes with resonant phonons mainly from the $Gamma-K$ high-symmetry direction. The asymmetry of the $D$ mode is explained by additional contributions from phonons next to the $Gamma-K$ line. Our results demonstrate the importance of inner contributions in the double-resonance scattering process and add a fast method to investigate acoustic phonons in graphene and carbon nanotubes by optical spectroscopy.
We present an analysis of deep-UV Raman measurements of graphite, graphene and carbon nanotubes. For excitation energies above the strong optical absorption peak at the $M$ point in the Brillouin zone ($approx 4.7,text{eV}$), we partially suppress double-resonant scattering processes and observe the two-phonon density of states of carbon nanomaterials. The measured peaks are assigned to contributions from LO, TO, and LA phonon branches, supported by calculations of the phonon dispersion. Moreover, we gain access to the infrared-active $E_{1u}$ mode in graphite. By lowering the excitation energy and thus allowing double-resonant scattering processes, we demonstrate the rise of the textit{2D} mode in graphite with ultra-short phonon wave vectors.
Raman spectroscopy on carbon nanotubes (CNT) yields a rich variety of information owing to the close interplay between electronic and vibrational properties. In this paper, we review the properties of double wall carbon nanotubes (DWCNTs). In particular, it is shown that SWCNT encapsulating C$_{60}$, so-called peapods, are transformed into DWCNTs when subject to a high temperature treatment. The inner tubes are grown in a catalyst free environment and do not suffer from impurities or defects that are usually encountered for as-grown SWCNTs or DWCNTs. As a consequence, the inner tubes are grown with a high degree of perfection as deduced from the unusually narrow radial breathing mode (RBM) lines. This apostrophizes the interior of the SWCNTs as a nano-clean room. The mechanism of the inner nanotube production from C$_{60}$ is discussed. We also report recent studies aimed at the simplification and industrial scaling up of the DWCNT production process utilizing a low temperature peapod synthesis method. A splitting of the RBMs of inner tubes is observed. This is related to the interaction between the two shells of the DWCNTs as the same inner tube type can be encapsulated in different outer ones. The sharp appearance of the inner tube RBMs allows a reliable assignment of the tube modes to (n,m) indexes and thus provides a precise determination of the relation between the tube diameter and the RBM frequencies.
Mixtures containing different weight ratios of single wall carbon nanotubes (SWCNT) and double wall carbon nanotubes (DWCNT) were prepared and studied by in-situ Raman spectroelectrochemistry. Two components of the G-prime mode in the Raman spectra, which can be resolved at high electrode potentials, were assigned to the signals from inner tubes of DWCNT and outer tubes of DWCNT together with SWCNT. The dependence of the ratios of these two components of the G-prime mode on the nominal amount of SWCNT and DWCNT in the samples was simulated so that the residual amount of SWCNT in the original DWCNT could be determined. Additionally, the individual contributions of all components of carbon nanotubes into the total area of the G-prime mode at high electrode potentials were estimated from the simulation.
A novel method is presented which allows the characterization of diameter selective phenomena in SWCNTs. It is based on the transformation of fullerene peapod materials into double-wall carbon nanotubes and studying the diameter distribution of the latter. The method is demonstrated for the diameter selective healing of nanotube defects and yield from C$_{70}$ peapod samples. Openings on small diameter nanotubes are closed first. The yield of very small diameter inner nanotubes from C$_{70}$ peapods is demonstrated. This challenges the theoretical models of inner nanotube formation. An anomalous absence of mid-diameter inner tubes is observed and explained by the suppressed amount of C$_{70}$ peapods due to the competition of the two almost equally stable standing and lying C$_{70}$ peapod configurations.
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