Vibrational modes of carbon nanotubes and nanoropes

Abstract

The vibrational modes of carbon nanotubes and nanoropes are studied. The Raman and infrared active modes are determined for armchair, zigzag, and chiral nanotubes. High-energy Raman and infrared modes exhibit distinct characteristic patterns for armchair, zigzag, and chiral tubes. In the nanorope the intertube interactions shifts the energy of certain vibrational modes dramatically. This has implications when using the vibrational spectra to identify tubes. In the nanorope we find Raman modes exhibit shifts under a change in pressure which differ from the corresponding shifts found in graphite. ͓S0163-1829͑99͒06133-0͔ PHYSICAL REVIEW B

Directly observable G band splitting in Raman spectra from individual tubular graphite cones

“…In this kind of unique atomic configuration, it is possible that the TGCs have extraordinary electronic and phonon density of states compared with poly-chiral MWCNTs [30]. The van der Waals interaction between the constituent inner tubes in the TGCs is no longer akin to that in SWCNT bundles and general MWCNTs [31].…”

Calculation of the vibrational frequencies of carbon clusters and fullerenes with empirical potentials

“…Raman spectroscopy is also used to probe the structure of carbon nanotubes and graphene. 33 The G band is a multiple peak feature at 1540-1595 cm 1 and is an important component of the Raman spectroscopy of these systems [34][35][36] Group theory pre-dicts the Raman-active G band in achiral nanotubes consists of A 1g , E 1g and E 2g modes. 35 Furthermore, in carbon nanotubes there is a radial breathing mode at 100 -400 cm 1 , where the frequency of this mode is dependent on the diameter of the nanotubes.…”

“…33 The G band is a multiple peak feature at 1540-1595 cm 1 and is an important component of the Raman spectroscopy of these systems [34][35][36] Group theory pre-dicts the Raman-active G band in achiral nanotubes consists of A 1g , E 1g and E 2g modes. 35 Furthermore, in carbon nanotubes there is a radial breathing mode at 100 -400 cm 1 , where the frequency of this mode is dependent on the diameter of the nanotubes. 37,38 There have been many theoretical studies of the vibrational frequencies of C 60 and C 70 using a wide range of different methodologies including force field, 39,40 semi-empirical and DFT.…”

Tight-binding vibrational analysis of single-wall carbon nanotubes

“…Previous theoretical work was essentially carried out by: (a) Normal mode analysis based on the dynamical matrix, constructed using force constants [5,6] or tight-binding force fields [7]; (b) Molecular dynamics (MD) simulations using interatomic potentials and vibration spectra derived as Fouriertransformed correlation functions [8,9,10]; (c) Continuum beam models based on the Euler-Bernoulli or Timoshenko equations, which, however, do not address the structural atomistic particularities of the CNTs [8,9,10,11,12,13].…”

“…[5] and [7] periodic boundary conditions are used in conjunction with the eigenvalue problem of the dynamical matrix, thus intrinsically modeling unsuspended CNTs of infinite lengths, in Ref. [6] time-averaged dynamical matrices for finite CNTs are derived from MD trajectories at ultra low temperatures to calculate the eigenfrequencies.…”