Calculation of Raman parameters of real-size zigzag (n, 0) single-walled carbon nanotubes using finite-size models

Abstract

Structural and selected Raman features of pristine single-walled carbon nanotubes (SWCTNs) with diameters from 0.4 to 1.2 nm and total lengths up to 2.15 nm were studied using the density functional theory (DFT) at the UB3LYP/6-31G* level. Models of different lengths (1, 4, 6 and 10 adjacent bamboo-units) of zigzag (n, 0) SWCNTs, for n ranging from 5 to 15, were studied. Highly systematic changes of individual CC bond lengths and angles along the nanotube axis were observed and described for the longest models. Predicted Raman active radial breathing mode (RBM) vibrational frequencies regularly decreased upon increasing the nanotube diameter and only a negligible effect of the tube length was observed. The changes in calculated RBM frequencies with increasing diameter were close to values estimated using empirical formulas. The experimental G-mode characteristics were reasonably well reproduced using the 4-unit model, especially for tubes with the diameter d > 1 nm. Raman features were also determined for cyclacenes representing the shortest models of SWCNTs. Calculated RBM frequencies of cyclacenes match closely the values for longer SWCNT models but are too inaccurate in the case of the G-mode. For the first time, the Raman properties of SWCNTs were also determined using the Cartesian coordinate tensor (CCT) transfer technique, thus providing reasonable frequencies of Raman active bands for long tubes consisting of 10 bamboo-units.

Simulation of the Raman spectroscopy of multi-layered carbon nanomaterials

“…33 The Raman spectroscopy of larger nanotubes have been studied exploiting a cartesian coordinate transfer technique. 34 Alternatively, a periodic formalism can be adopted and the effect of SW and di-vacancy defects on Raman spectra has been studied 35 using plane-wave based periodic DFT.…”

Unlocking Rapid Charging and Extended Lifetimes for Li-Ion Batteries Using Freestanding Quantum Conversion-Type Aerofilm Anode

“…In the full width at half-maximum (fwhm), as the growth of SnO 2 particles proceeds from 3 to 100 nm, a semicrystalline characteristic was observed, while the 200 nm nanoparticles denoted a polycrystalline nature showing considerable sharpness at the 2θ peaks (Figure b). Further, Raman spectroscopy was used to compare a structural fingerprint of the quantum SnO 2 -based anode (Figure c,d) . Their peak similarity denotes the preservation of the CNT nature upon chemical reactions to produce quantum SnO 2 particles, which is beneficial for realizing good electrochemical performances.…”

“…Further, Raman spectroscopy was used to compare a structural fingerprint of the quantum SnO 2 -based anode (Figure 3c,d). 32 Their peak similarity denotes the preservation of the CNT nature upon chemical reactions to produce quantum S2 and S3). The valence band spectrum in Figure 3e confirms the formation of quantum SnO 2 particles consisting of divalent Sn and two oxygen atoms.…”

Construct the Character Table of D7h Point Group and Apply it for Classify the (3N-6) Modes of Vibration for the [7] Cyclacene (Linear) Monoring Molecule

“…For the [7] cyclacene (linear) monoring molecule Figure-1, the number of the symmetry species can be calculated depending on the constructed character table of D 7h point group and by applying equation 1 [1,2] on the geometrical structures of the studied molecule: To study the vibration motions of [7] cyclacene monoring molecule, one has to define its geometric parameters and has to distinguish between the axial CCa (C-Caxial) and circumferential CC c (C-Ccircumferential) bonds. Figure -2 the molecule using PM3 and DFT method with the level of (B3LYP/ 6-31G and 6-311G bases set) [11][12][13][14][15][16][17]. Table 1 shown the following relationship: -Length of circumferences bonds length of axial bonds.…”