Interlayer Van Der Waals Interactions Research Articles

Symmetry Analysis of Relative Motions in a Double-Wall Carbon Nanotube

The binding energy of a double-wall carbon nanotube (DWNT) is theoretically studied as a function of the relative longitudinal shift and relative rotation of the component single-wall carbon nanotubes (SWNTs). It is shown that the binding energy is an oscillating function of the relative shift and rotation, with the oscillation period depending on the relations between symmetry elements of the SWNTs. The results of numerical calculations of the binding energy of DWNTs, performed in the approximation of weak van der Waals interlayer interaction, are presented.

Vibrational spectra of double-wall carbon nanotubes

The vibrational spectra of double-wall carbon nanotubes ($\mathrm{DWNTs}$) are studied theoretically within a continuum model in this paper. The phonon dispersion relations are derived numerically and analytically, and two radial breathing modes ($\mathrm{RBMs}$) are calculated analytically, which agree with experimental data [Phys. Rev. B 66, 075416 (2002)]. By comparison of the $\mathrm{RBM}$ frequencies with the ones of isolated single-wall carbon nanotubes, we find that there is a systematic upward shift for $\mathrm{DWNTs}$ $\mathrm{RBM}$ frequencies due to the interlayer van der Waals interactions. In case of counterphase modes, the upshift magnitude of $\mathrm{RBM}$ frequencies increases with an increase of the outer-layer radius $R$. However, for inphase $\mathrm{RBMs}$, the upshift magnitude of $\mathrm{RBM}$ frequencies may increase or decrease with an increase of $R$. We then discuss four acoustic phonons and find that there is no transverse acoustic phonon in $\mathrm{DWNTs}$. Finally, the general phonon dispersion relations are calculated.

Vibrational behaviors of multiwalled-carbon-nanotube-based nanomechanical resonators

This letter studies the promising application of carbon nanotubes as nanoresonators. Both single- and double-walled carbon nanotubes are considered and the significant difference in the vibration behavior between them has been identified. The individual tube wall is treated as frame-like structures and simulated by the molecular-structural-mechanics method. The interlayer van der Waals interactions are represented by Lennard–Jones potential and simulated by a nonlinear truss rod model. The results show that fundamental frequencies of double-walled carbon nanotubes are about 10% lower than those of single-walled carbon nanotubes of the same outer diameter. The noncoaxial vibration of double-walled nanotubes begins at the third resonant frequency and does not significantly diminish the value of double-walled nanotubes as high-frequency nanoresonators.

Electronic structure and scanning-tunneling-microscopy image of molybdenum dichalcogenide surfaces.

Electronic structures of ${\mathrm{MoS}}_{2}$ and ${\mathrm{MoSe}}_{2}$ surfaces are investigated by first-principles electronic-structure calculations. The ultrasoft pseudopotential by Vanderbilt is used to perform band calculations with a plane-wave basis. Calculated band structures are consistent with recent calculations using other methods. Scanning-tunneling-microscopy (STM) images are calculated from the results of the band calculations, and it is found that bright spots in experimental STM images correspond to chalcogen atoms of the outermost layer. First-principles band calculations by linear combination of atomic orbitals (LCAO) are also performed. It is found that the LCAO method is not so accurate in expressing the electronic properties of conduction bands of molybdenum dichalcogenides. The calculated band structures near the Fermi level show large dispersions along the direction perpendicular to the surface, which explains indirectly the fact that, in spite of the weak van der Waals interlayer interaction, moir\'e patterns are observed in the STM images of a ${\mathrm{MoSe}}_{2}$ surface grown on a ${\mathrm{MoS}}_{2}$ substrate. The appearance of the moir\'e patterns is more directly demonstrated by performing a band calculation of a ${\mathrm{MoSe}}_{2}$ surface with an irregular structure modeling the ${\mathrm{MoSe}}_{2}$/${\mathrm{MoS}}_{2}$ surface. It is found that the influence of the substrate on the outermost layer propagating through several Se-Mo-Se sandwiches is sufficiently large to reproduce the moir\'e patterns. However, the simulated image cannot explain some features of the experimental moir\'e patterns, which suggests that relaxation of atomic structures is also necessary to explain the moir\'e patterns.