Phonon modes in single-walled molybdenum disulphide nanotubes: Lattice dynamics calculation and molecular dynamics simulation

We study the phonon modes in single-walled MoS₂ nanotubes via lattice dynamics calculation and molecular dynamics simulation. The phonon spectra for tubes of arbitrary chiralities are calculated from a dynamical matrix constructed by the combination of an empirical potential with the conserved helical quantum numbers (κ, n). In particular, we show that the frequency (ω) of the radial breathing mode is inversely proportional to the tube diameter (d) as ω = 665.3/d cm^-1. The eigenvectors of the twenty lowest-frequency phonon modes are illustrated. Based on these eigenvectors, we demonstrate that the radial breathing oscillation is initially disturbed by phonon modes of three-fold symmetry, then eventually the tube is squashed by modes of two-fold symmetry . Our study provides fundamental knowledge for further investigations of the thermal and mechanical properties of MoS₂ nanotubes.