Lattice dynamics of single-walled carbon nanotubes

In this paper, the theory of lattice dynamics of single-walled carbon nanot ubes is presented. The screw symmetry of the system is used to reduce the r ank of the dynamical matrix to six, independent of the number of atoms in t he unit cell. Calculations of the lattice dynamics are carried out within a valence force field model and of the Raman intensity-within a bond-polariz ability model. It is found that the breathing mode frequency is inversely p roportional to the radius of the tube that can be used for the characteriza tion of the samples on the basis of Raman-scattering data. The results for the Raman intensity are compared to available Raman spectra. [S0163-1829(98 )06434-0].