  In this paper, we investigate the low frequency Raman spectra of multi-wall
carbon nanotubes (MWNT) prepared by the electric arc method. Low frequency
Raman modes are unambiguously identified on purified samples thanks to the
small internal diameter of the MWNT. We propose a model to describe these
modes. They originate from the radial breathing vibrations of the individual
walls coupled through the Van der Waals interaction between adjacent concentric
walls. The intensity of the modes is described in the framework of bond
polarization theory. Using this model and the structural characteristics of the
nanotubes obtained from transmission electron microscopy allows to simulate the
experimental low frequency Raman spectra with an excellent agreement. It
suggests that Raman spectroscopy can be as useful regarding the
characterization of MWNT as it is in the case of single-wall nanotubes.
