van der Waals interaction in nanotube bundles : consequences on vibrational modes

We have developed a pair-potential approach for the evaluation of van der Waals interaction between carbon nanotubes in bundles. Starting from a continuum model, we show that the intertube modes range from $5 cm^{-1}$ to $60 cm^{-1}$. Using a non-orthogonal tight-binding approximation for describing the covalent intra-tube bonding in addition, we confirme a slight chiral dependance of the breathing mode frequency and we found that this breathing mode frequency increase by $\sim$ 10 % if the nanotube lie inside a bundle as compared to the isolated tube.