Diameter distribution of single wall carbon nanotubes in nanobundles

The frequency of the Raman active Ale radial breathing mode has been widely used as a tool to estimate the distribution of diameters of single wail carbon nanotubes (SWNT). However, the relation between frequency and diameter is not straightforward and results are model-dependent. Because most of the experiments are performed on bundles and not on isolated tubes, the model should especially take into account the van der Waals inter tube interactions. Here. we use a pair-potential approach to account for such interactions and we derive a nonlinear relation between the SWNT diameter and the frequency of the A(1g) radial breathing modes. We demonstrate a good agreement between calculations and the diameters derived from diffraction experiments on the same samples.