Assignment of chiral vectors in carbon nanotubes

Double-wall carbon nanotubes were derived from peapods by annealing at high temperature. We report on the Raman response of the radial breathing mode (RBM) of the inner tubes. As a consequence of their small diameter the Raman spectra of these tubes show well distinguishable lines, besides the usual broad response from the outer tubes. An algorithm was developed to find the best $(n,m)$ assignment for the observed lines. As a result of the assignment, we received νRBM=233/d+14, νRBM in cm^-1 for the {ν} versus $1/d$ relation, where d is the tube diameter in nm. To bring the discrepancy between calculation of RBM frequencies and experiment to a minimum, the diameters were evaluated from density functional theory.