Radial breathing modes of multi-walled carbon nanotubes by an atomic beam-spring model

Based on molecular force fields, a new finite element model is constructed for multi-walled carbon nanotubes where the interlayer interactions and C-C bonds are simulated by the elements of piece-wise linear spring and rectangular cross section beam, respectively. For high computation efficiency and atomic reification, the radial breathing modes of multi-walled carbon nanotubes are studied systemically using this model. The results show the correspondence between carbon nanotube structures and vibrational modes, which provide unequivocal data for the experimental characterization of carbon nanotubes. An empirical relationship of radial breathing modes frequencies with the nanotube radius are also obtained for two-layer carbon nanotubes.