A new equivalent spring model for determining the G-band mode frequency of single-walled carbon nanotubes

The G-band mode frequency of single-walled carbon nanotubes (SWCNTs) is studied on the basis of a new equivalent spring model. To this end, the out of plane angle variation energy is incorporated into the model in order to obtain more precise results. Furthermore, a new analytical expression is introduced to evaluate the force constant corresponding to this kind of energy. For SWCNTs of different chiralities, the vibrational frequencies corresponding to axial and circumferential modes are determined. Also, the effects of diameter and chirality on the behavior of these frequencies are completely investigated. For a given diameter, it is found that the frequency of axial mode is always higher than that of the circumferential mode, regardless of the tube chirality. This finding may shed light on some contradictory reports in the literature. It is also found that the G-band mode frequency increases as the tube diameter gets larger, approaching the asymptotic value of 1592 cm−1 for large nanotubes. Additionally, the results indicate that the G-band mode frequency is slightly affected by the tube chirality.