Explicit solution for G-band mode frequency of single-walled carbon nanotubes

G-band mode is one of the most important Raman modes of single-walled carbon nanotubes (SWCNTs). The vibrational frequency of the mode can be used to characterize SWCNTs. However, analytical expression that can link the frequency to the geometrical parameters of a SWCNT is to date not reported. Based on a molecular mechanics model, the analytical solution is obtained for G-band mode frequency of SWCNTs. The result calculated from the present solutions is in good agreement with the existing experimental and numerical data.