Radial breathing-like mode of wide carbon nanoribbon

The radial breathing-like mode (RBLM), an interesting Raman mode, of the carbon nanoribbons (CNRs) with different widths have been calculated by the empirical Brenner potential. It is found that the RBLM frequencies of CNRs whose widths are larger than 25 Å follow a new 1/w1/w rule, which is different from the 1/w rule, obtained for the narrow CNRs [J. Zhou, J. Dong, Appl. Phys. Lett. 91 (2007) 173108]. A continuum rod model is proposed to explain the new 1/w1/w rule, which is also different from the previous simple one-dimensional oscillator model, suitable only for the narrow CNRs. Based upon the CNR's RBLMs, we have proposed a practical experimental method to determine the widths of CNRs by their Raman spectra.