Theoretical infrared phonon modes in double-walled carbon nanotubes
Abstract
In this theoretical work, we study the polarized infrared spectra of double-walled carbon nanotubes (DCNTs) as a function of their diameters, chiralities and lengths. For infinite DCNTs, mathematical relations are derived to estimate the diameter of the inner and outer tubes from the knowledge of their experimental mid-infrared spectra. The infrared spectra of DCNTs with a finite length are also calculated using the spectral moments method. We observe additional infrared bands as a function of the relative lengths of the inner and outer tubes. Bands located below 900 cm−1 give reliable information about these lengths.