Diameter dependence of the defect-induced Raman modes in functionalized carbon nanotubes

Covalent functionalization of single-walled carbon nanotubes typically leads to an intensity increase of the defect-induced Raman mode (D mode). A large intensity ratio of the D and G modes (D/G ratio) is therefore often used as evidence for a successful functionalization. Here, we discuss the effect of the D-mode resonance on the D/G ratio and compare pristine and covalently functionalized nanotubes. By resonance Raman spectroscopy we study the evolution of the lineshape and frequencies of the D and 2D modes of samples enriched with semiconducting and metallic nanotubes in comparison with the radial breathing mode. First, we experimentally demonstrate the dependence of the D- and 2D-mode frequencies on the tube diameter and derive an analytical expression for both frequencies as a function of the diameter and the optical transition. Furthermore, we demonstrate that the contribution of the D and 2D modes for small SWCNTs disappears in covalently functionalized samples due to partial destruction. In fact, this can change the measured D/G ratio significantly and has a fundamental impact on the determination of the degree of SWCNT functionalization by Raman spectroscopy.