Bundling effects on the intensities of second-order Raman modes in semiconducting single-walled carbon nanotubes

The second-order Raman modes in the range of $380--650\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ were investigated for individually dispersed and aggregated HiPco single-walled carbon nanotubes (SWNTs) using a $700--985\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ tunable laser source. For individually dispersed SWNTs, this Raman region displays relatively weak response from both intermediate frequency modes (IFMs) and the overtones of the radial breathing mode (RBM), with the latter dominating. In contrast, for aggregated SWNTs, the IFMs dominate and gain significant intensity relative to the RBM fundamental. Utilizing the correlation between RBM overtone and RBM fundamental intensity ratio as a function of laser energy, we derived Huang-Rhys factors for several $(n,m)$ nanotube species in both individually dispersed and aggregated states. These values were further used to obtain the corresponding absolute values of the exciton-phonon interaction matrix element for these nanotube species. It is demonstrated that the chiral-angle dependence of exciton-phonon coupling parameters is similar for dispersed and bundled samples. However, we find that bundling results in a decrease in the exciton-phonon coupling for the RBM, while the IFMs display the opposite behavior. These findings are particularly relevant for further clarifying the factors that govern Raman intensities and provide a tool for the selective characterization of various $\mathrm{mod}(n\ensuremath{-}m,3)=2$ $(n,m)$-SWNTs as a function of their aggregation state.