The spontaneous interaction between sulfuric acid and carbon nanotubes is studied using Raman spectroscopy. We are able to determine the charge transfer without any additional parameter using the spectral signature of inner and outer walls of double-wall carbon nanotubes. While for the outer wall both the lattice contraction and the nonadiabatic effects contribute to the phonon shift, only the lattice contraction contributes for the inner nanotube. For the outer nanotube, we are able to separate these two contributions of the Raman $G$-band shift as a function of the charge transfer. We have carried out density functional theory calculations on graphene to see how different chemical species (HSO${}_4{}^{-}$, H${}_2$SO${}_4$, H${}^{+}$) affect the electronic band structure and electron-phonon coupling. The Raman $G$-band shift for the outer nanotube, $\Delta \omega$, as a function of hole charge transfer per carbon atom, $f_{\mathrm{C}}$, is found to be $\Delta \omega \left({\text{cm}}^{-1}\right)=(350\pm 20)f_{\mathrm{C}}+(101\pm 8)\sqrt{f_{\mathrm{C}}}$.

• Received 17 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.205412