Stokes and anti-Stokes Raman spectra of small-diameter isolated carbon nanotubes
By measuring the anti-Stokes (AS) and Stokes (S) Raman spectra on the same isolated single-wall carbon nanotube (SWNT), we here determine the electronic transition energies Eii experimentally (Eiiexp), and then we compare these Eiiexp with the Eii values obtained with theoretical predictions (E iical). In such an approach, the nanotube (n,m) structure identification depends on the theory parameters, but the experimental determination of Eiiexp does not, and depends only on the experimental AS/S intensity ratio and the laser energy Elaser used in the experiment. We measured the radial breathing mode frequency ω RBM and Eiiexp for specific tubes, and we then performed the (n,m) identification by using the dt diameter dependence of the electronic transitions. We present such an analysis for a wide nanotube diameter range, focusing primarily on small diameter SWNTs (d t<1.1 nm), where there are very few (n,m) possibilities for SWNTs that can be in resonance with the appropriate laser energy Elaser. This allows an experimental determination of Eiiexp values to be made for a variety of (n,m) SWNTs. Our experimental results indicate that: (i) the large curvature in small diameter tubes induces a σ-π hybridization, thus lowering the electronic band energies, and (ii) the simple formulation of the tight binding model (γ0=2.89 eV) to determine Eii starts to deviate from Eiiexp for tubes with dt<1.1 nm, but the deviation ΔE22=E22exp-E22cal remains smaller than 20 meV for dt≥0.83 nm. A comparison between Eiiexp data obtained from Raman and photoluminescence is made, and a comparison is also made between Eiiexp data for SWNTs and double-wall carbon nanotubes.
