Assignment of chiral vectors in carbon nanotubes

TLDR

Small‑diameter double‑wall carbon nanotubes exhibit distinct Raman lines for inner tubes in addition to the broad outer‑tube response. The study reports the Raman response of the radial breathing mode of the inner tubes. Inner tubes were produced by annealing peapods, and an algorithm combined with density‑functional‑theory‑derived diameters was used to assign (n,m) indices to the observed Raman lines. The assignment yielded a ν_RBM = 233/d + 14 cm⁻¹ relation between radial breathing mode frequency and tube diameter.

Abstract

Double-wall carbon nanotubes were derived from peapods by annealing at high temperature. We report on the Raman response of the radial breathing mode (RBM) of the inner tubes. As a consequence of their small diameter the Raman spectra of these tubes show well distinguishable lines, besides the usual broad response from the outer tubes. An algorithm was developed to find the best $(n,m)$ assignment for the observed lines. As a result of the assignment, we received ${\ensuremath{\nu}}_{\mathrm{RBM}}=233/d+14,$ ${\ensuremath{\nu}}_{\mathrm{RBM}}$ in ${\mathrm{cm}}^{\ensuremath{-}1}$ for the \ensuremath{\nu} versus $1/d$ relation, where $d$ is the tube diameter in nm. To bring the discrepancy between calculation of RBM frequencies and experiment to a minimum, the diameters were evaluated from density functional theory.