Carbon species confined inside carbon nanotubes: A density functional study

Abstract

Density functional calculations have been performed of the energies, structures, and vibration frequencies of carbon chains, rings, graphitic sheets, bowls, cages, and tubes inside single-walled carbon nanotubes (CNT's) with different diameters. The calculated energies show that carbon chains can be inserted coaxially into 0.7 nm nanotubes, and nanotubes with diameters larger than 1.0 nm can also accommodate other structures. Small carbon species without dangling bonds do not touch the CNT walls, but those with dangling bonds can react with wall atoms, leading to structures with mixed hybridization $(sp,$ ${\mathrm{sp}}^{2},$ and ${\mathrm{sp}}^{3}).$ Carbon chains and rings have stretching modes between 1800 and $2160{\mathrm{cm}}^{\ensuremath{-}1},$ and chain modes are softened when inserted into CNT's. Normal modes of graphitic sheets and cages lie below $1645{\mathrm{cm}}^{\ensuremath{-}1}.$ The calculations suggest the existence of carbon nanowires, and nanopeapods ${\mathrm{C}}_{20}@\mathrm{CNT}$ should form if the CNT diameter is more than 1 nm. The smallest CNT (2,2) [diameter 0.3 nm] should be stable as the innermost tube of multiwalled nanotubes.