Phonons in ropes of single-wall carbon nanotubes

The vibrational density of states (DOS) of ropes of single-wall carbon nanotubes (SWNT) was obtained from inelastic neutron scattering data. The spectrum covers the entire predicted range of possible phonon energies from 0 to 225 meV. The DOS is similar to that of graphite above 40 meV, and markedly different below, where inter-tube features are clearly observed at 22 and 36 rneV. An unusual energy dependence below 10 meV is assigned to the inter-tube mode contributions in the crystalline lattice of the SWNT rope and to the inter-tube coupling of the intra-tube excitations. Good agreement between the theoretical calculations of the DOS and experiment is found over the entire energy range. The neutron scattering was complemented by measurements of the temperature dependence of the specific heat of ropes of SAINT from 100 mK to 700 K. The data are in excellent agreement with theoretical predictions for specific heat of isolated SWNT above 4 K. Detailed modeling yields an energy of 4.3 meV for the lowest optical phonon mode and a tube-tube Debye energy of 1.1 meV, implying the existence of a weak inter-tube coupling. The results of the specific heat measurement are found to be in a very good agreement with the results of the inelastic neutron scattering.