Low-frequency excitations of ${\mathrm{C}}_{60}$ chains inserted inside single-walled carbon nanotubes

The low-frequency excitations of ${\mathrm{C}}_{60}$ chains inserted inside single-walled carbon nanotubes (SWNTs) have been studied by inelastic neutron scattering on a high-quality sample of peapods. The comparison of the neutron-derived generalized phonon density of states (GDOS) of the peapods sample with that of raw SWNTs allows the vibrational properties of the ${\mathrm{C}}_{60}$ chains encapsulated in the hollow core of the SWNTs to be probed. Lattice dynamical models are used to calculate the GDOS of chains of monomers, dimers, and polymers inserted into SWNTs, which are compared to the experimental data. The presence of strong interactions between ${\mathrm{C}}_{60}$ cages inside the nanotube is clearly demonstrated by an excess of mode density in the frequency range around 10 meV. However, the presence of a quasielastic signal indicates that some of the ${\mathrm{C}}_{60}$’s undergo rotational motion. This suggests that peapods are made from a mixture of ${\mathrm{C}}_{60}$ monomers and ${\mathrm{C}}_{60}$ $n$-mer (dimer, trimer, …, polymer) structures.

Figure 1

Susceptibility of the peapods (squares) and of the nanotubes samples (triangles) measured at 300 K (open symbols) and 480 K (filled symbols).

Figure 2

(a) Generalized density of states (GDOS) of the peapod sample (top curve), of the reference SWNT sample (middle curve), and of inserted ${\mathrm{C}}_{60}$ chains (bottom curve) resulting from the substraction of the GDOS of SWNTs from the GDOS of peapods after adequate normalization. All measurements were performed at 480 K. Lines are guides to the eyes resulting in a three-point smoothing of the data. (b) Calculated GDOS of a chain of ${\mathrm{C}}_{60}$ monomers inserted into a SWNT. This line is the result of the substraction of the GDOS calculated for empty nanotubes from the GDOS calculated for the whole peapods.

Figure 3

Lattice-dynamical calculations of the GDOS of chains of (a) monomers ($M$ model), (b) dimers ($D$ model), and (c) polymers ($P$ model). The open squares are the experimental GDOS of the inserted ${\mathrm{C}}_{60}$ chain. The line on the experimental spectrum is a guide to the eyes. The star indicates the position of the mode observed by Raman spectroscopy at low temperature.