Experimental evidence of flexural phonons in low-temperature heat capacity of carbon nanotubes

Low-temperature specific heat of multi-walled carbon nanotubes (MWCNTs) with different grinding was studied. Two sets of modified, milled and oxidized/milled MWCNTs with an average outer diameter of 9.4 nm were used. The experimental results were compared with literature data for different carbon systems: bundles of single-walled carbon nanotubes (SWCNTs), graphite and other MWCNTs. The contributions of phonon spectrum characteristics and intertube interactions were found to be significant factors influencing the heat capacity both in the case of MWCNTs and bundles of SWCNTs. The grinding effect, associated with the reduction of the size of MWCNTs agglomerates, leads to an increased heat capacity. It was demonstrated that the lowest-temperature heat capacity consists of two main contributions: the Debye ( C 3 T 3 ) and the dispersive ( C 5 T 5 ) one. The obtained negative C 5 parameter indicated flexural dispersion for phonons. The magnitudes of Debye and flexural dispersive components depend on structural parameters of nanotubes: such as the diameter of individual nanotubes, the average diameter of the bundle and the size of agglomerates. A monotonic proportional correlation was observed between C 3 and | C 5 | parameters: | C 5 | increases following a power law with an exponent of 1.5 with the increase of C 3 . The maximum values of C 3 and | C 5 | correspond to SWCNT systems, while the minimum values correspond to MWCNTs. These results show that the heat capacity of the nanotube system increases if the interaction forces between neighbouring SWCNTs in the bundle or between the walls inside of MWCNTs decrease. This dependence is confirmed by the grinding effect in the MWCNTs.