Vibrational heat capacity of carbon nanotubes at low and ultra-low temperatures

Abstract To measure a heat capacity of a single carbon nanotube is impossible nowadays and experiments are performed with the nanotubes bundles. However, the existing theories of carbon nanotubes heat capacity do not take into account an interaction between an individual nanotube and its environment. Here we show that due to this fact the known theories overestimate the heat capacity in the ultra-low temperature limit. In this region the main contribution to heat capacity of a single free nanotube is caused by the bending phonon mode with a quadratic dispersion. At T =1 K different known models of the phonon dynamics lead to the theoretical specific heat which is at least 10 times greater than the experimentally measured value. To overcome this contradiction we take into account the interaction between an individual nanotube and its environment. As a result, the nanotube loses its Goldstone degrees of freedom and essential reconstruction of the lowest-energy part of its phonon spectrum occurs. The theory proposed explains experimental data on thermal capacity in the ultra-low temperature range and simultaneously demonstrates better agreement with experiments in the region 2.5 K T