Low-frequency phonon dynamics and related thermal properties of axially stressed single-walled carbon nanotubes

Synthesis temperatures of composite materials are usually far less than the ones of their use, thus carbon nanotubes (CNTs) embedded into a polymer matrix undergo significant axial stress. We develop a continuous theory, which describes the dynamics of stressed single-walled (SW-) CNTs and predicts their low-frequency phonon spectra. The changes in dispersion laws of SWCNT low-frequency phonon modes due to the axial stress of different signs are discussed. Then, the results obtained are used to analyze low-temperature (T<70 K) heat capacity and thermal conductivity of individual nanotubes. We demonstrate that compressive stress leads to increase in heat capacity CV of an individual SWCNT, while tensile stress causes CV to decrease. In the latter case at T→0 heat capacity diminishes according to a linear law ~T instead of a power one ~T1/2. Nevertheless, according to our results, axial stress hardly affects low-temperature thermal conductance of SWCNTs. Influence of investigated effects on the corresponding macroscopic properties of CNT-based composite materials are discussed as well.