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 C _V of an individual SWCNT, while tensile stress causes C _V to decrease. In the latter case at T  →  0 heat capacity diminishes according to a linear law ~T instead of a power one ~T ^1/2. 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 also discussed.