Peculiarities of low-frequency vibrational dynamics and low-temperature heat capacity of double-walled carbon nanotubes

A continuous model of double-walled carbon nanotube (DWCNT) low-frequency dynamics was constructed. In the frame of the approach proposed formation of a DWCNT low-frequency phonon spectrum from the ones of corresponding single-walled carbon nanotubes (SWCNTs) was considered. Environmental influence on the individual DWCNT phonon spectrum was studied. A combined method of van der Waals interlayer coupling coefficients evaluation was proposed, and it is based on Raman spectroscopy data and known values of graphite elastic moduli. Also DWCNT low-temperature specific heat was calculated. In the model applicability region (at temperatures lower than 35 K) DWCNT specific heat turned out to be significantly lower than the specific heat sum of corresponding individual single-walled SWCNTs. This effect is caused mainly by the interlayer coupling instead of DWCNT interaction with environment.