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

Abstract

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.

Phonon contribution to electrical resistance of acceptor-doped single-wall carbon nanotubes assembled into transparent films

“…At the same time, the low-energy phonon branches in the SWCNT differ significantly from the ones of graphite. For a quantitative description of these phonons we use a continuous model [49], which has been applied for the study of low-temperature specific heat of the carbon nanotubes [50]. Within this model the phonon state is determined with a 3 × 3 dynamic matrix, the structure of which depends on the phonon wave vector q and a discrete wave number n. During the intra-sub-band scattering process only the continuous electron wave vector is changed, while the discrete wave number along the circumference remains the same.…”