Abstract
Two hydrodynamic features of phonon transport, phonon drift and second sound, in a (20,20) single-wall carbon nanotube (SWCNT) are discussed using lattice dynamics calculations employing an optimized Tersoff potential for atomic interactions. We formally derive a formula for the contribution of drift motion of phonons to total heat flux at steady state. It is found that the drift motion of phonons carries more than 70% and 90% of heat at 300 and 100 K, respectively, indicating that phonon flow can be reasonably approximated as hydrodynamic if the SWCNT is long enough to avoid ballistic phonon transport. The dispersion relation of second sound is derived from the Peierls-Boltzmann transport equation with Callaway's scattering model and quantifies the speed of second sound and its relaxation. The speed of second sound is around 4000 m/s in a (20,20) SWCNT and the second sound can propagate more than 10 μm in an isotopically pure (20,20) SWCNT for frequency around 1 GHz at 100 K.
| Original language | English |
|---|---|
| Article number | 184304 |
| Journal | Physical Review B |
| Volume | 95 |
| Issue number | 18 |
| DOIs | |
| State | Published - May 18 2017 |
Funding
This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1548562. S.L. acknowledges support from the Central Research Development Fund of University of Pittsburgh (Grant No. 9012883) and National Science Foundation (Grant No. 1634261). L.L. acknowledges support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division.