Top and side view of the simulation setup for nonequilibrium energy dissipation from a (10,10) CNT to the substrate. The CNT consists of 1600 atoms, is 40 unit cells (98.4 Å) long and 13.6 Å in diameter. The amorphous substrate is produced by annealing a -cristobalite crystal at 6000 K and 1 bar for 10 ps before slow quenching to 300 K at a rate of . Its final dimensions are 53.5 Å by 13.7 Å by 98.4 Å. The CNT is then placed on top of the slab. The final structure is obtained after energy minimization.
(a) Time evolution of the CNT and temperature, showing thermal time constant which corresponds to . (b) Time integral of the autocorrelation of oscillates about its asymptotic value of after . This corresponds to . (c) Log-log plot of the power spectrum of scales as from 0–10 THz, and as at higher frequencies. Inset shows the same as a linear plot; both suggest the dominant contribution is between 0–10 THz. A small component of very high frequency phonons in the CNT also contribute to interfacial thermal transport via inelastic scattering, although there are no corresponding modes in the substrate. (d) Normalized phonon DOS for the atoms in the substrate and the atoms in the CNT.
Power spectrum of the isolated (10,10) CNT. (a) Transverse power spectrum. Closely spaced optical phonon branches are visible in the low frequency part. (b) Longitudinal power spectrum. Unlike the transverse power spectrum, it has fewer low frequency optical phonon branches. (c) Overall power spectrum as the sum of the transverse and longitudinal power spectra. We divide the power spectrum into different regions (I, II, III, and IV) to compute their spectral temperatures.
(a) Power spectrum of an isolated (10,10) CNT for (top left) to 5 (bottom right). There are 12 phonon branches for each value of (doubly degenerate for ). By decomposing the power spectrum with respect to , we observe the distinct phonon branches. (b) Detail near the origin of the plot, showing LA and TW branches. (c) Detail near the origin of the plot showing a doubly degenerate purely TO branch. The regions in (b) and (c) enclosed by the blue dotted lines are used for computing the spectral temperatures and respectively. They are also shown with dotted lines in the and 5 power spectra.
Spectral temperature decays of the (10,10) CNT with the initial CNT temperature at 500 K and the substrate at 300 K. (a) exhibits a fast initial decay followed by a slower decay rate of . (b) Shows the spectral temperature decay of . It relaxes at about the same rate as to and the average temperature of the CNT. The relaxation behavior of suggests that small , low phonon modes are much more strongly coupled to the substrate phonons and are the primary mechanism responsible for vibrational energy transfer to the substrate. (c) and (d) show the spectral temperature decay of and compared to and . , which corresponds to the energy relaxation of the small , low LA and TW modes, decays at approximately the same rate as . On the other hand, , which corresponds to the energy relaxation of the small , low TO mode for , decays even more rapidly than .
Frequency, angular number, and wave vector ranges for the spectral temperatures.
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