Thermal Conductivity of Isolated and Interacting Carbon Nanotubes: Comparing Results from Molecular Dynamics and the Boltzmann Transport Equation

We investigate the thermal conductivity of single-wall carbon nanotubes (SWCNT) either isolated or in contact with external media by using equilibrium molecular dynamics and the Boltzmann transport equation. We show that, contrary to existing controversies, both methods yield a finite value of the thermal conductivity for infinitely long tubes, as opposed to the case of 1D, momentum-conserving systems. Acoustic and flexure modes with mean free paths of the order of a few microns are identified as major contributors to the high value of SWCNT conductivity. We also find that the interaction with an external medium may substantially decrease the lifetime of the low-frequency vibrations, reducing the thermal conductivity by up to 2 orders of magnitude.

Figure 1

Thermal conductivity of a periodically replicated $(10,0)$ SWCNT as a function of the supercell length ($L$). Convergence is achieved for $L>20\mathrm{nm}$; however, a rather large uncertainty on $k$ remains, due to the strongly harmonic character of the phonons of the nanotube. The two square dots indicate the values of $k$ for a $(10,0)$ SWCNT deposited on a Si(100) $2\times 1$ substrate.

Figure 2

Phonon mean free path computed from the correlation function of the eigenmodes of a $(10,0)$ SWCNT in a 20 nm long supercell, and dispersion curves at zero (lines) and room temperature (dots) of the low-frequency modes (inset). The numbers on the dispersion curves indicate their degeneracy.

Figure 3

Thermal conductivity ($k$) computed by the BTE [Eq. (1)] using the phonon group velocities and lifetime computed by MD. The value of $k$ is shown as a function of the phonon frequencies included in the sum of Eq. (1) (the spectrum is shown on the $x$ axis), when using quantum (Bose-Einstein) (solid/black line) and classical (dashed/red line) occupation. The BTE with classic occupation of the vibrational states yields $k$ well within the error bar of the corresponding equilibrium MD simulation (see Fig. 1).

Figure 4

Effect of the relaxation time $\tau$ of the Langevin thermostat on the thermal conductivity of a $(10,0)$ SWCNT and on its power spectrum (inset). The viscosity $\eta$ of two media (air and acetone) at the corresponding $\tau$ is shown (see text).