Thermal boundary resistance between single-walled carbon nanotubes and surrounding matrices

Carl Fredrik Carlborg, Junichiro Shiomi, and Shigeo Maruyama

Phys. Rev. B 78, 205406 – Published 6 November 2008

Abstract

Thermal boundary resistance (TBR) between a single-walled carbon nanotube (SWNT) and matrices of solid and liquid argon was investigated by performing classical molecular-dynamics simulations. Thermal boundary conductance (TBC), i.e., inverse of TBR, was quantified for a range of nanotube lengths by applying a picosecond heat pulse to the SWNT and observing the relaxation. The SWNT-length effect on the TBC was confirmed to be absent for SWNT lengths from 20 to $500 Å$ . The heat transfer mechanism was studied in detail and phonon spectrum analysis provided evidence that the resonant coupling between the low-frequency modes of the SWNT and the argon matrix is present both in solid and liquid argon cases. The heat transfer mechanism was qualitatively analyzed by calculating the spectral temperature of the SWNT in different frequency regimes. It was found that the low-frequency modes that are resonantly coupled to the argon matrix relaxes roughly ten times faster than the overall TBC time scale, depending on the surrounding matrix. However, such resonant coupling was found to transfer little energy despite a popular picture of the linear transfer path. The analysis suggests that intrananotube energy transfer from high-frequency modes to low-frequency ones is slower than the interfacial heat transfer to the argon matrix.

Received 9 July 2008

DOI:https://doi.org/10.1103/PhysRevB.78.205406

Authors & Affiliations

Carl Fredrik Carlborg

Microsystem Technology Laboratory, KTH—Royal Institute of Technology, SE-100 44 Stockholm, Sweden

Junichiro Shiomi^* and Shigeo Maruyama

Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

^*Corresponding author. shiomi@photon.t.u-tokyo.ac.jp

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Vol. 78, Iss. 20 — 15 November 2008

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Images

Figure 1
(Color online) (a) Different stages of the MD simulation. The matrix including the SWNT is first temperature annealed then relaxed without heat sinks or sources. The temperature of the SWNT is then ramped up for 10 ps and the system is let to relax to a new equilibrium without temperature control. (b) The temperature is monitored during relaxation and (c) the difference between the SWNT and the argon matrix is fitted to an exponential function, from which the relaxation time and the thermal boundary conductance can be calculated.Reuse & Permissions
Figure 2
(Color online) (a) Molecular structure of the equilibrated solid argon matrix (argon density: $3000 kg / m^{3}$ ). (b) Radial density function of the argon matrix. The density peaks reflect the crystal arrangement of the solid. Close to the SWNT the crystal structure is broken and the density is significantly higher. (c) Molecular structure of equilibrated liquid argon matrix (argon density: $1200 kg / m^{3}$ ). (d) The density oscillation with three distinct peaks within $10 Å$ of the SWNT surface. During heat flow, the matrix radial density function does not change significantly.Reuse & Permissions
Figure 3
(Color online) TBC as a function of SWNT length $(20 - 500 Å)$ . The TBC converges to a stable value for both the solid and liquid systems and shows no apparent length dependence. The densities of the solid argon and the liquid argon are 3000 and $1200 kg / m^{3}$ , respectively.Reuse & Permissions
Figure 4
(Color online) (a) The phonon energy spectrum of the $225 -Å$ -long (5,5) SWNT submerged in the solid argon matrix {(blue) line with diamonds} compared to that of an isolated SWNT with the same temperature {(green) line without markers)}. (b) A closeup on the first 9 THz together with the phonon spectrum of the adsorbed argon layer {(red) line with circles}. (c) The phonon spectrum of the same SWNT in the liquid argon matrix compared with the isolated case. (d) A closeup of the first 9 THz compared with the vibrational spectrum of the adsorbed argon atoms. Damping is clearly visible in the spectral overlap range for both matrices.Reuse & Permissions
Figure 5
(Color online) 2D phonon spectrum maps for the SWNTs in (a) solid and (b) liquid matrices. In both the solid and liquid matrices, the dispersion branches in the range that overlaps with the argon spectra (0–7 THz for solid and 0–2 THz for liquid) are diffused because the phonons are scattered by interacting with the argon matrix (insets). The scattering is more pronounced in the solid matrix.Reuse & Permissions
Figure 6
(Color online) Spectral temperatures in the low-frequency region $T_{sp}^{low}$ , where the SWNT spectrum overlaps with the adsorbed argon layer, and in the high-frequency region $T_{sp}^{high}$ , where no overlap occurs, compared to the kinetic temperature of the SWNT $T_{SWNT}$ and the argon matrix $T_{Ar}$ . (a) Solid matrix. The spectral temperature in the low-frequency region (0–7 THz) drops within 50 ps to the argon matrix temperature. (b) The difference between $T_{sp}^{high}$ and $T_{Ar}$ (green squares) and the difference between $T_{sp}^{low}$ and $T_{Ar}$ (blue dotted curve) for the solid matrix are fitted with single exponential functions. (c) Liquid matrix. Also in the liquid matrix, the spectral temperature in the low-frequency region (0–2 THz) is not in equilibrium with the rest of the SWNT but drops to the argon matrix temperature within 100 ps after the external heating is turned off. (d) The difference between $T_{sp}^{high}$ and $T_{Ar}$ (green squares) and the difference between $T_{sp}^{low}$ and $T_{Ar}$ (blue dotted curve) for the liquid matrix are fitted with single exponential functions.Reuse & Permissions

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