Length Dependence of Carbon Nanotube Thermal Conductivity and the “Problem of Long Waves”

• Published in: Nano letters 2005-07, Vol.5 (7), p.1221-1225
• Main Authors: Mingo, N, Broido, D. A
• Format: Article
• Language: English
• Subjects: Applied sciences; Computer Simulation; Condensed matter: structure, mechanical and thermal properties; Electronics; Exact sciences and technology; Life Sciences (General); Materials Testing; Microelectronic fabrication (materials and surfaces technology); Models, Chemical; Molecular Conformation; Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals; Nanotubes, Carbon - analysis; Nanotubes, Carbon - chemistry; Physics; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Structure of solids and liquids; crystallography; Structure-Activity Relationship; Temperature; Thermal Conductivity
• ISSN: 1530-6984; 1530-6992
• DOI: 10.1021/nl050714d

We present the first calculations of finite length carbon nanotube thermal conductivity that extend from the ballistic to the diffusive regime, throughout a very wide range of lengths and temperatures. The long standing problem of vanishing scattering of the “long wavelength phonons” (Pomeranchuk, I. J. Phys. (U.S.S. R.) 1941, 4, 259; Phys. Rev. 1941, 60, 820) manifests itself dramatically here, making the thermal conductivity diverge as the nanotube length increases. We show that the divergence disappears if 3-phonon scattering processes are considered to second or higher order. Nevertheless, for defect free nanotubes, the thermal conductivity keeps increasing up to very large lengths (10 μm at 300 K). Defects in the nanotube are also able to remove the long wavelength divergence.