[Paper Review] Thermal Conductivity of Nanotubes Revisited: Effects of Chirality, Isotope Impurity, Tube Length, and Temperature

Gang Zhang, Baowen Li|arXiv (Cornell University)|Mar 16, 2004

Thermal properties of materials19 citations

TL;DR

This study investigates the thermal conductivity of single-walled carbon nanotubes (SWNTs) using nonequilibrium molecular dynamics with Tersoff bond order potentials, revealing that thermal conductivity is largely insensitive to chirality but strongly reduced (up to 60%) by isotope impurities. At low temperatures, heat conduction is ballistic, while at high temperatures, thermal conductivity scales with tube length as $\kappa \sim L^{\beta}$, where $\beta$ depends on temperature and radius, indicating phonon mode coupling effects.

ABSTRACT

We study the dependence of thermal conductivity of single walled nanotubes (SWNT) on chirality, isotope impurity, tube length and temperature by nonequilibrium molecular dynamics method with accurate potentials. It is found that, contrary to electronic conductivity, the thermal conductivity is insensitive to the chirality. The isotope impurity, however, can reduce the thermal conductivity up to 60% and change the temperature dependence behavior. We also found that the tube length dependence of thermal conductivity is different for nanotubes of different radius at different temperatures.

Motivation & Objective

• To understand the dependence of thermal conductivity on chirality, isotope impurity, tube length, and temperature in single-walled carbon nanotubes (SWNTs).
• To resolve open questions about whether thermal conduction in SWNTs behaves like 1D, quasi-1D, or 2D systems.
• To clarify the role of phonons versus electrons in thermal transport, focusing on lattice vibrations.
• To quantify how isotope impurities and structural parameters affect thermal transport properties for practical nanotube applications.

Proposed method

• Nonequilibrium molecular dynamics (NEMD) with Tersoff empirical bond order potential to model interatomic interactions in SWNTs.
• Two Nosé-Hoover heat baths applied at tube ends to establish a steady-state temperature gradient.
• Thermal conductivity $\kappa$ calculated via Fourier's law: $J = -\kappa \nabla T$, with $J$ as energy flux per unit area.
• Tube cross-sectional area defined as $2\pi r d$, with $d = 1.44\,\AA$ as effective thickness.
• Averaging over $10^6$–$10^7$ fs after transient equilibration to ensure statistical convergence.
• Systematic variation of chirality (e.g., (9,0), (10,0), (5,5)), isotope concentration, tube length, and temperature to isolate effects.

Experimental results

Research questions

• RQ1 Does thermal conductivity in SWNTs strongly depend on chirality, as electronic conductivity does?
• RQ2 To what extent does isotope impurity reduce thermal conductivity in carbon nanotubes?
• RQ3 How does thermal conductivity scale with tube length at different temperatures?
• RQ4 Is thermal transport in SWNTs ballistic at low temperatures, and how does this transition to diffusive behavior at high temperatures?
• RQ5 How do transverse and longitudinal phonon modes couple to influence thermal conductivity scaling?

Key findings

• Thermal conductivity is insensitive to chirality: (9,0), (10,0), and (5,5) tubes show similar conductivities despite differences in electronic character.
• Isotope impurity reduces thermal conductivity by up to 60%, significantly altering temperature dependence behavior.
• At 2 K, thermal conductivity is ballistic, resembling a 1D harmonic lattice with no temperature gradient.
• At 300 K and 800 K, a temperature gradient develops in SWNTs due to coupling between transverse and longitudinal phonon modes.
• Thermal conductivity scales with tube length as $\kappa \sim L^{\beta}$, where $\beta$ decreases with increasing temperature and tube radius.
• For (5,5) tubes at 300 K, $\beta \approx 0.4$, indicating near-1D behavior, while $\beta$ drops at higher temperatures and larger radii due to enhanced mode coupling.