中国物理B ›› 2026, Vol. 35 ›› Issue (3): 36302-036302.doi: 10.1088/1674-1056/ae3471

所属专题： SPECIAL TOPIC — Heat conduction and its related interdisciplinary areas

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Thermal conductivity of carbon nanotubes using nonequilibrium molecular dynamics combined with a machine learning potential

Jia-Hua Liu(刘嘉华)1, Shuo Cui(崔硕)1, Feng Guo(郭峰)1,†, Yu-Shi Wen(文玉史)2, Chun-Liang Ji(纪春亮)3, and Xiao-Chun Wang(王晓春)1   

  1. 1 School of Physical Science and Information Technology, Liaocheng University, Liaocheng 252000, China;
    2 Institute of Chemical Materials, China Academy of Engineering Physics (CAEP), Mianyang 621900, China;
    3 School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2025-10-28 修回日期:2026-01-06 接受日期:2026-01-07 出版日期:2026-02-11 发布日期:2026-03-19
  • 通讯作者: Feng Guo E-mail:gfeng.alan@foxmail.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11504153 and 12002325).

Thermal conductivity of carbon nanotubes using nonequilibrium molecular dynamics combined with a machine learning potential

Jia-Hua Liu(刘嘉华)1, Shuo Cui(崔硕)1, Feng Guo(郭峰)1,†, Yu-Shi Wen(文玉史)2, Chun-Liang Ji(纪春亮)3, and Xiao-Chun Wang(王晓春)1   

  1. 1 School of Physical Science and Information Technology, Liaocheng University, Liaocheng 252000, China;
    2 Institute of Chemical Materials, China Academy of Engineering Physics (CAEP), Mianyang 621900, China;
    3 School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
  • Received:2025-10-28 Revised:2026-01-06 Accepted:2026-01-07 Online:2026-02-11 Published:2026-03-19
  • Contact: Feng Guo E-mail:gfeng.alan@foxmail.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11504153 and 12002325).

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摘要： Large-scale and long-time-span nonequilibrium molecular dynamics simulations have been performed to determine the thermal conductivity of single-walled and double-walled carbon nanotubes (CNTs) using a machine learning potential trained on atomic energies and forces from density functional theory calculations for sp$^2$-hybridized carbon. The size dependence of graphene and CNTs up to 1 μm has been studied with 200000 atoms and simulation times up to 5 ns. The simulations reveal that thermal transport, whether ballistic, quasi-ballistic, or diffusive, is determined by the relationship between the sample length and the effective mean-free path (MFP). The system size has less effect on thermal conductivity when the sample length significantly exceeds the MFP. Radial tensile strain in CNTs causes the C-C bond length to increase in smaller-diameter CNTs, resulting in a phonon softening effect that subsequently reduces thermal conductivity. An analytical function is proposed to describe the relationship between phonon relaxation time and nanotube diameter. The thermal conductivity of the double-walled CNT is lower than that of an equivalent-size single-walled CNT. Phonon-phonon scattering, interlayer van der Waals interactions, and degenerate coupling of transverse acoustic modes are considered to contribute to the reduction in thermal transport.

关键词: graphene, carbon nanotube, phonon scattering, lattice thermal conductivity

Abstract: Large-scale and long-time-span nonequilibrium molecular dynamics simulations have been performed to determine the thermal conductivity of single-walled and double-walled carbon nanotubes (CNTs) using a machine learning potential trained on atomic energies and forces from density functional theory calculations for sp$^2$-hybridized carbon. The size dependence of graphene and CNTs up to 1 μm has been studied with 200000 atoms and simulation times up to 5 ns. The simulations reveal that thermal transport, whether ballistic, quasi-ballistic, or diffusive, is determined by the relationship between the sample length and the effective mean-free path (MFP). The system size has less effect on thermal conductivity when the sample length significantly exceeds the MFP. Radial tensile strain in CNTs causes the C-C bond length to increase in smaller-diameter CNTs, resulting in a phonon softening effect that subsequently reduces thermal conductivity. An analytical function is proposed to describe the relationship between phonon relaxation time and nanotube diameter. The thermal conductivity of the double-walled CNT is lower than that of an equivalent-size single-walled CNT. Phonon-phonon scattering, interlayer van der Waals interactions, and degenerate coupling of transverse acoustic modes are considered to contribute to the reduction in thermal transport.

Key words: graphene, carbon nanotube, phonon scattering, lattice thermal conductivity

中图分类号:  (Phonon interactions)

  • 63.20.K-
82.20.Wt (Computational modeling; simulation) 63.22.Rc (Phonons in graphene) 51.20.+d (Viscosity, diffusion, and thermal conductivity)