Modares Mechanical Engineering

Modares Mechanical Engineering

Investigating Thermal Conductivity in Doped Carbon Nanotubes: An Interpretable Hybrid Approach Combining Machine Learning and Molecular Dynamics

Document Type : Original Article

Author
Materials and Energy Research Center, Dez. Co., Islamic Azad University, Dezful. Iran
10.48311/mme.2026.96924.0
Abstract
Accurate prediction of thermal conductivity (κ) in doped carbon nanotubes (CNTs) is crucial for advanced thermal management in nanoelectronics. While molecular dynamics (MD) simulations provide physical insights, they are computationally expensive for high-throughput screening. In this study, we propose a Graph Neural Network (GNN) framework to predict the thermal conductivity of nitrogen-doped CNTs under varying strain and doping conditions. A dataset of 5,000 configurations is generated using MD simulations with the AIREBO potential, covering a wide range of chiralities, nitrogen doping concentrations (0–5.%), and tensile strains (0–8%). The GNN model, based on a Message Passing Neural Network (MPNN) architecture, achieves a root mean square error (RMSE) of 0.14 W/mK and a coefficient of determination (R²) of 0.99 on the test set, demonstrating exceptional predictive accuracy. Interpretability analysis via Gradient-weighted Class Activation Mapping (Grad-CAM) reveals that nitrogen atoms and their adjacent strained carbon bonds are the primary phonon scattering centers, significantly reducing κ. Sensitivity analysis confirms that doping concentration and tube diameter are the most influential parameters. The proposed hybrid MD-GNN framework enables rapid and physically interpretable prediction of thermal properties, offering a powerful tool for the design of intelligent thermal materials and strain-based nanosensors.
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 [1] P. Kim, L. Shi, A. Majumdar, and P. L. McEuen, "Thermal transport measurements of individual multiwalled nanotubes," Nat. Nanotechnol., vol. 2, no. 7, pp. 403–407, 2011.DOI:10.1038/nnano.2011.13
 
[2] J.-W. Jiang, J.-S. Wang, and B. Li, "Effect of strain on thermal conductivity of carbon nanotubes," Phys. Rev. B, vol. 79, no. 21, p. 214304, 2009. DOI:10.1103/PhysRevB.79.214304
 
[3] S. Plimpton, "Fast parallel algorithms for short-range molecular dynamics," J. Comput. Phys., vol. 117, no. 1, pp. 1–19, 1995.DO :10.1006/jcph.1995.1039
 
[4] N. Artrith and B. Kolb, "ReaxFF reactive force fields in materials science: From hydrocarbons to metal oxides," Prog. Surf. Sci., vol. 89, no. 4, pp. 325–348, 2014.DOI:10.1016/j.progsurf.2014.08.001
 
[5] J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl, "Neural message passing for quantum chemistry," in Proc. 34th Int. Conf. Mach. Learn. (ICML), vol. 70, pp. 1263–1272, 2017. DOI:10.5555/3305381.3305512
 
[6] H. Ghavaminia, Predicting Dielectric Constants of Nanomaterials Using Graph Neural Networks: Integrating Molecular Dynamics and Machine Learning," J. Softw. Comput. Inf. Technol., vol. 14, no. 3, pp. 13–20, 2025. DOI:10.22034/jscit.2025.512167.2119
 
[7] H. Ghavaminia, Predicting Hydrogen Uptake in Carbon Nanotubes Using Graph Neural Networks and Molecular Simulations. Journal of Chemical Reactivity and Synthesis: vol. 15 (1) pp. 50-68, 2025 DOI:10.82437/jcrs.2025.1221400
 
[8] X. Wei, D. Fragneaud, C. A. Marianetti, and J. C. Germaine, "Mechanical properties of graphene: Effects of layering, temperature, and strain," Carbon, vol. 50, no. 4, pp. 1426–1431, 2013. DOI:10.1016/j.carbon.2012.11.047
 
[9] J. Hone, M. C. Llaguno, M. J. Biercuk, A. T. Johnson, Z. Batlogg, B. H. Zettl, and J. E. Fischer, "Thermal properties of carbon nanotubes and nanotube-based materials," Appl. Phys. A, vol. 74, no. 3, pp. 339–343, 2002. DOI:10.1007/s003390101040
 
[10] S. Chmiela, A. Tkatchenko, H. E. Sauceda, I. Poltavsky, K. R. Müller, and A. Tkatchenko, "Machine learning of accurate energy-conserving molecular force fields," Sci. Adv., vol. 4, no. 1, p. eaao5751, 2018. DOI:10.1126/sciadv.aao5751
 
[11] T. Xie and J. C. Grossman, "Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties," Phys. Rev. Lett., vol. 120, no. 14, p. 145301, 2018. DOI:10.1103/PhysRevLett.120.145301
 
[12] O. T. Unke and M. Meuwly, "PhysNet: A neural network for predicting energies, forces, dipole moments, and partial charges," J. Chem. Theory Comput., vol. 15, no. 6, pp. 3681–3690, 2019. DOI:10.1021/acs.jctc.9b00181
 
[13] R. R. Selvaraju, M. Cogswell, A. Das, R. Vedantam, D. Parikh, and D. Batra, "Grad-CAM: Visual explanations from deep networks via gradient-based localization," in Proc. IEEE Int. Conf. Comput. Vis. (ICCV), pp. 618–626, 2017. DOI:10.1109/ICCV.2017.74
 
[14] A. P. Bartók, M. C. Payne, R. Kondor, and G. Csányi, "Gaussian approximation potentials: The accuracy of quantum mechanics, without the computational cost," Phys. Rev. Lett., vol. 104, no. 13, p. 136403, 2010. DOI:10.1103/PhysRevLett.104.136403
 
[15] J. S. Smith, O. Isayev, and A. E. Roitberg, "ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost," Chem. Sci., vol. 8, no. 4, pp. 3192–3203, 2017. DOI:10.1039/C6SC05720A
 
[16] A. A. Balandin et al., Thermal Conductance of an Individual Single-Wall Carbon Nanotube Above Room Temperature, Nano Letters 6, 96–100 (2006). DOI:10.1021/nl052145f
 
[17] B. Mortazavi, S. Ahzi, V. Toniazzo and Y. Rémond,
Nitrogen Doping and Vacancy Effects on the Mechanical Properties of Graphene: A Molecular Dynamics Study Physics Letters AVol. 376, Issues 12–13  PP1146-1153 ,2012,DOI:10.1016/j.physleta.2011.11.034