本研究採用分子動力學模擬方法系統性探討奈米碳管在不同加載過程中的挫曲行為及其對熱傳特性的影響，並輔以多面體模板匹配、聲子態密度、聲子相關性進行分析。本文首先說明分子動力學的基本理論，以及非平衡態分子動力學模擬方法的原理與計算流程，接著介紹多面體模板匹配、聲子態密度與聲子相關性之物理意涵與計算方式。
在研究流程上，首先對奈米碳管施加不同形式的機械載荷，包含軸向壓縮、扭轉與彎曲變形，並分析其長度、半徑與手性對臨界應變、臨界扭轉率與臨界曲率的影響，並透過多面體模板匹配觀察原子結構上的變化。隨後，針對完成變形後的模型，在碳管兩端設置控溫區，利用非平衡態分子動力學模擬進行熱流計算，觀察奈米碳管熱流隨變形程度增加的變化情形，並進一步探討幾何參數與手性對熱流行為的影響，並計算聲子態密度以及聲子相關性解釋熱傳行為的變化。
研究結果顯示，不同加載形式會造成截然不同的挫曲型態與原子結構變化，進而導致熱流變化呈現明顯差異，軸向壓縮加載下，殼牆型挫曲引發顯著的局部結構破壞，使原子結構均勻性降低，導致挫曲後熱流明顯下降；相較之下，圓柱型挫曲主要為整體彎曲變形，原子結構變化有限，熱流衰減幅度亦相對較小。扭轉加載下，挫曲後形成之螺旋狀起伏變形使熱流隨扭轉率增加而逐漸降低。彎曲加載則因破壞碳管圓柱對稱性，使原子結構在挫曲前即產生不對稱變化，導致熱流隨曲率增加而持續下降。整體而言，不同變形加載所引發之原子結構變化型態，為主導奈米碳管熱傳行為改變差異的關鍵因素。

This study employs molecular dynamics (MD) simulations to systematically investigate the buckling behavior of carbon nanotubes (CNTs) under various loading conditions and their subsequent impact on thermal transport properties. The analysis is supported by polyhedral template matching (PTM), phonon density of states (PDOS), and phonon coherence analysis. The paper first outlines the fundamental theories of MD and the computational procedures of non-equilibrium molecular dynamics (NEMD), followed by an introduction to the physical significance of the analysis methods used.
In the research process, mechanical loads—including axial compression, torsion, and bending—were applied to CNTs to analyze the effects of length, radius, and chirality on critical strain, torsion rate, and curvature. Atomic structural changes were monitored via PTM. Subsequently, NEMD simulations with temperature control zones were conducted to calculate heat flux. The study further examines the influence of geometric parameters and chirality on thermal behavior, utilizing PDOS and phonon coherence analysis to elucidate the mechanisms behind thermal transport variations.
The results indicate that different loading modes induce distinct buckling patterns, leading to significant differences in heat flux. Under axial compression, shell-like buckling triggers severe local structural distortion, reducing structural uniformity and causing a marked drop in heat flux. In contrast, columnar buckling primarily involves global bending with limited atomic structural alteration, resulting in a relatively smaller thermal attenuation. Under torsional loading, helical buckling causes a gradual decrease in heat flux as the torsion rate increases. Bending loading breaks the cylindrical symmetry of the nanotube, inducing asymmetric structural changes that lead to a continuous decline in heat flux. In conclusion, the specific morphology of atomic structural deformation is the key factor governing the changes in the thermal transport behavior of CNTs.

[1] B. I. Yakobson, C. J. Brabec and J. Bernholc, "Nanomechanics of carbon tubes: instabilities beyond linear response," Physical Review Letters, vol. 83, pp. 2973-2976, 1996.
[2] A. Sears and R. C. Batra, "Macroscopic properties of carbon nanotubes from molecular-mechanics simulations," Physical Review B, vol. 69, pp. 235406, 2004.
[3] M. J. Buehler, Y. Kong and H. Gao, "Deformation mechanisms of very long single-wall carbon nanotubes subject to compressive loading," Journal of Engineering Materials and Technology, vol. 126, pp. 245-249, 2004.
[4] G. Cao and X. Chen, "The effects of chirality and boundary conditions on the mechanical properties of single-walled carbon nanotubes," International Journal of Solids and Structures, vol. 44, pp. 5447-5465, 2007.
[5] I.-L. Chang and B.-C Chiang, "Mechanical buckling of single-walled carbon nanotubes: Atomistic simulations," Journal of Applied Physics, vol. 106, pp. 114313, 2009.
[6] Y. Wang, X. X. Wang and X. Ni, "Atomistic simulation of the torsion deformation of carbon nanotubes," Modelling and Simulation in Materials Science and Engineering, vol. 12, pp. 1099-1107, 2004.
[7] Z. Wang, M. Devel and B. Dulmet, "Twisting carbon nanotubes: A molecular dynamics study," Surface Science, vol. 604, pp. 496-499, 2010.
[8] L. G. Brazier, "On the flexure of thin cylindrical shells and other "thin" sections," Proceedings of the Royal Society A, vol. 116, pp. 104-114, 1927.
[9] E. Reissner and H. J. Weinitschke, "Finite pure bending of circular cylindrical tubes, " Quarterly of Applied Mathematics, vol. 20, pp. 305-319, 1963.
[10] X. Li, W. Yang and B. Liu, "Bending induced rippling and twisting of multiwalled carbon nanotubes," Physical Review Letters, vol. 98, pp. 205502, 2007.
[11] X. Li, K. Maute, M. L. Dunn and R. Yang, "Strain effects on the thermal conductivity of nanostructures," Physical Review B, vol. 81, pp. 245318, 2010.
[12] J. W. Jiang, "Strain engineering for thermal conductivity of single-walled carbon nanotube forests," Carbon, vol. 81, pp. 688-693, 2015.
[13] Z. Xu and M. J. Buehler, "Strain controlled thermomutability of single-walled carbon nanotubes," Nanotechnology, vol. 20, pp. 185701, 2009.
[14] H. Nagaya,, J. Cho and T. Hori, "Thermal conductivity of single-walled carbon nanotubes under torsional deformation," Journal of Applied Physics, vol. 130, pp. 215106, 2021.
[15] A. N. Volkov, T. Shiga, D. Nicholson, J. Shiomi and L. V. Zhigilei, " Effect of bending buckling of carbon nanotubes on thermal conductivity of carbon nanotube materials," Journal of Applied Physics, vol. 111, pp. 053501, 2012.
[16] J. Ma, Y.Ni, S. Volz and T. Dumitricăn, "Thermal transport in single-walled carbon nanotubes under pure bending," Physical Review Applied, vol. 3, pp. 024014, 2015.
[17] C. W. Chang, D. Okawa, H. Garcia, A. Majumdar and A. Zettl, "Nanotube phonon waveguide, "Physical Review Letters, vol. 99, pp. 045901, 2007.
[18] B. J. Alder and T. E. Wainwright, "Studies in molecular dynamics. I. General method," The Journal of Chemical Physics, vol. 31, pp. 459-466, 1959.
[19] J. E. Jones, "On the determination of molecular fields.—II. From the equation of state of a gas," Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 106, pp. 463-477, 1924.
[20] R. Saito, R. Matsuo, T. Kimura, G. Dresselhaus and M. Dresselhaus, "Anomalous potential barrier of double-wall carbon nanotube," Chemical Physics Letters, vol. 348, pp. 187-193, 2001.
[21] D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni and S. B. Sinnott, "A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons," Journal of Physics: Condensed Matter, vol. 14, pp. 783, 2002.
[22] D. W. Brenner, "Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films," Physical Review B, vol. 42, pp. 9458, 1990.
[23] J. Haile, I. Johnston, A. J. Mallinckrodt and S. McKay, "Molecular dynamics simulation: elementary methods," Computers in Physics, vol. 7, pp. 625-625, 1993.
[24] T. Dumitrica, Trends in Computational Nanomechanics: Transcending Length and Time Scales. Springer Science & Business Media, 2010.
[25] P. H. Hünenberger, "Thermostat algorithms for molecular dynamics simulations," in Advanced Computer Simulation: Approaches for Soft Matter Sciences I, C. Dr. Holm and K. Prof. Dr. Kremer, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005, pp. 105-149.
[26] G. Bussi, D. Donadio and M. Parrinello, "Canonical sampling through velocity rescaling," The Journal of Chemical Physics, vol. 126, pp. 014101, 2007.
[27] W. G. Hoover, "Canonical dynamics: Equilibrium phase-space distributions," Physical Review A, vol. 31, pp. 1695-1697, 1985.
[28] S. Nosé, "A unified formulation of the constant temperature molecular dynamics methods," The Journal of Chemical Physics, vol. 81, pp. 511-519, 1984.
[29] D. J. Evans and B. L. Holian, "The nose–hoover thermostat," The Journal of Chemical Physics, vol. 83, pp. 4069-4074, 1985.
[30] H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola and J. R. Haak, "Molecular dynamics with coupling to an external bath," The Journal of Chemical Physics, vol. 81, pp. 3684-3690, 1984.
[31] S. A. Adelman and J. D. Doll, "Generalized Langevin equation approach for atom/solid‐surface scattering: General formulation for classical scattering off harmonic solids," The Journal of Chemical Physics, vol. 64, pp. 2375-2388, 1976.
[32] T. Schlick, Molecular modeling and simulation: an interdisciplinary guide: an interdisciplinary guide. Springer Science & Business Media, 2010.
[33] T. Schneider and E. Stoll, "Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions," Physical Review B, vol. 17, pp. 1302-1322, 1978.
[34] G.-J. Hu and B.-Y. Cao, "Molecular dynamics simulations of heat conduction in multi-walled carbon nanotubes," Molecular Simulation, vol. 38, pp. 823-829, 2012.
[35] L. Verlet, "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules," Physical Review, vol. 159, pp. 98-103, 1967.
[36] W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters," The Journal of Chemical Physics, vol. 76, pp. 637-649, 1982.
[37] B. Quentrec and C. Brot, "New method for searching for neighbors in molecular dynamics computations," Journal of Computational Physics, vol. 13, pp. 430-432, 1973.
[38] T. N. Heinz and P. H. Hünenberger, "A fast pairlist-construction algorithm for molecular simulations under periodic boundary conditions," Journal of Computational Chemistry, vol. 25, pp. 1474-1486, 2004.
[39] D. Frenkel and B. Smit, Understanding Molecular Simulation, Second Edition: From Algorithms to Applications. San Diego: Academic, 2002.
[40] J. P. Hansen and I. R. McDonald, Theory of Simple Liquids. London: Academic, 1986.
[41] K. C. Fang, C. I. Weng, and S. P. Ju, "An investigation into the structural features and thermal conductivity of silicon nanoparticles using molecular dynamics simulations," Nanotechnology, vol. 17, pp. 3909-3914, 2006.
[42] T. Ikeshoji and B. Hafskjold, "Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface," Molecular Physics, vol. 81, pp. 251-261, 1994.
[43] P. K. Schelling, S. R. Phillpot, and P. Keblinski, "Comparison of atomic-level simulation methods for computing thermal conductivity," Physical Review B, vol. 65, pp. 144306, 2002.
[44] A. T. Fenley, H. S. Muddana, & M. K. Gilson, "Calculation and visualization of atomistic mechanical stresses in nanomaterials and biomolecules," PLoS One, vol. 9(12), pp. e113119, 2014.
[45] M. DeBerg, "Computational geometry: algorithms and applications," Springer Science & Business Media, 2000.
[46] P. M. Larsen, S. Schmidt and J. Schiøtz, "Robust structural identification via polyhedral template matching," Modelling and Simulation in Materials Science and Engineering, vol. 24, pp. 055007, 2016.
[47] S. J. Stuart, A. B. Tutein, and J. A. Harrison, "A reactive potential for hydrocarbons with intermolecular interactions," Journal of Chemical Physics, vol. 112, pp. 6472-6486, 2000.
[48] G. Cao and X. Chen, "Buckling of single-walled carbon nanotubes upon bending: Molecular dynamics simulations and finite element method," Physical Review B, vol. 73, pp. 155435, 2006.
[49] F. Khademolhosseini, R. K. N. D. Rajapakse, A. Nojeh, "Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models," Computational Materials Science, vol. 48, pp. 736-742, 2010.
[50] G. S. Schilling, " Buckling strength of circular tubes," Journal of the Structural Division, vol. 91, pp. 325-348, 1965.
[51] N. Yamaki, Elastic Stability of Circular Cylindrical Shells. North-Holland. 1984.
[52] N. Silvestre, "Length dependence of critical measures in single-walled carbon nanotubes," International Journal of Solids and Structures, vol. 45, pp. 4902-4920, 2008.
[53] Z. Chen, X. Luo, Q. Chen, W. Zheng and Q. Xie, "Molecular dynamics study on the influence of size on thermal conductivity of carbon nanotubes with different structures," Physics Letters A, vol. 554, pp. 130736, 2025.