本研究主要以非平衡態分子動力學模擬方法（NEMD），研究探討完美奈米碳管與各種分支構造之奈米碳管的熱傳行為。本文首先介紹平衡態分子動力學模擬方法與逆向非平衡態分子動力學模擬方法（rNEMD），並根據統計力學理論對模擬參數進行測試。而後分別在週期性邊界條件與固定邊界條件下，以非平衡態模擬法找出完美奈米碳管的熱傳導係數與奈米碳管長度之相依關係，並與各家文獻比對結果。又以非平衡態模擬法對各種分支構造奈米碳管進行研究，在對稱溫度控制與不對稱溫度控制下，藉由改變互相嵌合之奈米碳管的長度、管徑等幾何結構，觀察各種分支構造奈米碳管之熱傳行為，並以聲子之彈道性與擴散性傳輸行為解釋之。
本研究成立一套對完美及具分支構造奈米碳管的熱傳模擬之設計與流程方法，另外在非平衡態模擬法的參數設定上提出多項建議，作為往後研究奈米碳管結構的熱傳行為之參考。

Thermal transport behavior of perfect and branched carbon nanotubes (CNTs) was investigated using non-equilibrium molecular dynamics (NEMD) simulation method. First, we introduced NEMD and reverse non-equilibrium molecular dynamics (rNEMD) simulation methods, and based testing of simulation parameters on theory of statistical mechanics. In the NEMD simulations with periodic and fixed boundary conditions for perfect CNTs, we compared our results, the relation of the length of perfect carbon nanotube and its thermal conductivity, with other literature. Furthermore, we observed thermal transport behaviors of various branched CNTs, which were composed of different length and diameter, using symmetric and asymmetric temperature-controlled NEMD simulations, and we explained these behaviors with the ballistic and diffusion transport of phonon.
In this study, we established a heat transfer simulation procedure of investigating perfect and branched CNTs, and we proposed lots of suggestions about NEMD simulation parameters. This research could pave the way to study the thermal transport behavior of nanostructures in future works.

[1] S. A. Adelman, "Generalized Langevin Equation Approach for Atom/Solid-Surface Scattering: General Formulation for Classical Scattering Off Harmonic Solids," The Journal of Chemical Physics, vol. 64, p. 2375, 1976.
[2] B. J. Alder and T. E. Wainwright, "Studies in Molecular Dynamics. I. General Method," The Journal of Chemical Physics, vol. 31, p. 459, 1959.
[3] M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids: Oxford university press, 1989.
[4] 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, p. 3684, 1984.
[5] K. Bi, Y. Chen, J. Yang, Y. Wang, and M. Chen, "Molecular Dynamics Simulation of Thermal Conductivity of Single-Wall Carbon Nanotubes," Physics Letters A, vol. 350, pp. 150-153, 2006.
[6] D. W. Brenner, "Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor Deposition of Diamond Films," Physical Review B, vol. 42, pp. 9458-9471, 1990.
[7] 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. 783-802, 2002.
[8] G. Bussi, D. Donadio, and M. Parrinello, "Canonical Sampling through Velocity Rescaling," The Journal of chemical physics, vol. 126, p. 014101, 2007.
[9] C. W. Chang, D. Okawa, H. Garcia, A. Majumdar, and A. Zettl, "Breakdown of Fourier's Law in Nanotube Thermal Conductors," Phys Rev Lett, vol. 101, p. 075903, Aug 15 2008.
[10] J. Che, T. Cagin, and W. A. Goddard III, "Thermal Conductivity of Carbon Nanotubes," Nanotechnology, vol. 11, p. 65, 2000.
[11] A. Cummings, M. Osman, D. Srivastava, and M. Menon, "Thermal Conductivity of Y-Junction Carbon Nanotubes," Physical Review B, vol. 70, 2004.
[12] T. Dumitrica, Trends in Computational Nanomechanics: Transcending Length and Time Scales vol. 9: Springer Science & Business Media, 2010.
[13] D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications vol. 1: Academic press, 2001.
[14] C. J. Gomes, M. Madrid, and C. H. Amon, "Thin Film in-Plane Silicon Thermal Conductivity Dependence on Molecular Dynamics Surface Boundary Conditions," vol. 2004, pp. 345-352, 2004.
[15] E. Gonzalez Noya, D. Srivastava, and M. Menon, "Heat-Pulse Rectification in Carbon Nanotube Y Junctions," Physical Review B, vol. 79, 2009.
[16] K. R. Hahn, C. Melis, and L. Colombo, "Thermal Transport in Nanocrystalline Graphene Investigated by Approach-to-Equilibrium Molecular Dynamics Simulations," Carbon, vol. 96, pp. 429-438, 2016.
[17] J. Haile, "Molecular Dynamics Simulation: Elementary Methods," Computers in Physics, vol. 7, pp. 625-625, 1993.
[18] T. N. Heinz and P. H. Hunenberger, "A Fast Pairlist-Construction Algorithm for Molecular Simulations under Periodic Boundary Conditions," J Comput Chem, vol. 25, pp. 1474-86, Sep 2004.
[19] S. P. Hepplestone, A. M. Ciavarella, C. Janke, and G. P. Srivastava, "Size and Temperature Dependence of the Specific Heat Capacity of Carbon Nanotubes," Surface Science, vol. 600, pp. 3633-3636, 2006.
[20] W. G. Hoover, "Canonical Dynamics: Equilibrium Phase-Space Distributions," Physical Review A, vol. 31, pp. 1695-1697, 1985.
[21] W. Humphrey, A. Dalke, and K. Schulten, "Vmd: Visual Molecular Dynamics," Journal of Molecular Graphics, vol. 14, pp. 33-38, 1996.
[22] P. Hunenberger, "Thermostat Algorithms for Molecular Dynamics Simulations," Advanced Computer Simulation Approaches for Soft Matter Sciences I, vol. 173, pp. 105-147, 2005.
[23] S. Iijima, "Helical Microtubules of Graphitic Carbon," Nature, vol. 354, pp. 56-58, 1991.
[24] 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.
[25] B. Li and J. Wang, "Anomalous Heat Conduction and Anomalous Diffusion in One-Dimensional Systems," Physical Review Letters, vol. 91, p. 044301, 2003.
[26] G. C. Loh, E. H. T. Teo, and B. K. Tay, "Thermal Rectification Reversal in Carbon Nanotubes," Journal of Applied Physics, vol. 112, p. 103515, 2012.
[27] A. M. Marconnet, M. A. Panzer, and K. E. Goodson, "Thermal Conduction Phenomena in Carbon Nanotubes and Related Nanostructured Materials," Reviews of Modern Physics, vol. 85, pp. 1295-1326, 2013.
[28] S. Maruyama, "A Molecular Dynamics Simulation of Heat Conduction in Finite Length Swnts," Physica B: Condensed Matter, vol. 323, pp. 193-195, 2002.
[29] F. Müller-Plathe, "A Simple Nonequilibrium Molecular Dynamics Method for Calculating the Thermal Conductivity," The Journal of Chemical Physics, vol. 106, p. 6082, 1997.
[30] O. Narayan and S. Ramaswamy, "Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems," Physical Review Letters, vol. 89, p. 200601, 2002.
[31] S. Nosé, "A Unified Formulation of the Constant Temperature Molecular Dynamics Methods," The Journal of Chemical Physics, vol. 81, p. 511, 1984.
[32] J. Park, J. Lee, and V. Prakash, "Phonon Scattering at Swcnt–Swcnt Junctions in Branched Carbon Nanotube Networks," Journal of Nanoparticle Research, vol. 17, 2015.
[33] J. Park and V. Prakash, "Thermal Transport in 3d Pillared Swcnt–Graphene Nanostructures," Journal of Materials Research, vol. 28, pp. 940-951, 2013.
[34] S. Plimpton, "Fast Parallel Algorithms for Short-Range Molecular Dynamics," Journal of Computational Physics, vol. 117, pp. 1-19, 1995.
[35] S. Plimpton, A. Thompson, P. Crozier, and A. Kohlmeyer. Lammps Www Site. Available: http://lammps.sandia.gov
[36] 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.
[37] C. Ren, Z. Xu, W. Zhang, Y. Li, Z. Zhu, and P. Huai, "Theoretical Study of Heat Conduction in Carbon Nanotube Hetero-Junctions," Physics Letters A, vol. 374, pp. 1860-1865, 2010.
[38] J.-P. Salvetat, G. A. D. Briggs, J.-M. Bonard, R. R. Bacsa, A. J. Kulik, T. Stöckli, et al., "Elastic and Shear Moduli of Single-Walled Carbon Nanotube Ropes," Physical Review Letters, vol. 82, p. 944, 1999.
[39] P. K. Schelling, S. R. Phillpot, and P. Keblinski, "Comparison of Atomic-Level Simulation Methods for Computing Thermal Conductivity," Physical Review B, vol. 65, 2002.
[40] T. Schlick, Molecular Modeling and Simulation: An Interdisciplinary Guide: An Interdisciplinary Guide vol. 21: Springer Science & Business Media, 2010.
[41] 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.
[42] D. P. Sellan, E. S. Landry, J. E. Turney, A. J. H. McGaughey, and C. H. Amon, "Size Effects in Molecular Dynamics Thermal Conductivity Predictions," Physical Review B, vol. 81, 2010.
[43] J. Shiomi and S. Maruyama, "Molecular Dynamics of Diffusive-Ballistic Heat Conduction in Single-Walled Carbon Nanotubes," Japanese Journal of Applied Physics, vol. 47, pp. 2005-2009, 2008.
[44] A. Singh and E. B. Tadmor, "Removing Artificial Kapitza Effects from Bulk Thermal Conductivity Calculations in Direct Molecular Dynamics," Journal of Applied Physics, vol. 117, p. 185101, 2015.
[45] 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.
[46] M. M. J. Treacy, T. W. Ebbesen, and J. M. Gibson, "Exceptionally High Young's Modulus Observed for Individual Carbon Nanotubes," Nature, vol. 381, pp. 678-680, Jun 20 1996.
[47] J. E. Turney, E. S. Landry, A. J. H. McGaughey, and C. H. Amon, "Predicting Phonon Properties and Thermal Conductivity from Anharmonic Lattice Dynamics Calculations and Molecular Dynamics Simulations," Physical Review B, vol. 79, 2009.
[48] L. Verlet, "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules," Physical Review, vol. 159, pp. 98-103, 1967.
[49] X. Xu, L. F. Pereira, Y. Wang, J. Wu, K. Zhang, X. Zhao, et al., "Length-Dependent Thermal Conductivity in Suspended Single-Layer Graphene," Nat Commun, vol. 5, p. 3689, 2014.
[50] X. Yang, D. Chen, Y. Du, and A. C. To, "Heat Conduction in Extended X-Junctions of Single-Walled Carbon Nanotubes," Journal of Physics and Chemistry of Solids, vol. 75, pp. 123-129, 2014.
[51] G. Zhang and B. Li, "Thermal Conductivity of Nanotubes Revisited: Effects of Chirality, Isotope Impurity, Tube Length, and Temperature," The Journal of Chemical Physics, vol. 123, p. 114714, 2005.
[52] Y. G. Zhou, X. L. Zhang, and M. Hu, "Quantitatively Analyzing Phonon Spectral Contribution of Thermal Conductivity Based on Nonequilibrium Molecular Dynamics Simulations. I. From Space Fourier Transform," Physical Review B, vol. 92, Nov 30 2015.