隨著元件的不斷微縮和新的應用發展，未來將面臨更嚴峻的熱管理挑戰，對於微米及奈米尺度的熱傳分析也變得越來越重要。由於奈米尺度下的聲子（phonon）平均自由徑（MFP），會接近系統特徵長度，傳統巨觀理論可能無法解釋奈米尺度的傳輸行為，因此對奈米熱傳行為的觀察與理論的建立是必要的。然而實驗量測在奈米尺度下可能會遭遇許多挑戰，分子動力學模擬（MD）可以提供一種解決方案，直接觀察原子或分子的運動行為，藉此計算奈米尺度下的熱傳導係數或是探討其熱傳行為。然而傳輸係數的計算和奈米熱傳行為的機制，在不同的文獻中仍然存在著差異，其中問題還有待釐清與克服。而本論文藉由平衡法分子動力學（EMD）模擬來計算傳輸係數，並利用非平衡分子動力學（NEMD）模擬，觀察與研究奈米尺度下聲子傳輸的機制。
愛因斯坦（Einstein）公式和格林-庫波（Green-Kubo）公式是平衡法分子動力學中計算傳輸係數的兩個典型公式。愛因斯坦公式速度快，收斂性好，但其無法計算黏度（viscosity）和熱傳導係數（thermal conductivity）的缺點限制此公式的應用；格林-庫波公式可用於所有傳輸係數計算，但收斂性差是一個問題。這項工作提出使用原始格林-庫波 （Original Green-Kubo）公式，藉此結合愛因斯坦和格林-庫波公式的優點，計算所有傳輸係數，並且可以得到更好的收斂性和精確度結果。此公式已經在各種材料的傳輸係數計算，例如氬氣、苯、丁烷、鍺和碳納米管（CNT），證實其具有較好的收斂性和精確度。
　　分支型碳納米管（branched CNTs）因其多方向熱傳輸能力和高導熱性，而成為未來熱管理應用中最吸引人的候選材料之一。然而很少有文獻研究其在穩定熱流下的傳輸行為。本研究使用非平衡分子動力學模擬，研究十字型碳管和T字型碳管的熱傳輸行為。分別研究應變、分支長度、分支接點的缺陷，以及溫度的影響。研究指出，儘管所有分支的手性和長度都相同，但在十字型分支碳管的熱流傾向流往兩側的碳管而不是直向的碳管。然而對於 T 字型分支碳管，無論分支間點的缺陷分佈如何，熱流都更容易傳遞到直向的碳管。隨著分支變長，所有分支中的熱流接近傳統巨觀的熱擴散理論。此外，這種具備方向性（directional）熱傳行為在低溫（50K）下會變得更加明顯，此現象表示此方向性熱傳的成因可能與彈道型（ballistic）聲子傳輸特性有關。

關鍵字：分子模擬，彈道型， 擴散型，聲子，分支型碳管，熱傳

With the miniaturization of devices and new applications, more severe thermal conditions pose huge challenges to thermal management; the understanding of thermal transport in micro-nanoscale structures and materials is becoming increasingly vital. The conventional macroscopic theory fails to explain the micro-nanoscale thermal transfer owing to a comparable or shorter characteristic length than the phonon mean free path (MFP); a sophisticated understanding of thermal transfer at the micro-nanoscale is necessary. Owing to the challenge of measurement in nanoscale heat conduction, molecular dynamics (MD) simulation can provide a solution to characterize atomic/molecular collective and individual behaviors of nanoscale transport. However, the transport coefficient calculation of MD and underlying mechanism of micro-nanoscale behavior still vary according to different studies. This thesis uses MD to reliably calculate the transport coefficient by equilibrium molecular dynamics (EMD) to avoid the failure of Fourier’s law and elucidate the mechanism of nanoscale phonon transfer by nonequilibrium molecular dynamics (NEMD) simulation to mimic experimental situation.
The Einstein formula and Green-Kubo formula are two typical formulae used in transport coefficient calculation in EMD. The Einstein formula is faster and offers better convergence, but its application to viscosity and thermal conductivity calculation is limited; the Green-Kubo formula can be used on all transport coefficients, but the convergence issue is a problem. This work provides an original Green-Kubo (OGK) formula to combine the advantages of the Einstein and Green-Kubo formulae. Using OGK can achieve better convergence and accuracy results than the Green-Kubo formula for all transport coefficient calculations, and this is verified using various materials, such as argon, benzene, butane, germanium, and carbon nanotubes (CNTs).
Branched CNTs are the most promising candidates for thermal management applications because of their multi-direction thermal transport capabilities and high thermal conductivity. However, few reports have examined the stable heat flow behavior inside branched CNTs. This work investigates the thermal transport behavior of CNTs with cross- and T-junctions using NEMD simulation. The effects of strain, branch length, topological defects at the junction, and temperature on the thermal flow are studied. It is found that the heat transferred in branched CNTs with cross-junctions tends to go sideways rather than straight, although all the branches are identical in chirality and length. However, the heat transfers more easily into the straight branch for the T-junction case irrespective of the atomic configuration at the junction. As the branch becomes longer, the heat current in all the branches approaches the conventional prediction based on diffusive thermal transport. Moreover, the directional thermal transport behaviors become more obvious at low temperature (50 K), suggesting that ballistic phonon transport makes an important contribution to directional thermal transport. Our findings provide significant insight into the thermal transport mechanisms of branched CNTs, which may be useful in thermal management applications.

Keywords: molecular dynamics simulation, ballistic, diffusive, phonon, branched CNT, heat transfer

[1] Prasad, C.; Ramey, S.; Jiang, L., "Self-heating in advanced CMOS technologies," Process Technology Modeling, Logic Technology Development, 6A, pp. 4.1, 2017.
[2] Prasad, C., "A review of self-heating effects in advanced CMOS technologies," IEEE Transactions on Electron Devices, 66(11), pp. 4546-4555, 2019.
[3] Armstrong, K. O.; Das, S.; Cresko, J., "Wide bandgap semiconductor opportunities in power electronics," IEEE 4th Workshop on Wide Bandgap Power Devices and Applications (WiPDA), pp. 259-264, 2016.
[4] Sodan, V.; Stoffels, S.; Oprins, H.; Decoutere, S.; Altmann, F.; Baelmans, M.; De Wolf, I., "Fast and distributed thermal model for thermal modeling of GaN power devices," IEEE Transactions on Components, Packaging and Manufacturing Technology, 8(10), pp. 1747-1755, 2018.
[5] Baliga, B. J., "Advanced power MOSFET concepts," Springer, New York, NY, USA, 2010.
[6] Mohan, N.; Undeland, M. T.; Robbins, W. P., "Power electronics: converters, applications, and design", John Wiley & Sons, INC., Hoboken, NJ, USA, 2002.
[7] Moreno, G.; Narumanchi, S.; Feng, X.; Anschel, P.; Myers, S.; Keller, P., "Electric-drive vehicle power electronics thermal management: current status, challenges, and future directions," Journal of Electronic Packaging, 2021.
[8] Qian, C.; Gheitaghy, A. M.; Fan, J.; Tang, H.; Sun, B.; Ye, H.; Zhang, G., "Thermal management on IGBT power electronic devices and modules," IEEE Access, 6, pp. 12868-12884, 2018.
[9] Ho, R.; Mai, K. W.; Horowitz, M. A., "The future of wires," Proceedings of the IEEE, 89(4), pp. 490 - 504, 2001.
[10] Shukla, P.; Coskun, A. K.; Pavlidis, V. F.; Salman, E., "An overview of thermal challenges and opportunities for monolithic 3D ICs," Proceedings of the 2019 on Great Lakes Symposium on VLSI, pp. 439-444, 2019.
[11] Serafy, C.; Bar-Cohen, A.; Srivastava, A.; Yeung, D., "Unlocking the true potential of 3-D CPUs with microfluidic cooling," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 24(4), pp. 1515-1523, 2016.
[12] Ding, B.; Zhang, Z. H.; Gong, L.; Xu, M. H.; Huang, Z. Q., "A novel thermal management scheme for 3D-IC chips with multi-cores and high power density," Applied Thermal Engineering, 168, pp. 114832, 2020.
[13] Lin, L., "Thermal challenges in MEMS applications: phase change phenomena and thermal bonding processes," Microelectronics Journal, 34(3), pp. 179-185, 2003.
[14] Dede, E. M.; Zhou, F.; Schmalenberg, P.; and Nomura, T., "Thermal metamaterials for heat flow control in electronics," Journal of Electronic Packaging, 140(1), pp. 010904, 2018.
[15] Liu, Y.; Cheng, Y.; Hu, R.; and Luo, X., "Nanoscale thermal cloaking by in-situ annealing silicon membrane," Physics Letters A, 383(19), pp. 2296-2301, 2019.
[16] Jana, M. K.; and Biswas, K., "Crystalline solids with intrinsically low lattice thermal conductivity for thermoelectric energy conversion," ACS Energy Letters, 3(6), pp. 1315-1324, 2018.
[17] Cahill, D. G.; Braun, P. V.; Chen, G.; Clarke, D. R.; Fan, S.; Goodson, K. E.; Keblinski, P.; King, W. P.; Mahan, G. D.; Majumdar, A.; Maris, H. J.; Phillpot, S. R.; Pop, E.; and Shi, L., "Nanoscale thermal transport. II. 2003–2012," Applied Physics Reviews, 1(1), pp. 011305, 2014.
[18] Cahill, D. G.; Ford, W. K.; Goodson, K. E.; Mahan, G. D.; Majumdar, A.; Maris, H. J.; Merlin, R.; Phillpot, S. R., "Nanoscale thermal transport," Journal of Applied Physics, 93(2), pp. 793-818, 2003.
[19] Berber, S.; Kwon, Y. K.; Tománek, D., "Unusually high thermal conductivity of carbon nanotubes," Physical Review Letters, 84(20), pp. 4613-4616, 2000.
[20] Ruoff, R. S.; Lorents, D. C., "Mechanical and thermal properties of carbon nanotubes," Carbon, 33(7), pp. 925-930, 1995.
[21] Chang, C.; Okawa, D.; Garcia, H.; Majumdar, A.; Zettl, A., "Breakdown of Fourier’s law in nanotube thermal conductors," Physical Review Letters, 101(7), pp. 075903, 2008.
[22] Luo, T.; Chen, G., "Nanoscale heat transfer-from computation to experiment," Physical Chemistry Chemical Physics, 15(10), pp. 3389-3412, 2013.
[23] Chang, I. L.; Li, C. S.; Wang, G. S.; Wu, C. L.; Chang, C. W., "Does equilibrium or nonequilibrium molecular dynamics correctly simulate thermal transport properties of carbon nanotubes?," Physical Review Materials, 4(3), pp. 036001, 2020.
[24] Bao, H.; Chen, J.; Gu, X.; Cao, B., "A review of simulation methods in micro/nanoscale heat conduction," ES Energy & Environment, 1, pp. 16-55, 2018.
[25] Kubo, R., "The fluctuation-dissipation theorem," Reports on Progress in Physics, 29(1), pp. 255-284, 1966.
[26] Kubo, R., "Statistical-mechanical theory of irreversible processes. I. general theory and simple applications to magnetic and conduction problems," Journal of the Physical Society of Japan, 12(6), pp. 570-586, 1957.
[27] Dhar, A., "Heat transport in low-dimensional systems," Advances in Physics, 57(5), pp. 457-537, 2008.
[28] Liu, S.; Hänggi, P.; Li, N.; Ren, J.; Li, B., "Anomalous heat diffusion," Physical Review Letters, 112(4), pp. 040601, 2014.
[29] Salaway, R. N.; Zhigilei, L. V., "Molecular dynamics simulations of thermal conductivity of carbon nanotubes: resolving the effects of computational parameters," International Journal of Heat and Mass Transfer, 70, pp. 954-964, 2014.
[30] Marconnet, A. M.; Panzer, M. A.; Goodson, K. E., "Thermal conduction phenomena in carbon nanotubes and related nanostructured materials," Reviews of Modern Physics, 85(3), pp. 1295-1326, 2013.
[31] Che, J.; Cagin, T.; Goddard III, W. A., "Thermal conductivity of carbon nanotubes," Nanotechnology, 11(2), pp. 65-69, 2000.
[32] Maruyama, S., "A molecular dynamics simulation of heat conduction in finite length SWNTs," Physica B: Condensed Matter, 323(1-4), pp. 193-195, 2002.
[33] Yang, Y. C.; Chang, W. J.; Fang, T. H.; Fang, S. C., "Modelling of thermal conductance during microthermal machining with scanning thermal microscope using an inverse methodology," Physics Letters A, 372(4), pp. 519-523, 2008.
[34] Liu, C. K.; Yu, C. K.; Chien, H. C.; Kuo, S. L.; Hsu, C. Y.; Dai, M. J.; Luo, G. L.; Huang, S. C.; Huang, M. J., "Thermal conductivity of Si/SiGe superlattice films," Journal of Applied Physics, 104(11), pp. 114301, 2008.
[35] Chien, H. C.; Yao, D. J.; Huang, M. J.; Chang, T. Y., "Thermal conductivity measurement and interface thermal resistance estimation using SiO2 thin film," The Review of Scientific Instruments, 79(5), pp. 054902, 2008.
[36] Kim, P.; Shi, L.; Majumdar, A.; McEuen, P., "Thermal transport measurements of individual multiwalled nanotubes," Physical Review Letters, 87(21), pp. 215502, 2001.
[37] Choi, T.-Y.; Poulikakos, D.; Tharian, J.; Sennhauser, U., "Measurement of the thermal conductivity of individual carbon nanotubes by the four-point three-ω method," Nano Letters, 6(8), pp. 1589-1593, 2006.
[38] Pop, E.; Mann, D.; Wang, Q.; Goodson, K.; Dai, H., "Thermal conductance of an individual single-wall carbon nanotube above room temperature," Nano Letters, 6(1), pp. 96-100, 2006.
[39] Yu, C.; Shi, L.; Yao, Z.; Li, D.; Majumdar, A., "Thermal conductance and thermopower of an individual single-wall carbon nanotube," Nano Letters, 5(9), pp. 1842-1846, 2005.
[40] Li, Q.; Liu, C.; Wang, X.; Fan, S., "Measuring the thermal conductivity of individual carbon nanotubes by the Raman shift method," Nanotechnology, 20(14), pp. 145702, 2009.
[41] Pettes, M. T.; Shi, L., "Thermal and structural characterizations of individual single-, double-, and multi-walled carbon nanotubes," Advanced Functional Materials, 19(24), pp. 3918-3925, 2009.
[42] Fujii, M.; Zhang, X.; Xie, H.; Ago, H.; Takahashi, K.; Ikuta, T.; Abe, H.; Shimizu, T., "Measuring the thermal conductivity of a single carbon nanotube," Physical Review Letters, 95(6), pp. 065502, 2005.
[43] Wang, Z.; Tang, D.; Zheng, X.; Zhang, W.; Zhu, Y., "Length-dependent thermal conductivity of single-wall carbon nanotubes: prediction and measurements," Nanotechnology, 18(47), pp. 475714, 2007.
[44] Yang, X.; Chen, D.; Du, Y.; To, A. C., "Heat conduction in extended x-junctions of single-walled carbon nanotubes," Journal of Physics and Chemistry of Solids, 75(1), pp. 123-129, 2014.
[45] Shi, J.; Dong, Y.; Fisher, T.; Ruan, X., "Thermal transport across carbon nanotube-graphene covalent and van der Waals junctions," Journal of Applied Physics, 118(4), pp. 044302, 2015.
[46] Huang, B. W.; Hsiao, T. K.; Lin, K. H.; Chiou, D. W.; Chang, C. W., "Length-dependent thermal transport and ballistic thermal conduction," AIP Advances, 5(5), pp. 053202, 2015.
[47] Müller-Plathe, F., "A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity," The Journal of Chemical Physics, 106(14), pp. 6082-6085, 1997.
[48] Helfand, E., "Transport coefficients from dissipation in a canonical ensemble," Physical Review, 119(1), pp. 1-9, 1960.
[49] Haile, J. M., "Molecular dynamics simulation elementary methods," John Wiley & Sons, INC., Hoboken, NJ, USA, 1997.
[50] Rapaport, D. C., "The art of molecular dynamics simulation," Cambridge University Press, Cambridge, ENG, UK, 2004.
[51] Kinaci, A.; Haskins, J. B.; Cagin, T., "On calculation of thermal conductivity from Einstein relation in equilibrium molecular dynamics," The Journal of Chemical Physics, 137(1), pp. 014106, 2012.
[52] Viscardy, S.; Servantie, J.; Gaspard, P., "Transport and Helfand moments in the Lennard-Jones fluid. I. shear viscosity," The Journal of Chemical Physics, 126(18), p. 184512, 2007.
[53] Viscardy, S.; Servantie, J.; Gaspard, P., "Transport and Helfand moments in the Lennard-Jones fluid. II. thermal conductivity," The Journal of Chemical Physics, 126(18), pp. 184513, 2007.
[54] Li, J.; Porter, L.; Yip, S., "Atomistic modeling of finite-temperature properties of crystalline beta-SiC," Journal of Nuclear Materials, 255(2-3), pp. 139-152, 1998.
[55] Chen, J.; Zhang, G.; Li, B., "How to improve the accuracy of equilibrium molecular dynamics for computation of thermal conductivity," Physics Letters A, 374(23), pp. 2392-2396, 2010.
[56] Che, J.; Cagın, T.; Deng, W.; Goddard, W. A., "Thermal conductivity of diamond and related materials from molecular dynamics simulations," The Journal of Chemical Physics, 113(16), pp. 6888-6900, 2000.
[57] Schelling, P. K.; Phillpot, S. R.; Keblinski, P., "Comparison of atomic-level simulation methods for computing thermal conductivity," Physical Review B, 65(14), pp. 144306, 2002.
[58] Dong, H.; Fan, Z.; Shi, L.; Harju, A.; Ala-Nissila, T., "Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon," Physical Review B, 97(9), pp. 094305, 2018.
[59] Chalopin, Y.; Esfarjani, K.; Henry, A.; Volz, S.; Chen, G., "Thermal interface conductance in Si/Ge superlattices by equilibrium molecular dynamics," Physical Review B, 85(19), pp. 195302, 2012.
[60] Fan, Z.; Pereira, L. F. C.; Hirvonen, P.; Ervasti, M. M.; Elder, K. R.; Donadio, D.; Ala-Nissila, T.; Harju, A., "Thermal conductivity decomposition in two-dimensional materials: Application to graphene," Physical Review B, 95(14), pp. 144309, 2017.
[61] Kittel, C., "Introduction to solid state physics," John Wiley & Sons, INC., New York, NY, USA, 2004.
[62] Chen, G., "Nanoscale energy transport and conversion,” Oxford University Press, Oxford, ENG, UK, 2005.
[63] Dove, M. T., "Introduction to lattice dynamics", Cambridge University Press, Cambridge, ENG, UK, 1993.
[64] Maruyama, S., "A molecular dynamics simulation of heat conduction of a finite length single-walled carbon nanotube," Microscale Thermophysical Engineering, 7(1), pp. 41-50, 2010.
[65] Yao, Z. h.; Wang, J. S.; Li, B.; Liu, G. R., "Thermal conduction of carbon nanotubes using molecular dynamics," Physical Review B, 71(8), pp. 085417, 2005.
[66] Wang, Z.; Ruan, X., "On the domain size effect of thermal conductivities from equilibrium and nonequilibrium molecular dynamics simulations," Journal of Applied Physics, 121(4), pp. 044301, 2017.
[67] Qiu, B.; Ruan, X., "Reduction of spectral phonon relaxation times from suspended to supported graphene," Applied Physics Letters, 100(19), pp. 193101, 2012.
[68] Latour, B.; Chalopin, Y., "Distinguishing between spatial coherence and temporal coherence of phonons," Physical Review B, 95(21), pp. 214310, 2017.
[69] Latour, B.; Volz, S.; Chalopin, Y., "Microscopic description of thermal-phonon coherence: From coherent transport to diffuse interface scattering in superlattices," Physical Review B, 90(1), pp. 014307, 2014.
[70] Vollebregt, S.; Banerjee, S.; Chiaramonti, A. N.; Tichelaar, F. D.; Beenakker, K.; Ishihara, R., "Dominant thermal boundary resistance in multi-walled carbon nanotube bundles fabricated at low temperature," Journal of Applied Physics, 116(2), pp. 023514, 2014.
[71] Gharib-Zahedi; M. R.; Tafazzoli, M.; Bohm, M. C.; Alaghemandi, M., "Transversal thermal transport in single-walled carbon nanotube bundles: influence of axial stretching and intertube bonding," The Journal of Chemical Physics, 139(18), pp. 184704, 2013.
[72] Park, J.; Prakash, V., "Thermal transport in 3D pillared SWCNT–graphene nanostructures," Journal of Materials Research, 28(7), pp. 940-951, 2013.
[73] Shi, J.; Zhong, Y.; Fisher, T. S.; Ruan, X., "Decomposition of the thermal boundary resistance across carbon nanotube–graphene junctions to different mechanisms," ACS Applied Materials & Interfaces, 10(17), pp. 15226–15231, 2018.
[74] Gonzalez Noya, E.; Srivastava, D.; Menon, M., "Heat-pulse rectification in carbon nanotube Y junctions," Physical Review B, 79(11), pp. 115432, 2009.
[75] Park, J.; Lee, J.; Prakash, V., "Phonon scattering at SWCNT–SWCNT junctions in branched carbon nanotube networks," Journal of Nanoparticle Research, 17(1), pp. 59, 2015.
[76] Alaghemandi, M.; Muller-Plathe, F.; Bohm, M. C., "Thermal conductivity of carbon nanotube-polyamide-6,6 nanocomposites: reverse non-equilibrium molecular dynamics simulations," The Journal of Chemical Physics, 135(18), pp. 184905, 2011.
[77] Chen, J.; Gui, X.; Wang, Z.; Li, Z.; Xiang, R.; Wang, K.; Wu, D.; Xia, X.; Zhou, Y.; Wang, Q.; Tang, Z.; Chen, L., "Superlow thermal conductivity 3D carbon nanotube network for thermoelectric applications," ACS Applied Materials & Interfaces, 4(1), pp. 81–86, 2012.
[78] Aitkaliyeva, A.; Chen, D.; Shao, L., "Phonon transport assisted by inter-tube carbon displacements in carbon nanotube mats," Scientific Reports, 3(1), pp. 1-5, 2013.
[79] Lian, F.; Llinas, J. P.; Li, Z.; Estrada, D.; Pop, E., "Thermal conductivity of chirality-sorted carbon nanotube networks," Applied Physics Letters, 108(10), pp. 103101, 2016.
[80] Kaskela, A.; Nasibulin, A. G.; Timmermans, M. Y.; Aitchison, B.; Papadimitratos, A.; Tian, Y.; Zhu, Z.; Jiang, H.; Brown, D. P.; Zakhidov, A.; Kauppinen, E. I., "Aerosol-synthesized SWCNT networks with tunable conductivity and transparency by a dry transfer technique," Nano Letters, 10(11), pp. 4349–4355, 2010.
[81] Sun, D. M.; Timmermans, M. Y.; Tian, Y.; Nasibulin, A. G.; Kauppinen, E. I.; Kishimoto, S.; Mizutani, T.; Ohno, Y., "Flexible high-performance carbon nanotube integrated circuits," Nature Nanotechnology, 6(3), pp. 156-161, 2011.
[82] Hu, J.; Ouyang, M.; Yang, P.; Lieber, C. M., "Controlled growth and electrical properties of heterojunctions of carbon nanotubes and silicon nanowires," Nature, 399(6731), pp. 48–51, 1999.
[83] Aiyiti, A.; Zhang, Z.; Chen, B.; Hu, S.; Chen, J.; Xu, X.; Li, B., "Thermal rectification in Y-junction carbon nanotube bundle," Carbon, 140, pp. 673-679, 2018.
[84] Li, Y. L.; Kinloch, I. A.; Windle, A. H., "Direct spinning of carbon nanotube fibers from chemical vapor deposition synthesis," Science China Technological Sciences, 304(5668), pp. 276-278, 2004.
[85] Ma, X.; Wang, E. G., "CNx/carbon nanotube junctions synthesized by microwave chemical vapor deposition," Applied Physics Letters, 78(7), pp. 978-980, 2001.
[86] Terrones, M.; Banhart, F.; Grobert, N.; Charlier, J. C.; Terrones, H.; Ajayan, P., "Molecular junctions by joining single-walled carbon nanotubes," Physical Review Letters, 89(7), pp. 075505, 2002.
[87] Srivastava, D.; Menon, M.; Ajayan, P. M., "Branched carbon nanotube junctions predicted by computational nanotechnology and fabricated through nanowelding," Journal of Nanoparticle Research, 5(3), pp. 395–400, 2003.
[88] Li, W.; Feng, Y. H.; Tang, J. J.; Zhang, X., " Thermal conductivity and thermal rectification of carbon nanotube Y junctions," Acta Physica Sinica, 62(7), pp. 076107, 2013.
[89] Che, J.; Cagin, T.; III, W. A. G., "Thermal conductivity of carbon nanotubes," Nanotechnology, 11(2), pp. 65-69, 2000.
[90] Yamamoto, T.; Konabe, S.; Shiomi, J.; Maruyama, S., "Crossover from ballistic to diffusive thermal transport in carbon nanotubes," Applied Physics Express, 2(9), pp. 095003, 2009.
[91] Han, Y.; Yang, J. Y.; Hu, M., "Unusual strain response of thermal transport in dimerized three-dimensional graphene," Nanoscale, 10(11), pp. 5229-5238, 2018.
[92] Varshney, V.; Unnikrishnan, V.; Lee, J.; Roy, A. K., "Developing nanotube junctions with arbitrary specifications," Nanoscale, 10(1), pp. 403-415, 2017.
[93] Zhang, Z.; Kutana, A.; Roy, A.; Yakobson, B. I., "Nanochimneys: Topology and thermal conductance of 3D nanotube–graphene cone junctions," The Journal of Physical Chemistry C, 121(2), pp. 1257–1262, 2017.
[94] Shi, J.; Lee, J.; Dong, Y.; Roy, A.; Fisher, T. S.; Ruan, X., "Dominant phonon polarization conversion across dimensionally mismatched interfaces: Carbon-nanotube–graphene junction," Physical Review B, 97(13), pp. 134309, 2018.
[95] Plimpton, S., "Fast parallel algorithms for short-range molecular dynamics," Journal of Computational Physics, 117(1), pp. 1-19, 1995.
[96] Tersoff, J., "Modeling solid-state chemistry: Interatomic potentials for multicomponent systems," Physical Review B, 39(8), pp. 5566-5568, 1989.
[97] Donald, W. B.; Olga, A. S.; Judith, A. H.; Steven, J. S.; Boris, N.; Susan, B. S., "A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons," Journal of Physics: Condensed Matter, 14(4), pp. 783-802, 2002.
[98] Lindsay, L.; Broido, D. A., "Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene," Physical Review B, 81(20), pp. 205441, 2010.
[99] Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J., "Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids," Journal of the American Chemical Society, 118(45), pp. 11225–11236, 1996.
[100] Rahman, A., "Correlations in the motion of atoms in liquid argon," Physical Review, 136(2A), pp. A405-A411, 1964.
[101] Verlet, L., "Computer "experiments" on classical fluids. I. thermodynamical properties of Lennard-Jones molecules," Physical Review, 159(1), pp. 98-103, 1967.
[102] McQuarrie, D. A., “Statistical mechanics,” Halliday Lithograph Corporation, New York, NY, USA, 1976.
[103] Gale, J. D.; Rohl, A. L., "The general utility lattice program (GULP)," Molecular Simulation, 29(5), pp. 291-341, 2003.
[104] Bell, R. J.; Dean, P., "Atomic vibrations in vitreous silica," Discussions of The Faraday Society, 50(0), pp. 55-61, 1970.
[105] Pailhes, S.; Euchner, H.; Giordano, V. M.; Debord, R.; Assy, A.; Gomes, S.; Bosak, A.; Machon, D.; Paschen, S.; de Boissieu, M., "Localization of propagative phonons in a perfectly crystalline solid," Physical Review Letters, 113(2), pp. 025506, 2014.
[106] Feng, T.; Qiu, B.; Ruan, X., "Anharmonicity and necessity of phonon eigenvectors in the phonon normal mode analysis," Journal of Applied Physics, 117(19), pp. 195102, 2015.
[107] Yang, B.; Chen, G., "Partially coherent phonon heat conduction in superlattices," Physical Review B, 67(19), pp. 195311 2003.
[108] Luckyanova, M. N.; Garg, J.; Esfarjani, K.; Jandl, A.; Bulsara, M. T.; Schmidt, A. J.; Minnich, A. J.; Chen, S.; Dresselhaus, M. S.; Ren, Z.; Fitzgerald, E. A.; Chen, G., "Coherent phonon heat conduction in superlattices," Science, 338(6109), pp. 936-939, 2012.
[109] Landry, E. S.; McGaughey, A. J. H., "Effect of interfacial species mixing on phonon transport in semiconductor superlattices," Physical Review B, 79(7), pp. 075316, 2009.
[110] Jones, R. E.; Mandadapu, K. K., "Adaptive Green-Kubo estimates of transport coefficients from molecular dynamics based on robust error analysis," The Journal of Chemical Physics, 136(15), pp. 154102, 2012.
[111] McGaughey, A. J. H.; Kaviany, M., "Thermal conductivity decomposition and analysis using molecular dynamics simulations. Part I. Lennard-Jones argon," International Journal of Heat and Mass Transfer, 47(8-9), pp. 1783-1798, 2004.
[112] Lee, S. H., "Molecular dynamics simulation study of the transport properties of liquid argon: the Green-Kubo formula revisited," Bulletin of the Korean Chemical Society, 28(8), pp. 1371-1374, 2007.
[113] Parkhurst, H. J.; Jonas, J., "Dense liquids. II. the effect of density and temperature on viscosity of tetramethylsilane and benzene," The Journal of Chemical Physics, 63(6), pp. 2705-2709, 1975.
[114] Janz, G. J.; Tomkins, R. P. T., "Nonaqueous electrolytes handbook, " Academic Press, New York, NY, USA, 1972.
[115] Haynes, W. M.; Lide, D. R.; Bruno, T. J., "CRC handbook of chemistry and physics," CRC Press, Boca Raton, FL, USA, 2016.
[116] Yazdani, A.; Maini, B. B., "Measurements and modelling of phase behaviour and viscosity of a heavy oil/butane system," Journal of Canadian Petroleum Technology, 49(2), pp. 9-14, 2010.
[117] Dong, J.; Sankey, O. F.; Myles, C. W., "Theoretical study of the lattice thermal conductivity in Ge framework semiconductors," Physical Review Letters, 86(11), pp. 2361-2364, 2001.
[118] Lee, S. H.; Park, D. K.; Kang, D. B., "Molecular dynamics simulations for transport coefficients of liquid argon : new approaches," Bulletin of the Korean Chemical Society, 24(2), pp. 178-182, 2003.
[119] Cook, G. A., "Argon, helium and the rare gases," Physics Today, 15(6), pp. 59, 1962.
[120] Haynes, W. M., " Viscosity of gaseous and liquid argon," Physica D: Nonlinear Phenomena, 67(3), pp. 440-470, 1973.
[121] Lee, S. H., "Shear viscosity of benzene, toluene, and p-Xylene by non-equilibrium molecular dynamics simulations," Bulletin of the Korean Chemical Society, 25(2), pp. 321-324, 2004.
[122] Lipkin, M. R.; Davison, J. A.; Kurtz, S. S., "Viscosity of propane, butane, and isobutane," Industrial & Engineering Chemistry, 34(8), pp. 976-978, 1942.
[123] Slack, G. A.; Glassbrenner, C., "Thermal conductivity of germanium from 3°K to 1020°K," Physical Review, 120(3), pp. 782-789, 1960.
[124] Selezenev, A. A., Aleinikov, A. Y., Ermakov, P. V., Ganchuk, N. S., Ganchuk, S. N., and Jones, R. E., 2012, "Molecular-dynamics calculation of the thermal conductivity coefficient of the germanium single crystal," Physics of the Solid State, 54(3), pp. 462-467.
[125] Stuart, S. J.; Tutein, A. B.; Harrison, J. A., "A reactive potential for hydrocarbons with intermolecular interactions," The Journal of Chemical Physics, 112(14), pp. 6472-6486, 2000.
[126] Shiomi, J., "Molecular dynamics of diffusive-ballistic heat conduction in single-walled carbon nanotubes," Japanese Journal of Applied Physics, 47(4), pp.2005-2009, 2008.
[127] Hone, J.; Whitney, M.; Piskoti, C.; Zettl, A., "Thermal conductivity of single-walled carbon nanotubes," Physical Review B, 59(4), pp. R2514-R2516, 1999.
[128] Ren, C.; Xu, Z.; Zhang, W., Li; Y., Zhu, Z.; Huai, P., "Theoretical study of heat conduction in carbon nanotube hetero-junctions," Physics Letters A, 374(17-18), pp. 1860-1865, 2010.
[129] Chen, W. J.; Chang, I. L., "The atomistic study on thermal transport of the branched CNT," Journal of Mechanics, 36(5), pp. 721-727, 2020.
[130] 王冠雄, "以非平衡態分子動力學研究十字型與T型奈米碳管熱傳行為," 碩士, 機械工程學系, 國立成功大學, 台南市, 2019.
[131] 羅友威, "以非平衡態分子動力學研究完美及具分支構造奈米碳管之熱傳行為," 碩士, 機械工程學系, 國立成功大學, 台南市, 2016.