本研究利用分子動力學(molecular dynamic, MD)模擬方法，模擬層狀石墨烯/銅複合材料在受剪切負載下其界面變化與基體的特性，探討不同溫度、手性、層間距及銅晶粒尺寸對其機械特性所造成之影響，例如破裂機制、差排和剪切模數等。在不同溫度與手性下的結果表示隨著溫度的增加，Shockley差排的含量會隨之增加，鋸齒型與扶手椅型的破壞剪切應力隨之減少，也表示了鋸齒型的剪切強度對於溫度的依賴性高於扶手椅型，另一方面，在扶手椅型石墨烯破壞後，有發現裂紋的自我修復，修復後使其仍保有一定強度且會產生些許Stone-Wales缺陷結構；在不同重複層間距(λ)下則是隨著λ的增加，複合材料的破壞應力會隨之減少，剪切強度也隨之減少；最後在不同銅晶粒尺寸(D)下，以D=4.24 nm為有最大的破壞剪應力，而剪切強度則會隨著晶粒尺寸的減少而降低。

In this study, molecular dynamics (MD) simulation methods were used to simulate the characteristics of the interface and matrix of nanolaminated graphene/Cu under shear loads, including the effects of different temperature, chirality, repeating layer spacing and grain size on their mechanical properties, such as failure mechanism, dislocation and shear modulus. The results of different temperature and chirality simulation indicate that as the temperature increases, the content of Shockley dislocations will increase, and the failure shear stress of zigzag and armchair direction also decrease, which also shows the mechanical strength of the zigzag direction is more dependent on the temperature than the armchair direction. Moreover, after the armchair graphene was failed, it will be self-healing of the cracks. After the healing, it was still left with some Stone-Wales defect structure and maintain a certain strength. At different repeat layer spacing (λ), the failure stress and the shear strength of the composite material decreases as increasing the λ. At different grain size (D), the D = 4.24 nm has the largest failure shear stress, and the shear strength decreases as decreasing the grain sizes.

摘要 I
Abstract II
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VII
符號說明 XI
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 本文架構 4
第二章 文獻回顧 5
2.1 奈米材料機械性質之文獻回顧 5
2.2 複合材料之文獻回顧 6
2.3 二維材料與石墨烯文獻回顧 6
第三章 分子動力學與模擬方法 8
3.1分子動力學理論 8
3.1.1原子間作用力與勢能函數 9
3.1.2 系綜觀念 16
3.1.3 初始條件 17
3.1.4 邊界條件 19
3.2 模擬方法 20
3.2.1 速度預測法 20
3.2.2 截斷半徑 24
3.2.3 最小映像法則 25
3.2.4 無因次化 25
3.2.5 計算分析 27
3.3 軟體與平行運算之方法 28
3.3.1 空間分割法 28
第四章 物理模型與模擬條件設定 30
4.1物理模型及相關參數 30
4.2勢能參數 34
第五章 結果與討論 35
5.1 機械特性模型之驗證 35
5.2 溫度效應 36
5.2.1 鋸齒型 36
5.2.2 扶手椅型 57
5.3 層距效應 81
5.4 銅晶粒尺寸效應 86
第六章 結論 92
參考文獻 94
簡歷 100

[1]Yadav, R., Tirumali, M., Wang, X., Naebe, M., & Kandasubramanian, B. (2019). Polymer composite for antistatic application in aerospace. Defence Technology, DOI：https://doi.org/10.1016/j.dt.2019.04.008.
[2]Zhu, J., Wang, Z., & Ou, F. (2012). Application of Advanced Composite Materials in Aerospace J. New Technology & New Process, 10.
[3]Romanov, I., Chernyshov, E., & Romanov, A. (2019). Assessment of the possibility for substituting cast iron in vehicle brake disc with Aluminum-Based Metal-matrix composite material produced by internal oxidation. Materials Today: Proceedings, 19, 2125-2128.
[4]Xiao, Y., Zhang, Z., Yao, P., Fan, K., Zhou, H., Gong, T., Zhao, L., & Deng, M. (2018). Mechanical and tribological behaviors of copper metal matrix composites for brake pads used in high-speed trains. Tribology International, 119, 585-592.
[5]Qu, X. H., Zhang, L., Mao, W. U., & Ren, S. B. (2011). Review of metal matrix composites with high thermal conductivity for thermal management applications. Progress in Natural Science: Materials International, 21(3), 189-197.
[6]Prieto, R., Molina, J. M., Narciso, J., & Louis, E. (2008). Fabrication and properties of graphite flakes/metal composites for thermal management applications. Scripta Materialia, 59(1), 11-14.
[7]Smart, D. R., Kumar, J. P., & Cyrus, R. S. (2019). Development and investigations of Al5083/CNT/Ni/MoS2 metal matrix composite for offshore applications. Materials Today: Proceedings, 19, 682-685.
[8]Elanchezhian, C., Ramnath, B. V., Ramakrishnan, G., Raghavendra, K. S., Muralidharan, M., & Kishore, V. (2018). Review on metal matrix composites for marine applications. Materials Today: Proceedings, 5(1), 1211-1218.
[9]Weng, S., Ning, H., Fu, T., Hu, N., Zhao, Y., Huang, C., & Peng, X. (2018). Molecular dynamics study of strengthening mechanism of nanolaminated graphene/Cu composites under compression. Scientific Reports, 8(1), 3089.
[10]Wang, L., Yang, Z., Cui, Y., Wei, B., Xu, S., Sheng, J., Wang, Miao., Zhu, Y., & Fei, W. (2017). Graphene-copper composite with micro-layered grains and ultrahigh strength. Scientific Reports, 7, 41896.
[11]Xiang, S., Wang, X., Gupta, M., Wu, K., Hu, X., & Zheng, M. (2016). Graphene nanoplatelets induced heterogeneous bimodal structural magnesium matrix composites with enhanced mechanical properties. Scientific Reports, 6, 38824.
[12]Shin, S. E., Choi, H. J., Hwang, J. Y., & Bae, D. (2015). Strengthening behavior of carbon/metal nanocomposites. Scientific Reports, 5, 16114.
[13]Mi, B.(2019). Scaling up nanoporous graphene membranes. Science, 364(6445), 1033-1034
[14]Yang, Y., Yang, X., Liang, L., Gao, Y., Cheng, H., Li, X., Zou, M., Ma, R., Yuan, Q., & Duan, X. (2019) Large-area graphene-nanomesh/carbon-nanotube hybrid membranes for ionic and molecular nanofiltration. Science, 364(6445), 1057-1062.
[15]Gao, Z., Zhang, Y., Fu, Y., Yuen, M. M., & Liu, J. (2013). Thermal chemical vapor deposition grown graphene heat spreader for thermal management of hot spots. Carbon, 61, 342-348.
[16]Tian, J., Wu, S., Yin, X., & Wu, W. (2019). Novel preparation of hydrophilic graphene/graphene oxide nanosheets for supercapacitor electrode. Applied Surface Science, 496, 143696.
[17]Jeong, J. H., Lee, G. W., Kim, Y. H., Choi, Y. J., Roh, K. C., & Kim, K. B. (2019). A holey graphene-based hybrid supercapacitor. Chemical Engineering Journal, 378, 122126.
[18]Shang, Y., Wang, Y., Li, S., Hua, C., Zou, M., & Cao, A. (2017). High-strength carbon nanotube fibers by twist-induced self-strengthening. Carbon, 119, 47-55.
[19]Zhou, X., Liu, X., Lei, J., & Yang, Q. (2019). Atomic simulations of the formation of twist grain boundary and mechanical properties of graphene/aluminum nanolaminated composites. Computational Materials Science, 172, 109342.
[20]Wang, P., Yang, J., Sun, G., Zhang, X., Zhang, H., Zheng, Y., & Xu, S. (2018). Twist induced plasticity and failure mechanism of helical carbon nanotube fibers under different strain rates. International Journal of Plasticity, 110, 74-94.
[21]Jian, N., Xue, P., & Diao, D. (2019). Thermally induced atomic and electronic structure evolution in nanostructured carbon film by in situ TEM/EELS analysis. Applied Surface Science, 498, 143831.
[22]Liu, Z., Monclús, M. A., Yang, L. W., Castillo-Rodríguez, M., Molina-Aldareguía, J. M., & LLorca, J. (2018). Tensile deformation and fracture mechanisms of Cu/Nb nanolaminates studied by in situ TEM mechanical tests. Extreme Mechanics Letters, 25, 60-65.
[23]Thorkelsson, K., Bai, P., & Xu, T. (2015). Self-assembly and applications of anisotropic nanomaterials: A review. Nano Today, 10(1), 48-66.
[24]Zakaria, M. R., Akil, H. M., Kudus, M. H. A., & Saleh, S. S. M. (2014). Enhancement of tensile and thermal properties of epoxy nanocomposites through chemical hybridization of carbon nanotubes and alumina. Composites Part A: Applied Science and Manufacturing, 66, 109-116.
[25]Deng, S., Sumant, A. V., & Berry, V. (2018). Strain engineering in two-dimensional nanomaterials beyond graphene. Nano Today, 22, 14-35.
[26]Ovid'Ko, I. A., Valiev, R. Z., & Zhu, Y. T. (2018). Review on superior strength and enhanced ductility of metallic nanomaterials. Progress in Materials Science, 94, 462-540.
[27]Kumar, K. S., Van Swygenhoven, H., & Suresh, S. (2003). Mechanical behavior of nanocrystalline metals and alloys. Acta Materialia, 51(19), 5743-5774.
[28]Liu, L., Deng, Q., Su, M., An, M., & Wang, R. (2019). Strain rate and temperature effects on tensile behavior of Ti/Al multilayered nanowire: A molecular dynamics study. Superlattices and Microstructures, 135, 106272.
[29]Coluci, V. R., & Pugno, N. M. (2010). Molecular dynamics simulations of stretching, twisting and fracture of super carbon nanotubes with different chiralities: towards smart porous and flexible scaffolds. Journal of Computational and Theoretical Nanoscience, 7(7), 1294-1298.

[30]Ma, B., Rao, Q., & He, Y. (2016). Molecular dynamics simulation of temperature effect on tensile mechanical properties of single crystal tungsten nanowire. Computational Materials Science, 117, 40-44.
[31]Sofiah, A. G. N., Samykano, M., Kadirgama, K., Mohan, R. V., & Lah, N. A. C. (2018). Metallic nanowires: Mechanical properties–Theory and experiment. Applied Materials Today, 11, 320-337.
[32]Liu, H., & Zhou, J. (2016). Plasticity in nanotwinned polycrystalline Ni nanowires under uniaxial compression. Materials Letters, 163, 179-182.
[33]Fang, Q., Li, J., Luo, H., Du, J., & Liu, B. (2017). Atomic scale investigation of nanocrack evolution in single-crystal and bicrystal metals under compression and shear deformation. Journal of Alloys and Compounds, 710, 281-291.
[34]Guerra, V., Wan, C., & McNally, T. (2018). Thermal conductivity of 2D nano-structured boron nitride (BN) and its composites with polymers. Progress in Materials Science, 100, 170-186.
[35]Tertuliano, O. A., & Greer, J. R. (2016). The nanocomposite nature of bone drives its strength and damage resistance. Nature Materials, 15(11), 1195.
[36]Touny, A. H., Saleh, M. M., Abd El-Lateef, H. M., & Saleh, M. M. (2019). Electrochemical methods for fabrication of polymers/calcium phosphates nanocomposites as hard tissue implants. Applied Physics Reviews, 6(2), 021303.
[37]Pan, C., Zhang, J., Kou, K., Zhang, Y., & Wu, G. (2018). Investigation of the through-plane thermal conductivity of polymer composites with in-plane oriented hexagonal boron nitride. International Journal of Heat and Mass Transfer, 120, 1-8.
[38]Smith, A. T., LaChance, A. M., Zeng, S., Liu, B., & Sun, L. (2019). Synthesis, properties, and applications of graphene oxide/reduced graphene oxide and their nanocomposites. Nano Materials Science, 1(1), 31-47.
[39]Singh, N. P., Gupta, V. K., & Singh, A. P. (2019). Graphene and carbon nanotube reinforced epoxy nanocomposites: A review. Polymer, 180, 121724.
[40]Zhu, J. Q., Liu, X., & Yang, Q. S. (2019). Dislocation-blocking mechanism for the strengthening and toughening of laminated graphene/Al composites. Computational Materials Science, 160, 72-81.
[41]Hu, Z., Tong, G., Lin, D., Chen, C., Guo, H., Xu, J., & Zhou, L. (2016). Graphene-reinforced metal matrix nanocomposites–a review. Materials Science and Technology, 32(9), 930-953.
[42]Liu, J., Khan, U., Coleman, J., Fernandez, B., Rodriguez, P., Naher, S., & Brabazon, D. (2016). Graphene oxide and graphene nanosheet reinforced aluminium matrix composites: Powder synthesis and prepared composite characteristics. Materials & Design, 94, 87-94.
[43]Shin, S. E., Choi, H. J., Shin, J. H., & Bae, D. (2015). Strengthening behavior of few-layered graphene/aluminum composites. Carbon, 82, 143-151.
[44]Duan, K., Li, L., Hu, Y., & Wang, X. (2017). Interface mechanical properties of graphene reinforced copper nanocomposites. Materials Research Express, 4(11), 115020.
[45]Kim, Y., Lee, J., Yeom, M. S., Shin, J. W., Kim, H., Cui, Y., & Han, S. M. (2013). Strengthening effect of single-atomic-layer graphene in metal–graphene nanolayered composites. Nature Communications, 4, 2114.
[46]Cao, G., & Gao, H. (2019). Mechanical properties characterization of two-dimensional materials via nanoindentation experiments. Progress in Materials Science, 103, 558-595.
[47]Sha, Z. D., Wan, Q., Pei, Q. X., Quek, S. S., Liu, Z. S., Zhang, Y. W., & Shenoy, V. B. (2014). On the failure load and mechanism of polycrystalline graphene by nanoindentation. Scientific Reports, 4, 7437.
[48]Chen, S., Liu, L., & Wang, T. (2005). Investigation of the mechanical properties of thin films by nanoindentation, considering the effects of thickness and different coating–substrate combinations. Surface and Coatings Technology, 191(1), 25-32.
[49]Song, H., Liu, J., Liu, B., Wu, J., Cheng, H. M., & Kang, F. (2018). Two-dimensional materials for thermal management applications. Joule, 2(3), 442-463.
[50]Yankowitz, M., Chen, S., Polshyn, H., Zhang, Y., Watanabe, K., Taniguchi, T., Graf, D., Young, A. F., & Dean, C. R. (2019). Tuning superconductivity in twisted bilayer graphene. Science, 363(6431), 1059-1064.
[51]Papageorgiou, D. G., Kinloch, I. A., & Young, R. J. (2015). Graphene/elastomer nanocomposites. Carbon, 95, 460-484.
[52]Mogera, U., & Kulkarni, G. U. (2019). A new twist in graphene research: Twisted graphene. Carbon, 156, 470-487.
[53]Tian, C., Zhang, S., Wang, H., Chen, C., Han, Z., Chen, M., Zhu, Y., Cui, R., & Zhang, G. (2019). Three-dimensional nanoporous copper and reduced graphene oxide composites as enhanced sensing platform for electrochemical detection of carbendazim. Journal of Electroanalytical Chemistry, 847, 113243.
[54]Chen, J., Wang, L., Huang, Y., Li, Z., Zhang, H., Ali, M. C., Liu, J., Chen, X., & Qiu, H. (2019). Fabrication of nanoporous graphene/cuprous oxide nanocomposite and its application for chemiluminescence sensing of NADH in human serum and cells. Sensors and Actuators B: Chemical, 290, 15-22.
[55]Cay-Durgun, P., & Lind, M. L. (2018). Nanoporous materials in polymeric membranes for desalination. Current Opinion in Chemical Engineering, 20, 19-27.
[56]Machrafi, H., & Lebon, G. (2015). Size and porosity effects on thermal conductivity of nanoporous material with an extension to nanoporous particles embedded in a host matrix. Physics Letters A, 379(12-13), 968-973.
[57]Irving, J. H., & Kirkwood, J. G. (1950). The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. The Journal of chemical physics, 18(6), 817-829.
[58]Hoover, W. G. (1985). Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, 31(3), 1695.
[59]Smith, R. (Ed.). (2005). Atomic and ion collisions in solids and at surfaces: theory, simulation and applications. Cambridge University Press.
[60]Xue, G. L. (1997). Minimum inter-particle distance at global minimizers of Lennard-Jones clusters. Journal of Global Optimization, 11(1), 83-90.
[61]Cotterill, R. M. J., & Doyama, M. (1968). Energies and atomic configurations of line defects and plane defects in fcc metals. Argonne National Lab., Ill..
[62]Daw, M. S., & Baskes, M. I. (1984). Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Physical Review B, 29(12), 6443.
[63]Stuart, S. J., Tutein, A. B., & Harrison, J. A. (2000). A reactive potential for hydrocarbons with intermolecular interactions. The Journal of Chemical Physics, 112(14), 6472-6486.
[64]Brenner, D. W. (1990). Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Physical Review B, 42(15), 9458.
[65]李哲緯, “石墨烯量子點與碳複合結構之熱傳導與力學特性分析,” 國立高雄應用科技大學碩士論文, 2017
[66]宋柏賢 “鎳鈦形狀記憶合金之微奈米力學特性分析,” 國立高雄應用科技大學碩士論文, 2012
[67]Rapaport, D. C., & Rapaport, D. C. R. (2004). The art of molecular dynamics simulation. Cambridge University Press.
[68]Nosé, S. (1984). A unified formulation of the constant temperature molecular dynamics methods. The Journal of Chemical Physics, 81(1), 511-519.
[69]Haile, J. M., Johnston, I., Mallinckrodt, A. J., & McKay, S. (1993). Molecular dynamics simulation: elementary methods. Computers in Physics, 7(6), 625.
[70]Gear, C. W. (1971). Numerical initial value problems in ordinary differential equations. Prentice Hall.
[71]Fincham, D., & Heyes, D. M. (1982). Integration algorithms in molecular dynamics. CCP5 Quarterly, 6, 4-10.
[72]Haile, J. M. (1992). Molecular dynamics simulation: elementary methods. John Wiley & Sons, Inc.
[73]Rapaport, D. C., & Rapaport, D. C. R. (2004). The art of molecular dynamics simulation. Cambridge university press.
[74]Kelchner, C. L., Plimpton, S. J., & Hamilton, J. C. (1998). Dislocation nucleation and defect structure during surface indentation. Physical Review B, 58(17), 11085.
[75]Plimpton, S. (1995). Fast parallel algorithms for short-range molecular dynamics. Journal of Computational Physics, 117(1), 1-19.
[76]Peng, W., & Sun, K. (2020). Effects of Cu/graphene interface on the mechanical properties of multilayer Cu/graphene composites. Mechanics of Materials, 141, 103270.
[77]Bashirvand, S., & Montazeri, A. (2016). New aspects on the metal reinforcement by carbon nanofillers: a molecular dynamics study. Materials & Design, 91, 306-313.
[78]Zhang, S., Xu, Y., Liu, X., & Luo, S. N. (2018). Competing roles of interfaces and matrix grain size in the deformation and failure of polycrystalline Cu–graphene nanolayered composites under shear loading. Physical Chemistry Chemical Physics, 20(36), 23694-23701.
[79]Weng, S., Fu, T., Peng, X., & Chen, X. (2019). Anisotropic phase transformation in B2 crystalline CuZr alloy. Nanoscale Research Letters, 14(1), 1-12.
[80]Yu, K. Y., Bufford, D., Khatkhatay, F., Wang, H., Kirk, M. A., & Zhang, X. (2013). In situ studies of irradiation-induced twin boundary migration in nanotwinned Ag. Scripta Materialia, 69(5), 385-388.
[81]Wirth, B. D., Bulatov, V., & de la Rubia, T. D. (2000). Atomistic simulation of stacking fault tetrahedra formation in Cu. Journal of Nuclear Materials, 283, 773-777.
[82]Thompson, N. (1953). Dislocation nodes in face-centred cubic lattices. Proceedings of the Physical Society. Section B, 66(6), 481.
[83]Liang, H. Y., Woo, C. H., Huang, H., Ngan, A. H. W., & Yu, T. X. (2003). Dislocation nucleation in the initial stage during nanoindentation. Philosophical Magazine, 83(31-34), 3609-3622.
[84]Zhang, C. L., & Shen, H. S. (2007). Self-healing in defective carbon nanotubes: a molecular dynamics study. Journal of Physics: Condensed Matter, 19(38), 386212.
[85]VijayaSekhar, K., Acharyya, S. G., Debroy, S., Miriyala, V. P. K., & Acharyya, A. (2016). Self-healing phenomena of graphene: potential and applications. Open Physics, 14(1), 364-370.
[86]Nardelli, M. B., Yakobson, B. I., & Bernholc, J. (1998). Mechanism of strain release in carbon nanotubes. Physical Review B, 57(8), R4277.
[87]Nardelli, M. B., Yakobson, B. I., & Bernholc, J. (1998). Brittle and ductile behavior in carbon nanotubes. Physical Review Letters, 81(21), 4656.
[88]Li, J., Liu, B., Luo, H., Fang, Q., Liu, Y., & Liu, Y. (2016). A molecular dynamics investigation into plastic deformation mechanism of nanocrystalline copper for different nanoscratching rates. Computational Materials Science, 118, 66-76.
[89]Doan, D. Q., Fang, T. H., & Chen, T. H. (2020). Nanotribological characteristics and strain hardening of amorphous Cu64Zr36/crystalline Cu nanolaminates. Tribology International, 147, 106275.