本文以分子動力學（Molecular Dynamics）方法來研究奈米碳管金屬基複合材料的機械性質，主要著重在幾個因素的探討：
1. 奈米碳管在複合材料裡重量比例
2. 奈米碳管螺旋效應（不同結構）
3. 金屬基材與奈米碳管之間黏著效應
在模擬中，針對這些因素來創造出不同的奈米複材模型，承受軸向拉伸並加以分析奈米複合材料的彈性性質。本研究發現，1.奈米碳管重量比越高時，其楊氏係數也會跟著提高；2.在相近的重量比下，埋置不同螺旋性的碳管，得知扶手椅形單壁奈米碳管在複材裡楊氏係數的提升比其他兩種形式碳管來的好；3.當結合能量ε越大時，金屬基材與奈米碳管之間黏著效應越好，複材楊氏係數也會跟著提升，而平衡距離σ對彈性係數影響不大。經由本論文對奈米複合材料的研究，希望將來有助於工業界對奈米複材的瞭解與製成，並對奈米複合材料性能上的優化設計有所幫助。

The mechanical properties of carbon nanotube metal matrix composites were studied using molecular dynamics simulations. The atomic models were constructed in order to investigate several effects, i.e. carbon nanotube weight ratio effect, chiral effect and the adhesion between nanotube and metal matrix. It was found that the Young’s modulus of composites increase as carbon nanotube weight ratios increase. The Young’s modulus of armchair carbon nanotube composites were found to be higher than those with zigzag and chiral carbon nanotubes for similar weight ratios. It was concluded that the Young’s modulus of composites would improve if the adhesion between nanotube and matrix becomes stronger.

致謝……………………………………………………………………Ⅰ
摘要……………………………………………………………………Ⅱ
Abstract………………………………………………………………Ⅲ
目錄……………………………………………………………………Ⅳ
圖目錄…………………………………………………………………Ⅶ
表目錄…………………………………………………………………XI
符號說明………………………………………………………………XII

第一章 緒論………………………………………………………1
1-1 前言………………………………………………………1
1-2 研究動機與目的…………………………………………2
1-3 文獻回顧…………………………………………………3
1-4 本文架構…………………………………………………11
1-5 研究流程圖………………………………………………12
第二章 分子動力學理論…………………………………………18
2-1 分子動力學基本理論與假設……………………………18
2-2 分子間作用力與勢能函數………………………………19
2-2-1分子間作用力………………………………19
2-2-2勢能函數……………………………………21
2-3 原子應力…………………………………………………25
2-4 週期性邊界條件與最小映像法…………………………26
2-4-1 週期性邊界條件……………………………26
2-4-2 最小映像法則………………………………27
2-5 初始條件設定……………………………………………28
2-6 運動方程式………………………………………………30
2-7 截斷半徑法與Verlet表列法……………………………33
第三章 分子動力學數值模擬方法………………………………43
3-1 勢能函數之選擇…………………………………………43
3-1-1 奈米碳管與金屬基材………………………44
3-1-2 金屬基材……………………………………44
3-1-3 奈米碳管……………………………………45
3-1-4 Tersoff函數變數之關係……………………48
3-1-5 Tersoff微分形式……………………………49
3-2 原子模型…………………………………………………53
3-3 無因次化…………………………………………………55
3-4 系統之平衡………………………………………………56
3-5 程式模擬流程圖…………………………………………57
第四章 奈米碳管結果分析………………………………………67
4-1 程式驗證…………………………………………………67
4-1-1 鑽石結構……………………………………67
4-1-2 石墨結構……………………………………70
4-2 奈米碳管…………………………………………………71
4-2-1 尺寸及螺旋性效應…………………………71
4-2-2 碳管塑性行為………………………………74
第五章 奈米碳管金屬基複合材料結果分析……………………91
5-1 非結晶形（Amorphous）金屬……………………………91
5-2 奈米碳管金屬基複合材料模擬過程……………………92
5-3 奈米碳管重量比效應……………………………………92
5-4 奈米碳管螺旋效應………………………………………94
5-5 金屬基材與奈米碳管之間黏著效應……………………94
第六章 結論與未來展望…………………………………………104
6-1 結論………………………………………………………104
6-2 未來展望…………………………………………………105
參考文獻……………………………………………………………108

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