本研究利用分子動力學與耗散粒子動力學模擬石墨烯(graphene)與聚甲基丙烯酸甲酯(Poly(methyl acrylate))複合材料於不同混合方式下的平衡結構。我們發現即使改變體積分率以得到不同的交互作用參數，仍然會導致石墨烯產生團聚(cluster)的現象，而團聚現象會明顯影響強化基材的能力。因此我們透過改變交互作用參數來觀察其平衡結構的差異，而結果發現當交互作用參數大於95.4335時發生團聚，交互作用參數小於80為石墨烯分散，最後，當其數值介於95.4335和80之間其結構稱之為相轉變。我們從結果中得知隨著體積分率的減少，只需要較少的官能化程度即可分散石墨烯。另外，我們利用不同的官能化修飾比例，發現到隨著官能化修飾比例的上升，石墨烯之間的排列會變為鬆散，最終達到分散。為了瞭解石墨烯平衡結構上的不同，我們透過石墨烯質量中心距離與石墨烯的表面積來解釋相轉變、分散的效應。

In this study, the nanocomposite of graphene and PMMA at the different volume fractions was investigated by molecular dynamics and dissipative particle dynamics simulations. The MD simulation can be performed to simulate the nanocomposite system at different weight fractions to obtain the different repulsive parameters. After obtaining the repulsive parameters, the DPD simulation can be utilized to study the equilibrium phase of graphene and PMMA nanocomposite. From our result, all equilibrium phases at different volume fractions are cluster. However, it is difficult to enhance the property for nanocomposite material due to the aggregated graphene (cluster). Hence, we change the interaction repulsive parameters to stand for the different degrees of functionalized graphene. When the interaction repulsive parameter is smaller than 80, the equilibrium phase is dispersion. In addition, the different number of functionalized garphene bead per graphene was studied, and results show that the equilibrium phase is dispersion when all graphene beads per graphene are functionalized.

目錄
目錄 I
圖目錄 IV
表目錄 VI
中文摘要 VII
Abstract VIII

第一章 序論 1
1.1研究動機與目的 1
1.2石墨烯與聚甲基丙烯酸甲酯簡介 4
1.2.1 石墨烯 4
1.2.2聚甲基丙烯酸甲酯(PMMA) 6
1.3石墨烯與聚甲基丙烯酸甲酯簡介 8
1.3.1機械性質 8
1.3.2熱傳導性質 9
1.3.3理論模擬研究 10
1.4本文架構 14

第二章 模擬方法與理論介紹 15
2.1分子動力學 16
2.1.1勢能函數 16
2.1.2運動方程式 17

2.1.3積分法則(velocity verlet) 18
2.1.4系綜 18
2.1.5壓力修正 19
2.1.5.1 Andersen修正理論 19
2.1.5.2 Parrinello-Rahman修正理論 21
2.1.6溫度修正 22
2.1.6.1 Velocity Scaling修正理論 22
2.1.6.2 Nose-Hoover修正理論 22

2.2耗散粒子動力學 24
2.2.1連接DPD與MD的參數 24
2.2.1.1 壓縮係數 24
2.2.1.2 福洛伊哈金斯參數與珠子間作用力參數 25
2.2.2耗散粒子動力學中的作用力 26
2.2.3積分法則 29

第三章 數值模擬方法 30
3.1週期邊界 30
3.2鄰近原子表列法 31
3.2.1截斷半徑法 31
3.2.2維理表列法 32
3.2.3巢室表列法 32
3.2.4維理表列結合巢室表列法 33
3.3物理參數與無因次化 34
3.3.1耗散粒子動力學的無因次化 34

3.4分子動力學模擬流程圖 35
3.5耗散粒子動力學模擬流程圖 36
3.6統計參數之介紹 37
3.6.1溶解度參數 37
3.6.2石墨烯質量中心間的距離分佈 37

第四章 結果分析與討論 38
4.1分子動力學的物理模型及求取DPD必要參數 38
4.2耗散粒子動力學的物理模型及設定 41
4.3不同體積分率下的平衡結構 43
4.3.1不同官能化程度之石墨烯平衡結構和石墨烯中心分佈分析 45
4.3.2不同修飾比例之官能化石墨烯平衡結構 52

第五章 結論與未來展望 54
5.1結論 54
5.2未來展望 54

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