本研究利用分子動力學模擬探討聚甲基丙烯酸甲酯混和不同比例(重量百分比0.60 wt%以及1.77 wt%)銀奈米粒子複合物以及在不同溫度下(室溫、熔點溫度、550K)之機械性質，為確保模擬之準確性，本研究建立一套混合勢能系統以完整描述高分子及金屬之作用能量。聚甲基丙烯酸甲酯在添加進銀奈米粒子之後，其複合物的楊氏模數(Young’s modulus)以及最大抗拉強度(ultimate stress)與純聚甲基丙烯酸甲酯相比之下皆會提昇，這也代表混入銀奈米粒子會有效的提升聚甲基丙烯酸甲酯的機械性質。但是，在高溫下不管是純聚甲基丙烯酸甲酯或著是混入銀奈米粒子之複合物其楊氏模數以及最大抗拉強度與在室溫下相比皆會降低，這也代表溫度是影響機械性質的重要因素。

The effect of weight fraction on the tensile behavior of the polymethylmethacrylate (PMMA) with mixing silver nanoparticles (PMMA/AgNPs) was investigated using molecular dynamics simulation (MD). The mechanical properties of PMMA/AgNPs were calculated and analyzed at different weight fraction of AgNPs (0.60 wt%, and 1.77 wt%) and different temperature which corresponding room temperature, melting point (400K) and molten phase (550K). After adding AgNPs into PMMA, the Young’s modulus, and tensile strength of PMMA were greatly increased with weight fraction rising indicating that the AgNPs enhanced its mechanical properties. However, at high temperature, the Young’s modulus of both the PMMA and the PMMA /AgNPs exhibited significantly reduced from room temperature to high temperature, as the mechanical properties of PMMA /AgNPs were primarily dominated by temperature.

論文審定書 i
誌謝 ii
中文摘要 iii
Abstract iv
圖次 vii
表次 ix
符號說明 x
第一章 緒論 1
1.1 研究動機與目的 1
1.2 聚甲基丙烯酸甲酯與銀奈米粒子簡介 3
1.2.1 聚甲基丙烯酸甲酯 (PMMA) 3
1.2.2 銀奈米粒子 (Ag nanoparticle, AgNP) 4
1.3聚甲基丙烯酸甲酯混和銀奈米粒子之文獻回顧 5
1.3.1實驗文獻 5
1.3.2模擬文獻 8
1.4 本文架構 9
第二章 模擬方法與理論介紹 10
2.1 分子動力學 10
2.1.1 PCFF力場 11
2.1.2金屬元素優化PCFF力場 13
2.1.3 Tight-Binding勢能 14
2.1.4 運動方程式 15
2.1.5 積分法則 16
2.1.6 系綜 17
2.1.7 諾斯-胡佛恆溫法 18
第三章 數值模擬方法 19
3.1 週期性邊界 19
3.2 鄰近原子表列法 20
3.2.1 截斷半徑法 20
3.2.2 維理表列法 21
3.2.3 巢室表列法 22
3.2.4 維理表列法結合巢室表列法 23
3.3 分子動力學流程圖 24
3.4 統計之參數計算 25
3.4.1徑向密度分布(Radial density profile) 25
3.4.2分子表面網格(surface mesh)的建構 26
3.4.3區域應變分析 (Local shear strain) 26
3.4.4原子級應力計算理論 27
3.4.5自由體積計算 (Free volume increase percentage) 28
第四章 結果分析與討論 30
4.1聚甲基丙烯酸甲酯混和銀奈米粒子之物理模型 30
4.1.1聚甲基丙烯酸甲酯物理模型 30
4.1.2聚甲基丙烯酸甲酯混和銀奈米粒子物理模型 30
4.1.3平衡結構之徑向密度分佈 33
4.2拉伸試驗與機械性質探討 35
4.2.1拉伸模型建立 35
4.2.2應力應變圖 36
4.2.3區域應變圖 37
4.2.4孔隙率分析 40
4.2.5自由體積增加率(FVIP) 42
4.2.6第一鄰近原子鍵長變化 44

4.3不同溫度下的機械性質分析以及結構的變化 48
4.3.1複合物之熱穩定性 48
4.3.2不同溫度之應力應變曲線 50
4.3.3高溫之區域應變分析 50
4.3.4高溫之鄰近原子鍵長分析 52
第五章 結論與未來展望 56
5.1 結論 56
5.1.1 PMMA/AgNP複合物於室溫環境下之結論 56
5.1.2 PMMA/AgNP複合物於高溫環境下之結論 57
5.2 未來展望 58
參考文獻 59

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