本研究利用分子動力學預測四代聚醯胺-胺樹枝狀高分子封裝不同尺寸金奈米粒子於乾燥及水溶液環境下之結構。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。於乾燥環境下，我們將探討四代聚醯胺-胺樹枝狀高分子與金奈米粒子之複合結構及熱穩定性。研究結果顯示四代聚醯胺-胺樹枝狀高分子於乾燥環境下主要透過其支鏈與內部空腔結構封裝金奈米粒子，且被封裝後之金奈米粒子將具有較高的熔點。為模擬生物條件，本研究亦考慮溶劑之影響，將該複合物置於中性 (pH ~7) 及酸性 (pH ~5) 環境之水溶液中，分析其結構與擴散行為。由結果得知當四代聚醯胺-胺樹枝狀高分子於中性環境下封裝金奈米粒子時，結構將大幅收縮；於酸性條件下其結構則保持著擴張狀態。除此之外，我們也發現於中性環境下，其複合物之擴散係數較酸性環境高，具備較佳的擴散能力。透過本研究之模擬方法即可深入觀察四代聚醯胺-胺樹枝狀高分子與金奈米粒子複合物之內部結構與特性，結果可作為未來相關催化劑、生物傳感器及藥物載體之設計依據。

Molecular dynamics (MD) simulation was carried out to investigate the structural evolutions of fourth generation polyamidoamine (G4 PAMAM) dendrimer encapsulating different size Au nanoparticles (AuNPs) in both dry and aqueous environments. To ensure the accuracy of the simulation model, a hybrid potential system was applied to describe the interactions between polymers and metals. The conformations and the thermal stability of G4 PAMAM dendrimer covering AuNPs were investigated under a dry environment. We determined that the AuNPs are covered by branched structures and the internal cavities of the G4 PAMAM dendrimers. Moreover, the melting points of the dendrimer-encapsulated AuNPs increase significantly when compared to non-encapulated nanoparticles. To simulate the biological conditions, the conformations and the diffusion behavior of G4 PAMAM encapsulated AuNPs under neutral and low pH conditions (pH ~7 and pH ~5, respectively) were also investigated for studying the effects of solution. The results show that the conformations of dendrimers become more compact when covering the AuNPs at neutral pH; however, when at low pH, the extended conformations can be observed. We also obtained the higher diffusion coefficients of these composites at neutral pH. This study helps clarify the internal conformations and characteristics of PAMAM-AuNP composites, as well as contributing to the designs of catalysts, biosensors and drug carriers.

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 聚醯胺-胺樹枝狀高分子與金奈米粒子簡介 3
1.2.1 聚醯胺-胺樹枝狀高分子 (PAMAM dendrimer) 3
1.2.2 金奈米粒子 (Au nanoparticle, AuNP) 4
1.3樹枝狀高分子封裝金奈米粒子屬之文獻回顧 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 CVFF力場 11
2.1.2金屬元素優化CVFF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 迴轉半徑 (Radius of gyration) 25
3.4.2 非球面參數 (Asphericity parameter) 26
3.4.3 徑向密度分布 (Radial density profile) 26
3.4.4 分形維度 (Fractal dimension) 27
3.4.5 平方位移 (Square displacement) 27
3.4.6 平均平方位移 (Mean square displacement) 28
3.4.7 擴散係數 (Diffusion coefficient) 28
3.4.8 斯托克斯-愛因斯坦關係 (Stokes–Einstein relation) 29
第四章 結果分析與討論 30
4.1 聚醯胺-胺樹枝狀高分子封裝金奈米粒子之物理模型 30
4.1.1 乾燥系統物理模型 30
4.1.2 水溶液系統物理模型 33
4.2 乾燥環境性質分析 39
4.2.1 平衡結構之迴轉半徑 39
4.2.2 平衡結構之非球面參數 40
4.2.3 平衡結構之徑向密度分佈 41
4.2.4 結構表面之分形維度 43
4.2.5 複合物之熱穩定性 46
4.3 水溶液環境性質分析 52
4.3.1 平衡結構之迴轉半徑 52
4.3.2 平衡結構之徑向密度分佈 54
4.3.3 聚醯胺-胺樹枝狀高分子對金奈米粒子之作用能量 61
4.3.4 複合物之擴散係數 62
第五章 結論與未來展望 65
5.1 結論 65
5.1.1 G4 PAMAM/AuNP複合物於乾燥環境下之結論 65
5.1.2 G4 PAMAM/AuNP複合物於水溶液環境下之結論 66
5.2 未來展望 67
參考文獻 68

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