本文利用密度泛函理論 (Density Functional Theory, DFT)及分子動力學
(Molecule Dynamics, MD)來模擬計算聚甘醇酸分子受機械應力作用時是否會加 速其降解速度，本文研究分為兩個部分：
1. 利用 DFT 模擬來研究聚甘醇酸及其中間態受機械應力時的水解機制， 並對其在不同應變時的鍵角、扭轉角、鍵長及電子特性進行分析，從應
力應變圖來看聚甘醇酸中間態比聚甘醇酸更容易受到應力的影響，當受 應力作用時聚甘醇酸中間態降解成兩個聚甘醇酸所需的能障也大幅度 的明顯降低，透過 DFT 模擬計算證明了機械負荷是可以提高聚甘醇酸
的降解率。
2. 藉由分子動力學搭配 pcff 勢能參數建構不同分子量的聚甘醇酸模型，
並透過拉伸測試得出各模型的極限強度並推得無限分子量的極限強度， 且利用上一部分求得出之不同應力下的能障及頻率計算出不同應力下 的反應速率。藉由計算來證明不同應力下極限強度隨降解天數變化的關
係，以及在受到不同應力的作用下，確實會加速聚甘醇酸的降解速度。

In this study, the degradation rate variation of polyglycolic acid molecule with mechanical stress are investigated by density functional theory (DFT) and molecular dynamics (MD), this study can be arranged into two parts:
In part I: The biodegradation mechanism of polyglycolic acid (PGA) and PGA intermediate of hydrolysis under mechanical stress was studied by the DFT calculation. The variations of bending angle, torsion angle, bond length as well as the electronic properties of PGA and PGA intermediate at different strains were presented. From the stress-strain profile, it shows the variation of the stress of PGA intermediate is more sensitive to the strain as compared to that of PGA. The decrease of energy barrier for the dissociation of PGA intermediate to two PGA molecules under the increasing strains causes the promotion of PGA hydrolysis. Our DFT calculation results have provided a clear explanation for the experimental observation, which the mechanical loading can enhance the PGA degradation rate.
In part II: This study, which employed molecular dynamics combine pcff potential parameters to construct polyethylene glycolic model with different molecular weight. Furthermore, the ultimate strength are obtained through tensile test of each model, and deduced that the ultimate strength of infinite molecular weight. Besides, the reaction rates under different stress are calculated by different barrier and frequency from part I. According to above-mentioned results, the relationship between degradation time and the ultimate strength under different stress are demonstrated by this simulation study, the degradation rate of polyglycolic acid indeed are accelerated under the stress effect.

中文摘要 i
Abstract ii
目錄 iii
圖目錄 vi
表目錄 viii
第一章 緒論 1
1.1 研究背景及動機 1
1.2材料介紹 3
1.3文獻回顧 4
1.3.1 聚甘醇酸應用特性文獻回顧 4
1.3.2 理論模擬方法文獻回顧 6
1.4 本文架構 9
第二章 模擬方法之理論介紹 10
2.1密度泛函理論 10
2.1.1多粒子系統薛丁格方程式 10
2.1.2 Born-Oppenheimer絕熱近似 11
2.1.3 Hohenberg-Kohn 理論 12
2.1.4 Kohn-Sham equation 13
2.1.5交換相關能之近似-(LDA、GGA) 14
2.1.7過渡態理論 (Transition state theory) 17
2.1.6 Nudged elastic band (NEB)方法 18
2.2分子動力學 20
2.2.1勢能參數 20
2.2.2運動方程式 22
2.2.3積分法則 22
2.2.4系綜 23
2.2.5壓力修正 24
2.2.5.1 Andersen修正理論 24
2.2.5.2 Parrinello-Rahman修正理論 25
2.2.6溫度修正方法 26
2.2.6.1 Velocity Scaling 修正理論 26
第三章 數值模擬方法 27
3.1週期邊界 27
3.3原子級應力計算方法 28
3.4鄰近原子表列法 31
3.4.1截斷半徑法 31
3.4.2維理(Verlet)表列法 32
3.4.3巢室(Cell Link)表列法 33
3.4.4維理表列法結合巢室表列法 34
3.6聚酯類分子量與極限應力關係式 35
3.7 LEAST-SQUARES最小二平方法 36
3.8 SCALING LAW 37
3.9分子動力學流程圖 38
第四章 結果與討論 39
4.1 單條聚甘醇酸結構分析 39
4.1.1 聚甘醇酸分子模型建構及參數設定 39
4.1.2 初始態聚甘醇酸拉伸結構與電荷分析 43
4.1.3 中間態聚甘醇酸拉伸結構與電荷分析 48
4.1.4 拉伸行為與能障關係分析 53
4.2 分子動力學模擬 55
4.2.1 物理模型之建構 55
4.2.2 聚甘醇酸物理模型機械性質分析 59
4.2.3 聚甘醇酸反應速率計算及最大應力與降解時間關係 64
第五章 結論與未來展望 67
5.1 結論 67
5.2 未來展望 69
參考文獻 70

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