Polybenzimidazole摻雜無水磷酸的系統以及poly(vinylphosphonic acid) 摻雜無水吡唑的系統可藉由分子動力模擬來進行研究。兩系統所計算出的質子導電度都相當接近實驗上所量測的值，顯示出建立的模型在條件的設定上是相當成功的。再者，也可利用模擬體系給予的相關資訊來進行實驗上無法提供的分析結果。其中，在兩個模擬體系的配對相關函數就顯示不同種類的氫鍵的存在。而這些氫鍵可建構出一個網絡系統。此外，配位數則顯示出氫鍵主導粒子分布的因素，尤其是質子的分布。質子軌跡也指出了氫鍵的形成與斷裂的發生。因此，質子軌跡提供一個有利的證據說明質子可利用氫鍵網絡在系統中進行流動。

Molecular dynamics (MD) simulations are excuted to investigate that the conductive properties of anhydrous phosphoric acid doped polybenzimidazole system and anhydrous pyrazole doped poly(vinylphosphonic acid) system. The proton conductivities which are calculated by both simulation systems quite approach the values which are measured in real experiments. These results can show the simulation models built are quite successful in the setting of simulation conditions. Furthermore, the relative data of simulation systems can provide an insightful observation that real experiments can not attain.
Pair correlation function of both simulation systems shows that different kinds of hydrogen bonds exist. The hydrogen bonds can form a network in the systems. Further, coordination number indicates the interaction of hydrogen bonds dominate the location of particles population, especially for protons. The results of proton trajectory point out that the formation of hydrogen bond happen and the break of hydrogen bond happen. Hence, it provide a powerful evidence that the proton can use the network of hydrogen bonds to mobilize in the systems.

論文審定書 i
論文公開授權書 ii
誌 謝 iii
摘　要 iv
關鍵詞：分子動力模擬、氫鍵、配對相關函數、配位數。 iv
Abstract v
List of Figures ix
List of Tables xiii
Chapter 1. Introduction 1
1.1 Fuel cell 1
1.2 Polybenzimidazole(poly[2,2′-(m-phenylene)-5,5′-bibenzimidazole], (PBI). 4
1.3 Poly(vinylphosphonic acid) 7
Chapter 2. Computer Simulation Method 9
2.1 Computer Simulation introduction 9
2.2 Calculation Principle of Molecular Dynamics 12
2.3 Newton's Law of Motion and Equations of Verlet Algorithm 15
2.4 Force Field 17
2.5 Thermodynamics Ensembles 21
2.6 Periodic boundary conditions 23
2.7 Analysis of Dynamics Properties 24
Chapter 3. Anhydrous phosphoric acid doped polybenzimidazole system 27
3.1 Introduction 27
3.2 Simulation Methods 30
3.3 The Interactive Relationship between Particles 33
3.3.1 Pair Correlation Function and Coordination Number Study in o1–h Pair, o2–h Pair, n2a–h Pair and n3a–h Pair 33
3.3.2 Pair Correlation Function and Coordination Number Study in o1–h1o Pair, o2–h1o Pair, n2a–h1o Pair and n3a–h1o Pair 34
3.3.3 Pair Correlation Function and Coordination Number Study in o1–h1n Pair and o2–h1n Pair 35
3.4 Dynamical Property of Proton and Polybenzimidazole 37
3.4.1 Diffusion Coefficient and Conductivity of Proton 37
3.4.2 Analysis of Proton Trajectory 38
3.4.3 Path of Proton Transfer 41
3.5 Dihedral Angle Distribution 45
3.6 Conclusion 47
Chapter 4. Anhydrous pyrazole doped poly(vinylphosphonic acid) system 48
4.1 Introduction 48
4.2 Simulation Methods 51
4.3 The Interactive Relationship between Particles 53
4.3.1 Pair Correlation Function and Coordination Number Study in o1–h1 Pair, n1–h1 Pair, n2–h1 Pair. 53
4.4 Dynamical Property of Proton 57
4.4.1 Diffusion Coefficient and Conductivity of Proton 57
4.4.2 Analysis of Proton Trajectory 58
4.5 Conclusion 65
Chapter 5. Summary 66
References 68

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