本研究結合恆定電位法CPM(Constant Potential Method)和分子動力學(Molecular Dynamics, MD) 模擬技術的優勢，建構一個全新的雙電層電容器模型，能透過觀察電極表面離子的吸附和內部微觀結構分子的擴散過程，預測超級電容器的電容與充放電速率。在電解液部分，利用OPLS-AA (Optimized Potentials for Liquid Simulations- all atom) 力場來描述全原子模型中原子間的作用力，OPLS-AA力場在先前的研究中已被證明能準確的描述有機液體分子，所以本研究以OPLS-AA作為力場建構拓樸結構，透過分子動力學模擬平衡並產生參考用的軌跡檔，然後參考由Voth 團隊開發的Multi-Scale Coarse-Graining(MSCG)方法，擬合出粗殼粒子模型(Coarse graining)的有效參數。在電極材料方面，採用二維石墨烯以及三維活性碳結構，做為對稱型雙電層電容器的電極材料。本研究以存储最大電容量為目標，第一步在三維週期的系統裡，比較不同濃度的平均平方位移和擴散數，結果顯示隨著濃度上升，雖然電容上升，但擴散數將下降；第二步在石墨烯電極系統裡探討不同濃度下電解液的平均數量密度分佈和電容；第三步由建構三種密度活性碳電極系統開始，我們分析了在不同電壓下三種活性碳的電極中微觀結構的分子吸附行為，發現結果與數量密度和電容的變化息息相關，本研究旨在開發一套分子模擬程序，針對超級電容器的充放電機制研究與篩選最適配的電極材料與電解液配方提供有力的工具。

關鍵字：分子動力學、雙電層電容器、粗殼粒子模型、恆定電位法、微觀結構

Combining the advantages of constant potential method (CPM) and molecular dynamics (Molecular Dynamics, MD) simulation technology, this study constructs a new electric- double layer capacitor model that can observe the adsorption of molecules on the surface of the electrode and the diffusion process of ions internal microscopic structure, which can predicts the capacitance and charge and discharge rate of the supercapacitor. In the electrolyte part, the OPLS-AA (Optimized Potentials for Liquid Simulations All Atom) force field is used to describe the interaction between atoms in all-atom model, which was proven as good describing for organic liquid in previous work. So this study uses OPLS-AA as a force field to construct a topological structure, through molecular dynamics simulation to balance and generate a reference trajectory file, then refer to the Multi-Scale Coarse-Grained method (MSCG) developed by the Voth group, fitting the effective parameters of the Coarse grained (CG) model. In terms of electrode materials, two-dimensional graphene and three-dimensional activated carbon structure are used as electrode materials for symmetrical electric double layer capacitors. In this study, we aim to store the maximum capacitance. The first step is to compare the average squared displacement and the diffusion number of different concentrations in the three-dimensional periodic boundary system. The results show that as the concentration increases, the capacitance decreases, but the diffusion number decreases. The average number density distribution and capacitance of electrolytes in different concentrations were investigated in a graphene electrode system. The third step was to construct three density activated carbon electrode systems, we analyzed the molecular adsorption behavior of the microstructure in activated carbon electrodes at different electric potential. The results are closely related to the changes in the number density and capacitance. The aim of this project is to develop a powerful tool and provide some useful information for study the charging mechanism of supercapacitor and screen optimal electrode material and electrolyte solution.

Keywords: Molecular dynamics, EDLC, Coarse-graining, CPM, Microstructure

目錄
誌謝 i
中文摘要 ii
Abstract iii
圖目錄 vi
表目錄 viii
第一章 緒論 1
1.1研究動機與目的 1
1.2文獻回顧 4
1.3本文架構 6
第二章 模擬方法與理論介紹 7
2.1 分子動力學理論基礎與方法 7
2.1.1 Optimized Potentials for Liquid Simulation-All Atom力場 (OPLS-AA) 8
2.1.2 運動方程式 10
2.1.3 積分法則 11
2.1.4 系綜 12
2.1.5 諾斯-胡佛恆溫法 13
2.1.6 週期性邊界 15
2.1.7 鄰近原子表列法 16
2.1.8 截斷半徑法 (Cut-off method) 16
2.1.9 維理表列法 (Verlet list) 17
2.1.10 巢室表列法 (Cell Link) 18
2.1.11 維理表列法結合巢室表列法 19
2.2 恆定電位法(Constant Potential Method) 20
2.3 平均平方位移 (Mean square displacement) 23
2.3.1 擴散係數 (Diffusion coefficient) 23
2.4 Degree of confinement (DoC) 24
2.5 孔體積與表面積之統計 26
2.6 孔徑大小分佈 26
2.7 物理模型的建構 27
2.7.1 有機溶液之全原子模型和粗殼粒子模型-電解液 27
2.7.2 建構石墨烯電極 30
2.7.3建構活性碳電極 34
第三章 粗殼粒子模型 39
3.1 Multiscale Coarse-Graining (MSCG) 39
3.2粗殼粒子模型之電解液分子 40
3.3 擬合粗殼粒子模型參數 41
3.4 驗證粗殼粒子模型參數 42
第四章 結果與討論 45
4.1電解液的性質分析 45
4.2雙電層石墨烯電容器的性質分析 47
4.3雙電層活性碳電容器的性質分析 52
第五章 結論與未來展望 62
5.1 結論 62
5.2 未來展望 64
參考文獻 65

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