分子模擬一直被用來計算分析材料性質以取代成本昂貴或所需環境嚴苛的實驗，如何準確模擬計算出與實驗值誤差較小的結果一直是科學家所努力的方向。而在這些模擬方法中分子動力學和蒙地卡羅法是較常被使用的模擬方法，分子動力學透過解牛頓方程產生確定性隨著時間變化的粒子位置但也因此較費時，同時在較高粒子數的計算上容易使計算電腦當機；而蒙地卡羅法則透過亂數產生器進行隨機運動，以能量作為移動的篩選，因此常被用來計算多粒子的模擬。
熔融鹽 (molten salt)是目前儲熱材料較佳的選擇，是許多無機鹽類的總稱，在固態狀態下為離子晶體，高溫加熱後會熔化變成液態的離子熔融鹽。本研究模擬計算硝酸鈉NaNO3，並透過結果比較各方法差異，希望找出較佳模擬方式。鋁參雜石墨烯(Al-doped Graphene, AlDG)目前常被用來進行二氧化碳捕獲，以減少和再利用二氧化碳來減緩溫室效應，本文利用蒙地卡羅法模擬搜索出二氧化碳CO2 在鋁參雜石墨烯(Al-doped Graphene, AlDG)基底中最穩定的吸附位置，以利接下來對二氧化碳還原再利用機制的研究。
本論文在熔融鹽模擬計算中，利用結合蒙地卡羅法嘗試補足分子動力學不足之處，在模擬過程利用定分子數等溫等壓系綜(NPT ensemble)以符合真實原子狀態，得出在不同溫度下熔融鹽的性質並比較不同粒子數和方法時的結果差異，以找出較準確的模擬方法。在二氧化碳吸附於鋁參雜石墨烯模擬計算中，則透過勢能方程式計算能量再利用蒙地卡羅方法在定分子數等溫等體積系綜(NVT ensemble)中篩選找出二氧化碳在基底材料鋁參雜石墨烯上的最小能量吸附組態，得出穩定的吸附位置。期望以這些模擬計算取代昂貴繁雜的實驗，並提供幫助相關研究做更進一步的探討。

Molecular simulation has been employed to calculate the properties of materials to replace expensive and tedious experiments, especially during parametric study. In those simulation methodologies, molecular dynamics (MD) and Monte Carlo (MC) methods are most commonly used simulation methods. Molecular dynamics simulation calculates the deterministic particle position with respect to time by solving the Newton equation, but it is also more time consuming and is easy to crash the computer when involved with large number of particles. Monte Carlo method performs random motion prediction through a random generator. It needs less memory and less computation time to deal with a multi-particle system.
Molten salts, a general term for inorganic salts, are a good choice for thermal storage and heat transfer fluids. They are normally ionic crystals in a solid state and melt into a liquid ionic molten salt after heating at a high temperature. This thesis uses sodium nitrate to perform MD and MC simulations, and compare them with experimental results to verify the accuracy and computational cost for each method. We found that MC is capable of dealing with millions of particles and is within an acceptable accuracy. Hence, we start to develop the MC algorithm to tackle the problem of gases absorbed on the Al-doped Graphene (AlDG), which is currently used to capture carbon dioxide to reduce to useful fuels. We use the MC simulation to predict the most stable adsorption position of carbon dioxide on the AlDG substrate, so as to study the mechanism of carbon dioxide reduction. Monte Carlo method was used to screen the minimum energy adsorption configuration of carbon dioxide on the AlDG using the NVT ensemble. This is a preliminary work to prepare further study using more expensive quantum simulation of the catalytic reaction which needs the initial position of each CO2 position with respect to the AlDG.

摘要……….. I
Abstract…………………………………………………………………………… II
誌謝……………………………………………………………………………….III
圖目錄 VI
表目錄 VIII
符號定義 IX
第一章　緒論 1
1.1. 前言 1
1.2. 聚光太陽能熱發電構造 2
1.2.1. 聚光技術 3
1.2.2. 熱能傳遞 5
1.2.3. 儲熱與發電 6
1.3. 儲熱材料 6
1.4. 碳捕獲(carbon capture)與二氧化碳再利用 10
1.5. 石墨烯參雜鋁(Al-doped graphene) 11
1.6. 文獻回顧 12
1.6.1. 熱傳導率 14
1.7. 研究動機與目的 15
第二章 研究方法 16
2.1. 蒙地卡羅模擬 16
2.1.1. 細部平衡(detailed balance) 16
2.1.2. Metropolis criterion 17
2.1.3. Metropolis MC 演算法 19
2.1.4. 虛擬亂數產生器(pseudo random number generator) 19
2.2. 分子動力學 (Molecular Dynamics, MD) 20
2.2.1. 分子動力學模擬流程 20
2.3. 分子間交互作用力勢能 22
2.3.1. 鍵結作用力勢能 23
2.3.2. 非鍵結作用力勢能 26
2.4. 溫控器(Thermostat) 28
2.5. 邊界條件(Boundary condition) 31
第三章 模擬方法 33
3.1. 模擬流程 33
3.2. 模擬工具 33
3.3. 模型建構 34
3.4. 蒙地卡羅演算法 35
3.5. 分子動力學 36
3.6. 數據後處理 37
3.6.1. 均方位移 (Mean Square Displacement, MSD) 37
3.6.2. 熱傳導率 (Thermal Conductivity) 38
3.6.3. 比熱 (Specific Heat) 39
第四章 結果與討論 40
4.1. 熔融鹽 40
4.1.1. 建構模型與設定條件 40
4.1.2. 材料密度模擬 42
4.1.3. 均方位移(MSD) 44
4.1.4. 熱容量 45
4.1.5. 熱傳導率 47
4.2. 氣體吸附於參雜鋁石墨烯 48
4.2.1. 建構模型與設定條件 48
4.2.2. 氣體分子在鋁參雜石墨烯(平面)上吸附位置 50
4.2.3. 氣體分子在鋁參雜石墨烯(突起)上吸附位置 56
4.2.4. 二氧化碳轉化為甲醇和水 …………………………………..61
4.2.5. 二氧化碳在不同尺寸鋁參雜石墨烯(突起)上吸附位置 65
第五章 結論與未來工作建議 67
5.1. 結論 67
5.2. 未來工作建議 68
參考文獻 69

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