臺灣博碩士論文加值系統

本研究係針對奈米尺度系統下冰晶分子之氫鍵結構形成進行研
究。利用分子動力法(MD) 來分析冰晶分子在奈米尺度下之最小位
勢能之晶格結構以及其對於飄浮水分子之影響。本研究採用
Carravetta-Clementi (CC)位勢能來得到分子與分子之間的作用力，在
假設各分子仍然受牛頓第二運動定律支配的條件下，利用電腦對介質
分子的運動作直接模擬。各介質分子由於本身的慣性、分子間的作用
力、以及分子與邊界的相互作用，而產生平移與旋轉速度及位置與角
度的改變。本研究包括下列工作項目：(1)探討氫鍵結構之形成，(2)
研究冰晶結構受溫度之影響，以及(3)預測飄浮水分子在撞擊冰晶後
之表面躍動情形等。

The present study is concerned with the formation and stability of
hydrogen-bond structure for ice crystal in nanoscale. Molecular dynamics
method is adopted to analyze the ice crystal formed by water molecules.
In the molecular dynamics analysis, Newton’s second law of motion is
applied for predictions of the motion of any molecules. Translational and
angular velocities as well as the locations of all the molecules can be
predicted at any instant when the inertial and external forces acting on the
molecules have been known. The interactive forces between any two
molecules are determined based on Carravetta-Clementi (CC) potential in
this study. The van der Waals force and the electrostatic force are
evaluated between water molecules and then the translational and angular
velocity vectors and the position of the molecules can be predicted. The
study includes: (1) the annealing of hydrogen-bond structure for ice
crystal, (2) the influence of temperature on the vibration of the molecules
within a fixed ice crystal layers, and (3) the leaping behavior of the
drifting molecules on the crystal layer surface after they impinge on the
surface at different temperatures and incident angles.

中文摘要………………………………………………………………I
英文摘要………………………………………………………………II
誌謝……………………………………………………………………III
目錄……………………………………………………………………IV
表目錄…………………………………………………………………VI
圖目錄…………………………………………………………………VII
符號索引………………………………………………………………X
第一章緒論..............................................1
1-1 背景………………………………………………………………1
1-2 研究目的…………………………………………………………7
1-3 論文架構…………………………………………………………9
第二章分子動力學法…………………………………………………10
2-1 運動方程式………………………………………………………10
2-2 系統能量…………………………………………………………15
2-3 熱特性量…………………………………………………………17
2-4 運動方程式之數值積分…………………………………………19
2-5 重複性邊界………………………………………………………20
2-6 系綜平均…………………………………………………………21
2-7 溫度控制…………………………………………………………22
2-8 水分子之既有位勢能函數………………………………………23
2-8-1 Lennard-Jones Potential…………………………………23
2-8-2 ST2 Potential………………………………………………24
2-8-3 SPC 及SPC/E Potentials…………………………………25
2-8-4 TIP4P Potential…………………………………………26
2-8-5 Carravetta & Clementi Potential……………………26
第三章冰晶之氫鍵結構……………………………………………28
3-1 冰晶的基本排列………………………………………………28
3-2 冰晶分子最小位能距離………………………………………33
第四章結果與討論…………………………………………………34
4-1 數值測試………………………………………………………34
4-2 固定冰晶層間飄浮水分子平衡態結構………………………35
4-3 在固定晶格內的震動分子穩定性……………………………38
4-4 飄浮水分子入射冰晶分子層之表面躍動行為………………40
4-5 冰晶層表面之冰晶形成………………………………………43
第五章結論…………………………………………………………45
參考文獻……………………………………………………………47
表目錄
表2-1 惰性氣體分子之Lennard-Jones Potential 參數。……52
表2-2 水分子Lennard-Jones Potential 之參數。……………53
表2-3 不同位勢能函式之參數。…………………………………54
圖目錄
圖2-1 水分子結構之示意圖。……………………………………55
圖2-2 重複性邊界示意圖。………………………………………56
圖2-3 CC、MCY、TIP4P、SPC/E 位勢能的比較。………………57
圖2-4 典型Lennard-Jones Potential 表示圖。………………58
圖2-5 ST2 中的水分子結構。……………………………………59
圖2-6 SPC、SPC/E 及TIP4P 中的水分子結構。………………60
圖3-1 水的氫氧原子結構排列。…………………………………61
圖3-2 冰晶分子的排列方式。……………………………………62
圖3-3 冰晶的基本形式。…………………………………………63
圖3-4 冰晶分子之座標系統。……………………………………64
圖3-5 預排列三層冰晶分子層(1008 顆)之氧原子之間距離與位能關
係圖。………………………………………………………………65
圖4-1 當ρ=380 kg/m3時，分別於溫度300K、400K及600K下水分子
平衡態結構圖。( 本研究與Ohara and Aihara [48] 之比
較)…………………………………………………………………66
圖4-2 ρ=380 kg/m3及T=300K時，速度關聯函數之比較圖。(本研究
結果與Ohara and Aihara [48]之比較)…………………………67
圖4-3 圖4-3 飄浮水分子及冰晶分子層起始的相關位置，圖中下方
三層冰晶分子，上方亦有三層冰晶分子層，上下冰晶分子層
之間為飄浮水分子(128 顆~448 顆)。…………………………68
圖4-4 不同溫度下，在上下冰晶層間的飄浮水分子平衡態分佈結
構。本例之飄浮水分子數為128；冰晶層間的距離為11.503
Å，此距離恰為三層冰晶層之高度。……………………………69
圖4-5 不同活動高度下，在上下冰晶層間的飄浮水分子平衡態分佈
結構。本例之溫度為200K。………………………………………70
圖4-6 相同溫度下，在上下冰晶層間的飄浮水分子平衡態分佈結
構。本例之溫度為200K；冰晶層間的距離為11.503 Å，此距
離恰為三層冰晶層之高度。………………………………………71
圖4-7 單顆震動分子(深顏色者)被周圍固定不動的冰晶分子所環
繞。…………………………………………………………………72
圖4-8 單顆震動分子的位置變化圖。……………………………73
圖4-9 十八顆震動分子的位置變化圖。…………………………74
圖4-10 溫度控制為200K 時，1008 顆震動分子在無固定分子約束下
逐漸變成非晶體結構。……………………………………………75
圖4-11 不同溫度下，單顆水分子在冰晶層表面的躍動情況。…76
圖4-12 溫度200K 時，水分子分別以10°、30°、60°、90°水平角入射
撞擊冰晶層後之躍動現象。………………………………………77
圖4-13 溫度300K 時，水分子分別以10°、30°、60°、90°水平角入射
撞擊冰晶層後之躍動現象。………………………………………78
圖4-14 溫度200K 時，單顆飄浮水分子分別以不同角度撞擊冰晶層之
動能變化圖。………………………………………………………79
圖4-15 冰晶層表面之冰晶形成。溫度設定為300K，並每隔2.5
picosecond 放入一顆飄浮水分子。………………………………80
圖4-16 不同之溫度下，每隔2.5 picosecond 加入一飄浮水分子，圖上
分別為時間50 picosecond、150 picosecond 及250 picosecond
時飄浮水分子的結構圖。…………………………………………81

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