在本研究中，首先透過分子動力學研究水分子在兩晶格排列為100之金平板間，相距分別為24.48、16.32、12.24、11.22及10.20 等不同侷限空間下之行為。模擬結果顯示水分子的分佈與空間大小有關。在觀察隨著距離變化改變的自我擴散係數中，發現水分子存在著z方向與x-y平面上隨著兩平板間距離增大而有不同的下降趨勢的動態特性。另外，更討論了不同金平板在(100)、(111)、(110)三種不同晶格排列下對水分子的影響。模擬結果顯示金平板的排列對水分子的分佈亦有影響。在(100)和(111)排列的金平板中，吸附層中的水分子皆平坦的附著在金平板上，然而在(110)排列下，水分子出現一層波浪狀的結構。且水分子在(110)的排列中將會最接近兩金平板。另外，水分子在z方向的自我擴散細數以(110)排列時最大，而x-y平面上的擴散則以(100)排列時為最大。
最後，研究庫耶流中的密度分佈，速度分佈，及擴散係數。並探討水分子的剪切黏滯度與水薄膜的剪切速率之間的關係。發現擴散係數在某一個剪切速率之上會突然的升高。而隨著剪切速率增高，剪切黏滯度降低，尤其是在水分子層非常薄的時候，這意味著侷限空間下之奈米薄膜的黏滯度有著剪切稀釋的性質。另外，研究中也發現隨著水薄膜厚度的降低，剪切黏滯度增高。

In the beginning of this study, Molecular dynamics simulation is utilized to investigate the behavior of water molecules confined between two Au plates of (001) planes separated by gaps of 24.48, 16.32, 12.24, 11.22, and 10.20 . The simulation results indicate that the arrangements of the water molecules are dependent on the gap size. An inspection of the variation of the self-diffusion coefficients with the gap size suggests that the difference between the dynamic properties of the water molecules in the z-direction and the x-y plane decreases as the distance between the two Au plates increases. Moreover, we discuss the effects of different lattice structures, (100), (110) and (111)，on the water molecules. The simulation results indicate that the arrangements of the water molecules are dependent on Au plate surface structures. The adsorption of the plate creates flat water layers in the proximity of each plate surface for (100) and (111) cases, but wave-like water layer for Au (110) plate. The absorbed water layer is the most close to plate surface for (110) lattice structure. Moreover, the self-diffusion coefficient in the z-direction for (110) case is the largest, meanwhile, the water molecules have a greater ability to diffuse in the x-y plane for (100) case.
Finally，the density distribution, velocity profile, and diffusion coefficients of the water film in a Couette flow are studied. Shear viscosity and its dependence on the shear rate of the water film are also examined in the present research. The diffusion of the whole film increases dramatically as the shear rate greater than a critical value. The shear viscosity decreases as the shear rate increases, especially for the water film with a small thickness, which implies the shear-thinning behavior for viscosity of the nanoconfined film. Moreover, increase in shear viscosity with a decrease in the film thickness can also be found in the present study.

目錄
中文摘要 1
ABSTRACT 2
第1章 緒論 4
1.1 研究動機 4
1.2 文獻回顧 9
1.3 本文架構 11
第2章 分子動力學理論 12
2.1 勢能函數 13
2.2 運動方程 21
2.3 週期性邊界條件 22
2.4 原子級應力計算方法 24
第3章 分子動力學數值方法 28
3.1 鄰近原子表列法 28
3.1.1 Verlet List表列法 28
3.1.2 Cell Link表列法 29
3.1.3 Verlet List表列法結合Cell Link表列法 30
3.2 無因次化 32
第4章 結果分析與討論 34
4.1 靜態 34
4.1.1 物理模型 34
4.1.2 相對密度( )、氫鍵( )、定向因子(s(z))、擴散係數 35
4.2 不同平面之影響 46
4.2.1相對密度( )、氫鍵( )、定向因子(s(z))、擴散係數 46
4.2.2氫鍵鍵長 53
4.2.3正向應力 57
4.3 剪切 60
4.3.1物理模型 60
4.3.2擴散係數 61
4.3.3相對密度( )與速度分佈 63
4.3.4剪切應力對時間 63
4.3.5黏滯係數 64
第5章 結論與建議 73
5.1 結論 73
5.2 建議與未來展望 75

表目錄
表2.1 三種水勢能參數。 18
表2.2 金原子之TIGHT-BINDING勢能參數。 18
表2.3 F3C勢能參數表。 19
表2.4 SPOHR勢能中之參數。 20
表 3.1無因次化基準量。 33
表 3.2各物理量之無因次化量。 33
表4.1. 不同空間下的每一個水分子的平均氫鍵鍵結數值。 45

圖目錄
圖 2.1 VELOCITY VERLET演算法。 21
圖 2.2 週期性邊界條件示意圖。 22
圖 2.3 局部原子P0的VORONOI 體積。 27
圖 2.4 局部原子P0的VORONOI 體積。 27
圖 3.1 VERLET LIST示意圖。 29
圖 3.2 CELL LINK示意圖。 30
圖 3.3 VERLET LIST 結合 CELL LINK建立鄰近表列。 31
圖 4.1.0水薄膜位於探針與基版間之物理模型(A)立體圖(B)側視圖。 40
圖4.1.1分子動力學模擬之流程圖。 41
圖 4.1.2水在Z方向上不同寬度下時氫與氧的數密度、ORIENTATION FACTOR及氫鍵圖 (A) 24.48 (B) 16.32 (C) 12.24 (D) 11.22 (E) 10.20 。 44
圖4.1.3 Z方向上及X-Y平面上的自我擴散係數圖。 45
圖4.2.1 靠近不同金平板晶格排列下的第一層水分子結構圖 (A) (100) (B) (110) (C) (111) 其中黃色為氧原子，綠色為氫原子。 49
圖 4.2.2水分子在10.2 下，不同金平板的晶格排列下之氧原子相對數密度的空間分佈比較圖。 50
圖 4.2.3 水分子在10.2 下，不同金平板的晶格排列下之定向因子 的空間分佈比較圖。 50
圖4.2.5 不同金平板的晶格結構下之自我擴散係數圖 (A) Z方向 (B) X-Y 平面。 52
圖4.2.6水在Z方向上寬度24.48 時，氫與氧的數密度及氫鍵鍵長圖。 55
圖4.2.7水在Z方向上寬度10.2 下，氫與氧的數密度及氫鍵鍵長圖。 55
圖4.2.8水在Z方向上寬度24.48 下時，不同平面下之氫鍵鍵長比較圖。 56
圖4.2.9水在Z方向上寬度10.2 下，金平板排列(110)時，氫與氧的數密度及氫鍵鍵長圖。 56
圖4.2.10水在Z方向上寬度24.48 下，金平板排列(100)時氫與氧的數密度及X、Y、Z方向上之正向應力分佈圖。 59
圖4.2.11水在Z方向上寬度24.48 下，金平板排列(110)時氫與氧的數密度及X、Y、Z方向上之正向應力分佈圖。 59
圖4.3水薄膜在兩金平板動態剪切下之側面圖。 66
圖4.3.0分子動力學模擬剪切之流程圖。 67
圖4.3.1水在Z方向上的寬度為10.2 時，不同剪切速率下之X、Y及Z方向上之擴散係數圖。 68
圖4.3.2水在Z方向上的寬度為10.2 時，不同剪切速率下之X方向上之擴散係數圖。 68
圖4.3.3水在Z方向上的寬度為24.48 時，不同剪切速率下之X、Y及Z方向上之擴散係數圖。 69
圖4.3.4水在Z方向上的寬度為24.48 時，不同剪切速率下之X方向上之擴散係數圖。 69
圖4.3.5水在Z方向上的寬度為10.2 及剪切速率為 時之數密度與速度分佈圖。 70
圖4.3.6水在Z方向上的寬度為24.48 及剪切速率為 時之氫與氧之數密度與速度分佈圖。 70
圖4.3.7水在Z方向上的寬度為10.2 時，不同剪切速率下之剪切應力對時間圖。 71
圖4.3.8水在10.2A下1011的速度下的氫鍵對時間與剪應力之比較圖。 71
圖4.3.9水在Z方向上的寬度為10.2 及24.48 時之不同剪切速率對黏滯係數圖。 72

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