本論文利用蒙地卡羅演算法(Monte Carlo)與Configurational Bias Monte Carlo 演算法結合簡化模型(coarse-grained model)研究液晶分子的結構特性。由分子數量較少所組成的奈米團蔟中，可觀察到奈米團蔟形成管狀螺旋有序的結構，隨著分子數量的增加發現結構有慢慢形成團蔟的趨勢。對於少條分子形成管狀結構，主要是因為作用點較為單純，奈米團蔟易於行程有序的結構。對於多條分子而言則由於作用點較多較為複雜，因此形成像球狀的團蔟，而在表面呈現局部有序的結構。另外，根據秩序參數的數值將結構分類，秩序參數為0.5 以上的結構歸類為管狀的結構，而在0.5 之下則歸類為團蔟結構。

Configuration-bias Monte Carlo simulation is used to investigate the structural property of liquid crystal. Our results show that the surface molecules of the smaller nanoclusters are formed the helical structure, In addition, the morphologies of nanoclusters show a tube-like structure when the surface molecules formed the helical structure; however, as the surface molecules do not form the helical structure, the morphologies of nanoclusters become a ball-like structure. For the tube-like structure, because of the configurations of nanoclusters are simpler, the nanoclusters will show an order structure. In the case of the ball-like structure, the molecules will attract with others, so the nanocluster reveals an ordered structure at local area. According to the result of the averaged order parameters, as the averaged order parameter larger than 0.5, the configuration of nanocluster will be a tube-like structure, while as the averaged order parameters smaller than 0.5, the configuration of nanocluster will form a ball-like structure.

目錄

目錄 I
圖目錄 III
表目錄 V
中文摘要 VI
英文摘要 VII

第一章 緒論 1
1.1 研究動機 1
1.2 液晶分子簡介 4
1.2.1 熱向性液晶： 4
1.2.2 液向性液晶： 8
1.3 文獻回顧 9
1.4 本文架構 11
第二章 簡化模型理論與勢能函數 12
2.1 簡化模型理論 12
2.1.1 Linked vector簡化法 12
2.1.2 等效能量 13
2.2 勢能函數 15
2.2.1 液晶分子之作用勢能 15
第三章 蒙地卡羅演算法與CBMC演算法 19
3.1 蒙地卡羅演算法(Metropolis Monte Carlo Algorithm) 20
3.2 Configurational Bias Monte Carlo(CBMC)演算法 22
第四章 數值方法 24
4.1 物理參數與無因次化 24
4.2 數值統計方法 26
4.2.1 方向秩序參數(orientation order parameter) 26
4.2.2 迴轉半徑(radius of gyration) 27
4.3 模擬流程圖 29
4.3.1 主要模擬流程圖 29
4.3.2 蒙地卡羅演算法之流程圖 30
4.3.3 CBMC演算法之流程圖 31
第五章 結果分析與討論 32
5.1 不同數量的液晶分子所形成之結構 32
5.1.1 物理模型之建構 32
5.1.2 液晶分子的結構排列 44
5.2 不同尾鏈的效應 54
5.2.1 物理模型之建構 54
5.2.2 不同尾鏈的結構排列 56
5.2.3 尾鏈的效應 66
第六章 結論與建議 69
6.1 結論 69
6.2 建議與未來展望 71
參考文獻 72

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