本論文將結合粗殼粒子(coarse grained, CG)分子動力學(molecular dynamics, MD)模擬與密度泛函理論(density functional theory, DFT)計算提出一個預測液晶分子系統的相態行為、光學和介電性質的流程。4-Cyano-4′-pentylbiphenyl (5CB)是早期最著名被合成的液晶分子，它有著豐富的相關文獻和現有的實驗與理論數據，所以選擇5CB作為發展設計新型液晶分子流程的基準。根據Maier-Meier和Vuks理論公式，我們需要得到液晶分子的偶極矩、極化率、秩序參數和分子的密度等材料參數才能計算液晶分子系統的光學和介電性質。因此，我們建立5CB分子的粗殼粒子模型並分別找出它們之間的鍵長、鍵角和凡得瓦力的作用力參數，並且找到一組合適的勢能函數，再藉由粗殼粒子分子動力學模擬，研究5CB分子系統的相態變化並得到它的秩序參數和分子密度；利用密度泛函理論計算5CB分子的偶極矩和極化率，上述求得的參數將代入理論公式計算並預測介電常數、介電異向性、折射率和折射率異向性等液晶性質。另外，我們發現介電性質的預測結果能夠透過Dunmur-Palffy-Muhoray理論所提出的有效偶極矩修正而大幅改善。最後，將預測結果與實驗值相互比較證明我們的模擬流程是可行且準確的。

We combine coarse grained (CG) molecular dynamics simulation and density functional theory (DFT) calculation to predict the phase behavior, the dielectric and the optical properties of liquid crystal molecule system. 4-Cyano-4′-pentylbiphenyl (5CB) is the earliest synthesized and the most popular liquid crystal molecule, which have prosperous related bibliographies and available experimental and theoretical data, so 5CB molecule is chosen to be the benchmark molecule. According to the Maier-Meier and Vuks equations, we have to obtain some parameters such as the dipole moment, the polarizability, the polarizability anisotropy, the order parameter and the molecular density to calculate dielectric and optical properties of liquid crystal molecule system. The CG model for the 5CB molecules is constructed, and the bond length, bending angle and nonbonded interaction parameters between CG beads, and then applied to the CGMD simulation to obtain the order parameter and molecular density. In addition, the polarizability and dipole moment of 5CB were obtained by DFT; therefore, the order parameter, the molecular density, the polarizability, and the dipole moment of 5CB were used to determine the dielectric constant, the dielectric anisotropy, refractive indices, and optical anisotropy by means of the Maier-Meier theory. Particularly, the calculation results from Maier-Meier theory can be improved by using effective dipole moment of the Dunmur-Palffy-Muhoray theory. Finally, our results show a good agreement with the experimental results, and it indicates that our simulation method is feasible and the results are accuracy.

論文審定書 i
誌謝 ii
中文摘要 iii
英文摘要 iv
目錄 v
圖次 viii
表次 x
第一章 緒論 1
1.1 研究背景及目的 1
1.2 液晶的種類 3
1.3 液晶的性質 6
1.4 文獻回顧 8
1.4.1 實驗文獻 8
1.4.2 理論模擬文獻 9
1.5 本文架構 11
第二章 模擬方法與理論介紹 12
2.1 分子動力學 12
2.1.1 勢能函數 12
2.1.2 運動方程式 14
2.1.3 積分法則 14
2.1.4 系綜 15
2.1.5 壓力修正Souza-Martins 15
2.1.6 溫度修正Nosé-Hoover-Langevin (NHL) 16
2.1.7 分子動力學流程圖 18
2.2 粗殼粒子理論 19
2.2.1 勢能函數 19
2.2.2 波茲曼反轉換方法流程圖 21
2.3 密度泛函理論 22
2.3.1 多粒子系統薛丁格方程式 22
2.3.2 Born-Oppenheimer絕熱近似 23
2.3.3 Hohenberg-Kohn理論 23
2.3.4 Kohn-Sham方程式 25
2.3.5 交換相關能之近似-(LDA、GGA) 26
2.4 ONSAGER理論 29
2.5 MAIER-MEIER理論 30
第三章 數值模擬方法 32
3.1 週期性邊界 32
3.2 鄰近原子表列法 33
3.2.1 截斷半徑法 33
3.2.2 維理(Verlet)表列法 34
3.2.3 巢室(Cell Link)表列法 35
3.2.4 維理表列法結合巢室表列法 36
3.3 方向秩序參數(ORIENTATIONAL ORDER PARAMETER) 37
第四章 結果分析與討論 38
4.1 5CB液晶分子結構模擬 38
4.1.1 勢能函數分析 40
4.1.2 相態行為分析 50
4.2 密度泛函理論計算結果分析 52
4.3 光學與介電性質分析 53
4.3.1 有效偶極矩 53
4.3.2 藉由有效偶極矩再次分析介電性質 56
第五章 結論與未來展望 57
5.1 結論 57
5.2 未來展望 58
參考文獻 59

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