本研究是利用分子模擬探究共軛高分子在分子尺度下的有序疊積。根據文獻上的記載，聚芴分子(ployfluorene)的衍生物poly(9,9-di-n-octyl-2,7-fluorene) (PFO)及poly(9,9-di-n-hexyl-2,7-fluorene) (PFH)在冷卻過程中會發生相變化以致冷卻後形成兩相共存；對於前者而言，由於相變化前後的結晶系統(crystal system)並未改變，只有在晶格參數上的略有差異且並未對其發光行為產生巨大影響，所以並未受到太多的關注。相較之下，PFH在冷卻過程中所發生的相變化就更為明確(高溫α 相熔點為230 oC在冷卻溫低低於190 oC時會相變成α′ 相；α 單斜晶: a = 2.15 nm, b = 2.47 nm, c = 3.32 nm, ; α′ 三斜晶: a = 2.05 nm, b = 2.58 nm, c = 3.30 nm)。此研究的目的是在還原PFH中兩相的分子疊積模型，藉由先得到在單一分子鏈中接連兩單體間的扭轉角必須要落在 ±40o與 ±140o左右才會具有相對穩定的結構；再者，利用上述的關係推測可能存在的穩定分子構型(mono-radial, bi-radial, and tetra-radial)並以此構型去執行分子疊積。經由比較實驗所得與計算所得的選區繞射與粉末繞射圖，我們得到的結果如下：對α 相而言，其可能的空間群為C2且分子鏈是以bi-radial的構型存在；相較於α 相，α′ 相的分子鏈是以tetra-radial的構型存在且其空間群為P1。藉由重疊此兩相計算所得的選區繞射圖，我們間接的證明了兩相共存的可能性；此兩相的疊積模型亦符合我們在實驗上所觀察到的single-crystal-like faceting (α 相)與tensile cracking (α + α′ 相)

By means of molecular simulation, we propose possible packing models for α and α′ phases in poly(9,9-di-n-hexyl-2,7-fluorene) (PFH). Simulated multi-chain unit cell structures are compared with experimental diffraction patterns of PFH where the unit cell structure (and the space group) of the high-temperature α crystals was identified as monoclinic (C2) and that of α′ phase (kinetically favored upon programmed cooling) triclinic (P1). Results show that α phase prefers to adopt bi-radial side-chain conformation whereas the α′ phase prefers tetra-radial one. Both models exhibit embracing behavior between adjacent chains in spite of differences in inter-chain distance. A group of embracing chains aligned along b-axis in α phase and the comparatively greater inter-chain distance in α′ phase are consistent with the observed faceting along (100) planes and the tensile cracking along the a-axis. A qualitative analysis of co-existing α and α′ phases reproduce the [001] SAED pattern quite well. In addition, we also show that arbitrary alternation of 40o and 140o in dihedral angle between neighboring monomers generates equally stable single-chain conformations in this case of linear alkyl side-chains.

摘要 I
Abstract II
Table of Contents III
List of Tables V
List of Figures VI
1. Background 1
1.1. Introduction 1
1.1.1. Phase Behavior and Molecular Packing of Poly(9,9-di-n-octyl-2,7-fluorene) 1
1.1.2. Phase Behavior of Poly(9,9-di-n-hexyl-2,7-fluorene) 4
1.2. Unresolved Issues 6
1.3. Objectives and Approaches 6
2. Simulation & Crystallographic Details 7
2.1. Energy Minimization via Molecular Mechanics Simulation 7
2.1.1. Force Field 7
2.1.2. Basic Principle for Energy Minimization 8
2.2. Procedures in Performing Molecular Simulation 9
2.2.1. Extract an Energy Minimized Single Chain 9
2.2.2. Build Crystals with Specified Space Group 10
2.2.3. Calculate the Powder-XRD and SAED Zone Pattern 10
2.3. Crystallography 10
2.3.1. Fundamentals of Crystallography 10
2.3.1.1. Symmetry Elements 11
2.3.1.2. Seven Crystal Systems, 14 Bravais Lattices, and 230 Space Groups 11
2.3.2. Diffraction by Crystals 13
2.3.3. Systematic Absences 14
3. Molecular Packing in Crystalline Poly(9,9-di-n-hexyl-2,7-fluorene) 16
3.1. Space Group Determination 16
3.2. Number of Polymer Chains in a Unit Cell 19
3.3. Single Chain Simulation 20
3.3.1. Dihedral Angle Study 20
3.3.2. Chain Conformations 23
3.4. Molecular Packing in Crystalline α phase in PFH 24
3.4.1. Effects of the Side Chain Conformations on the Calculated Diffraction Patterns 24
3.4.2. Effects of the Backbone Configurations and the Dihedral Angles on the Calculated Diffraction Patterns 28
3.5. Molecular Packing in Crystalline α′ phase in PFH 32
4. Conclusion 35
5. References 36
6. Appendices 38

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