Frank-Kasper（FK）相，最初由Charles Frank和Raymond Kasper所提出，其代表了一類引人入勝且獨特的晶體結構。FK相的發現不僅在冶金學領域引起了極大的興趣，還在材料科學、軟物質物理和化學等各個學科中激發了創新的研究課題。近年的研究指出，透過化學結構和分子架構的設計或物理摻混等方法，也可以誘導嵌段共聚物（block copolymer，BCP）形成FK相。特別是最近的一項研究展示了在BCP/均聚物摻合體中引入低濃度金屬鹽可以擴展FK σ相的窗口，基於這個研究的發現，本論文擬探索引入金屬鹽類(在沒有均聚物成分的輔助下)是否可以誘導純BCP形成FK相。BCP/鹽類混合物在高分子電解質中廣被研究，並發掘了它們在固態電解質中的獨特性能和應用。其中以聚乙烯醚（PEO）為主體的高分子電解質最受重視;PEO和鹽類陽離子可形成配位錯合物，該錯合反應顯著影響了電解質的導電性和相行為。
本研究在一個僅能形成六角形密堆柱狀（HEX）結構的聚乙烯醚-聚（1,2-丁二烯）嵌段共聚物（PEO-b-PB）中添加金屬鹽類，期望可誘導FK相形成。我們選擇性地將過氯酸鋰（LiClO4）引入微胞中的PEO核心，增強了PB和PEO鏈段之間的分離強度，導致有序-無序轉變溫度（TODT）的增加。值得注意的是，TODT的上升導致在高溫度處出現了球相的窗口。在此球相窗口中，微胞根據鹽濃度和溫度的不同，會傾向排列成十二邊形準晶（DDQC）或FK σ相。加入二價鹽，過氯酸鎂（Mg(ClO4)2），可進一步擴充球相窗口。此系統在加熱過程中，微胞仍然偏向σ和DDQC相的排列。然而隨後從無序相冷卻過程中，微胞卻組織成拉弗斯C14 (Laves C14)相，而不是DDQC或σ相。本實驗結果揭露了金屬鹽在促進微胞複雜排列中的重要作用。
我們提出，鹽類增加了嵌段共聚物的有效相互作用參數，透過形成更大的微胞來減少界面自由能，如此導致共聚物鏈段更大的伸展，使得柱-球相的邊界推向更高的核心體積分率，從而促進微胞組裝成FK相。本研究揭示了一種可促進嵌段共聚物中複雜球形相熱力學穩定性的簡易方法。此外，它也揭露透過操控聚合物-鹽相互作用來設計新型軟物質晶體結構的潛力。

The Frank-Kasper (FK) phase, originally described by Charles Frank and Raymond Kasper, represents a fascinating and unique category of crystal structures. The discovery of FK phases has not only piqued significant interest within the field of metallurgy but has also sparked profound research enthusiasm across various disciplines, including materials science, soft matter physics, and chemistry. The FK phase of block copolymer (BCP) micelles has been accessed through the delicate design of the chemical structure and architecture as well as blending with homopolymer or another BCP component. Inspired by recent work by Chen et al., which demonstrated that incorporating a low concentration of metal salt into the core of micelles formed in a BCP/homopolymer blend can expand the window of the FK σ phase, we aim to investigate the accessibility of FK phases using this simple approach in neat BCP, without the presence of homopolymer to promote the formation of FK phase. BCP/salt blends are well-known in polymer electrolyte research, with numerous studies highlighting their unique properties and applications in solid-state electrolytes for batteries. The formation of coordination complexes between poly(ethylene oxide) (PEO) and the cation of the salt is a key aspect that significantly influences the conductivity and phase behavior of the PEO-based electrolyte.
In this study, we introduced metal salts into a poly(ethylene oxide)-block-poly(1,2-butadiene) (PEO-b-PB) which formed hexagonally packed cylinder (HEX) structure. The selective incorporation of lithium perchlorate (LiClO4) into PEO domain enhanced the segregation strength between PB and PEO, leading to an increase in the order-disorder transition temperature (TODT). Notably, this increase of TODT opened up a window for the spherical phase at the higher temperature. The micelles in such a spherical phase window packed preferentially into dodecagonal quasicrystal (DDQC) or FK  phase depending on the salt concentration and temperature. The addition of a bivalent salt, magnesium perchlorate (Mg(ClO¬4)2), expanded the spherical phase window further. The packing of the micelles still favored  and DDQC phase in the heating cycle. Interestingly, during the subsequent cooling from the disordered micelle phase, the micelles organized into a metastable Laves C14 instead of DDQC or phase. The experimental results highlighted the crucial role of metal salts in facilitating the complex packing of micelles, even in the absence of homopolymer.
We proposed that the preferential solubilization of salts increased the effective interaction parameter of the BCP, leading to greater stretching of the constituent blocks due to the formation of larger core to reduce the interfacial free energy. The increased tendency to reduce the conformational free energy penalty shifted the cylinder-sphere phase boundary to higher core volume fractions, thereby promoting the micelles to assemble into the FK phases. This research reveals a straightforward approach to enhance the thermodynamic stability of complex spherical phases in BCPs. Additionally, it highlights the potential for engineering novel soft crystallographic phases through manipulation of polymer-salt interactions.

Abstract......ii
摘要......iv
致謝......vi
Content......vii
List of Figures......ix
List of Tables......xiii
Chapter 1. Introduction......1
1.1 General Issues on Phase Behavior of Block Copolymer......1
1.2 Phase behavior of block copolymers......2
1.3 Classical Spherical structures in diblock copolymer......4
1.4 Frank-Kasper phases in block copolymer systems......6
1.5 Effect of high conformational asymmetry and self-concentration on stability of FK phases in neat BCP systems......8
1.6 Stabilizing Frank-Kasper phases through blending......13
1.6.1 Franks-Kasper phase in block copolymer/homopolymer blend......14
1.6.2 Franks-Kasper phase in block copolymer/block copolymer blends......17
1.7 Crystal structure of complex phases observed in this study......19
1.7.1 Frank-Kasper σ Phase......19
1.7.2 Laves Phases......20
1.7.3 Dodecagonal Quasicrystal Phase (DDQC)......21
1.8 Phase Behavior of Polymer-Salt Blends......22
1.9 Research Motivation and Objectives......25
Chapter 2. Experimental Section......27
2.1 Materials......27
2.2 Preparation of block copolymer-salt mixture......27
2.3 Small Angle X-ray Scattering (SAXS) Measurement......28
Chapter 3. Results and Discussion......29
3.1 Phase Behavior of Neat PEO1.3k -b- PB2.9k......29
3.2 Promoting the Access of Frank-Kasper Phase through Salt Incorporation into PEO1.3k-b- PB2.9k......30
3.2.1 Phase Behavior of PEO-b- PB/ LiClO4 Blend......31
3.2.2 Phase Behavior of PEO1.3k-b- PB2.9k/ Mg(ClO4)2 Blends......41
3.3 Mechanism of Salt-Induced Formation of Complex Spherical Phases......55
Chapter 4. Conclusion......62
Chapter 5. Reference......64

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