準晶體及其近似結構—弗蘭克-卡斯柏相 (FK相) 主要在具有多種粒徑的不等價球體組成的原子系統中觀察到，例如多種元素的金屬合金。最近，在包括樹枝狀聚合物、表面活性劑、形狀兩親物和嵌段共聚物 (bcps) 在內的軟物質中發現了這些複雜的有序相，從而開闢了一個令人興奮的“軟準晶”領域。在嵌段共聚物的系統中，自洽場論 (SCFT) 的計算和實驗研究已經證實了在構象不對稱的二嵌段共聚物中四個 FK相（即 σ、A15、Laves C14和C15）的存在。此外，具有局部12倍旋轉對稱性和非週期位置序特徵的十二邊形準晶相 (DDQC) 是嵌段共聚物中主要發現的準晶結構。然而，人們普遍認為 嵌段共聚物所形成的DDQC相是一種長期存在的亞穩態結構，隨著時間的推移最終會轉變成平衡態的FK σ相。儘管已在各種系統中觀察到準晶序和FK相的存在，但軟準晶形成的基本原理仍然不明確。

本論文研究揭示了DDQC和FK相在具有星形分子結構的單分散含醣基嵌段寡聚物中的形成。我們首先揭示了DDQC相在具有 miktoarm星形結構且組成不對稱的含醣基嵌段寡聚物glucose-block-[oligo(isoprene)]2 (簡稱Glc1-b-(OI)2) 中的形成，其中Glc和OI鏈段分別形成球形膠束的核和冠的部分。由於醣類鏈段的剛性和分子的分支化結構，該寡聚系統具有高度的構象不對稱性。當從30°C加熱至85°C時， Glc1-b-(OI)2形成DDQC結構，並且隨著進一步加熱發生從DDQC到BCC相的有序轉變(OOT)。儘管BCC相在隨後的冷卻實驗時間尺度內沒有轉變回DDQC，但DDQC相最終在BCC形成的樣品於30°C下長時間退火後重新生成。退火過程中的時間分辨的X光小角度散(SAXS)實驗表明，由於兩個有序相的局部和整體結構存在很大的差異，從BCC到DDQC的轉變是通過非外延途徑發生的，並以類液體填充相 (LLP) 作為亞穩態中間體。Glc1-b-(OI)2形成的DDQC相即使在30°C下退火近三個月後也沒有轉變為FK σ相，這一事實強烈表明DDQC是Glc1-b-(OI)2在較低溫度下的熱力學平衡結構，這與嵌段共聚物中DDQC是沿自由能路徑朝向穩定σ相的亞穩態前驅體的普遍觀點相反。

在研究的第二部分中，我們將Glc1-b-(OI)2和帶有兩個葡萄糖分子的 Glc2-b-(OI)2與十二烷基苯 (DB) 混合，其中十二烷基苯能選擇性地溶解到 OI 結構域中以增加組成不對稱性，生成球形膠束以填充於各種晶格中。Glc2-b-(OI)2在純態下表現出六邊形柱狀堆積 (HEX) 結構，當與少量的DB 混合能成功地在球狀和 HEX 形態之間的組成邊界附近形成 FK σ 相。此外，在Glc2-b-(OI)2/DB 混合物中能觀察到隨著選擇性溶劑組成的增加，從σ到BCC和從 BCC到FCC相的溶致相變行為，其與嵌段共聚物中的理論預測定性一致。對於Glc1-b-(OI)2/DB混合物，在基質中摻入少量DB能使在純寡聚物中發現的DDQC相轉變為σ相。隨著 DB 組成的進一步增加，BCC 成為主要的晶格。總結來說，我們的實驗結果表明，含醣基嵌段寡聚物是一種理想的軟物質系統，可通過其固有的高度構象不對稱性和非極性溶劑的選擇性摻入來獲得非規範球相結構。此外，本研究中發展的概念和方法可用於創建其他準晶或FK相，用於開發功能材料，其中感興趣的有序結構的長度尺度將會在10奈米範圍內。

Quasicrystals and their approximants known as Frank-Kasper (FK) phase have been mainly observed in atomistic systems composed of inequivalent spheres with multiplicity in particle size, such as metallic alloys of multiple elements. Recently, these complex ordered phases have been found in soft matters including dendrimers, surfactants, shape amphiphiles, and block copolymers (bcps), thereby opening up an exciting field of “soft quasicrystal”. In the case of bcps, self-consistent field theory (SCFT) calculations and experimental studies have identified four FK phases (i.e., , A15, and Laves C14 and C15) in conformationally asymmetric diblock copolymers. Besides, dodecagonal quasicrystalline (DDQC) phase with the characteristics of local 12-fold rotational symmetry and aperiodic positional order is the main quasicrystalline structure found in bcps. It is however a common belief that the DDQC phase of bcps is a long-lived metastable structure which would eventually evolve into the equilibrium FK σ phase over time. Although quasicrystalline order and FK phases have been observed in various systems, the underlying principles of the formation of soft quasicrystals remain ambiguous.

This thesis research discloses the emergence of DDQC and FK phases in a monodisperse sugar-based block co-oligomers bearing star molecular architecture. We first revealed the formation of DDQC phase in a compositionally asymmetric glucose-block-[oligo(isoprene)]2 (Glc1-b-(OI)2) with miktoarm star architecture, in which the Glc and OI block formed core and corona of the micelle, respectively. This oligomeric system possessed high conformational asymmetry stemming from the rigidity of the saccharidic moiety and the branched architecture. Upon heating from 30 to 85 °C, Glc1-b-(OI)2 was found to exhibit DDQC structure, and an order-order transition (OOT) from DDQC to BCC phase occurred with further heating. Though the BCC phase did not transform back to DDQC within the time scale of the subsequent cooling experiment, DDQC phase was eventually recovered upon prolonged annealing of the BCC-forming sample at 30 °C. A time-resolved small angle X-ray scattering (SAXS) experiment during the annealing process revealed that the transition from BCC to DDQC occurred through a non-epitaxial route with a liquidlike packing (LLP) phase as a metastable intermediate due to large disparity in both local and global structure of the two ordered phases. The fact that the accessed DDQC phase of Glc1-b-(OI)2 did not transform into FK σ phase even after annealing at 30 °C for nearly three months strongly suggested that DDQC was a thermodynamically equilibrium structure of Glc1-b-(OI)2 at the lower temperature, which was contrary to the common view that DDQC is a metastable precursor along the free energy path towards the stable σ phase in bcps.

In the second part of the study, we blended Glc1-b-(OI)2 and Glc2-b-(OI)2 bearing two glucose moieties with dodecyl benzene (DB) which dissolved selectively into the OI domain to increase the compositional asymmetry for generating the spherical micelle packed in various lattices. The mixing of Glc2-b-(OI)2, which exhibited hexagonally packed cylinder (HEX) morphology in pure state, with a small amount of DB successfully introduced the FK σ phase near the composition boundary between sphere and HEX morphology. In addition, the lyotropic phase transitions from σ to BCC and from BCC to FCC phase with increasing selective solvent composition were observed in Glc2-b-(OI)2/DB mixture, in qualitative agreement with the theoretical prediction for bcps. For the Glc1-b-(OI)2/DB mixture, the DDQC phase found in neat co-oligomer transformed to σ phase with a small level of incorporation of DB into the matrix phase. BCC then became the predominant packing lattice upon further increase of DB composition. To sum up, our experimental results demonstrate that sugar-based bco is an ideal soft matter system for attaining non-canonical spherical phases through its intrinsically high conformational asymmetry and the selective incorporation of a nonpolar solvent. Moreover, the concepts and methodology developed here may be implemented to create other quasicrystalline or FK phases for the development of functional materials wherein the length scale of ordered structure of interest is in the sub-10 nm range.

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