嵌段共聚物的微相分離可以產生各種長程有序的奈米結構。影響奈米結構的重要參數包含Flory-Huggins interaction parameter (χ) 以及體積分率。當兩個嵌段的組成極不對稱時，會微相分離形成排列成晶格的球狀結構。體心立方 (BCC) 是嵌段共聚物的主要晶格結構。但是，自洽場理論的計算預測嵌段共聚物的相圖中存在狹小範圍的面心立方 (FCC) 或六方密堆積 (HCP) 晶格之緊密堆積球 (CPS) 相。由於FCC和HCP晶格之間的自由能差異非常小，先前研究尚未斷定哪一個晶格的結構較為穩定，而且由於相的穩定區域非常窄，CPS相極難形成。與均聚物摻混提供了一種簡便的方法來調整嵌段共聚物的微相形態。理論計算表明，CPS相的穩定區域在摻合物中更寬廣，這使得這種極為罕見的結構更容易形成。
本文為研究對稱的嵌段共聚物poly(ethylene oxide)-block-poly(1,4-butadiene) (簡稱PEO-b-PB) 混掺均聚物 poly(1,4-butadiene) 或均聚物 poly(ethylene oxide) 的系統。通過將摻合物加熱至無序微胞 (DM) 相，然後冷卻進行微胞重排，從而消除了溶劑誘導的熱履歷，再進一步探索獲得的緊密堆積的晶格結構。我們證明了在有序-無序相轉換溫度(TODT)以下的過冷微胞液相會轉化成HCP相，並且該晶格結構在冷卻過程的整個溫度範圍內均不再進行相轉變，這表明HCP是比FCC更穩定的晶格。在PEO-b-PB/h-PEO摻合物中也發現了HCP相。HCP比FCC更好的熱力學穩定性歸因於HCP排列下的空隙在晶格中較具連通性，使均聚物鏈在八面體空隙中具有更高的熵。
通過計算FCC，HCP和BCC晶格中的微胞核心的表面到Voronoi cell表面的距離分佈，我們進一步分析了PEO-b-PB /均聚物摻合物的CPS相相對於BCC的熱力學穩定性。結果表明，如果將大多數位於微胞殼層中的分子鏈限制在Voronoi cell內，那麼它們將被壓縮，使得構形熵大幅下降。因此，位於微胞殼層中的分子鏈傾向於從Voronoi cell向外延伸並進入相鄰的微胞，使微胞間相互重疊，以釋放因分子鏈壓縮而產生的熵損失。在這種情況下，緊密堆積的晶格比BCC更受青睞，因為它可以獲得更高的重疊率，而且重疊的部分在微胞周圍的分佈較均勻。
最後，藉由疊差機率的計算，可在X光小角度散射(SAXS)圖譜中發現CPS相具有不同程度的疊差，我們觀察到HCP晶格中疊差的程度隨著溫度的降低而增加，並且這種變化是熱可逆的。我們提出疊差的程度主要受位於微胞殼層中的均聚物溶解的均勻性的控制，其中較低溫度下微胞的邊界附近形成富有均聚物的區域，均聚物的富集有效降低了微胞間的相關性，從而增加了疊差的程度。

The microphase separation of block copolymers can produce a variety of long-range ordered nanostructures. The key parameters governing the microphase-separated structure formed are the segregation strength (χN) and the volume fractions of the constituents. When the composition is highly asymmetric, the microphase separation yields spherical microdomains packed in macrolattices. Body-centered cubic (BCC) is the predominant lattice structure observed for diblock copolymers. Self-consistent field theory calculations however predict a narrow region in the phase diagram where the copolymer forms the close-packed sphere (CPS) phase in which the microdomains packed in face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice. It however remains unclear whether FCC or HCP is the more stable packing structure, because the free energy difference between them is very small, and moreover the CPS phase is extremely difficult to access due to very narrow phase window. Blending with a homopolymer offers a facile way to tailor the microdomain morphology of block copolymers. Theoretical calculations have shown that the phase window of CPS structure is broader in the blends, making this highly rare structure easier to be accessed.
This dissertation is centered on the CPS structure formed by the blends of a symmetric poly(ethylene oxide)-block-poly(1,4-butadiene) (PEO-b-PB) with poly(1,4-butadiene) (PB) or poly(ethylene oxide) (PEO) homopolymers. We explored the stable close-packed lattice structure attained after removing the history of solvent casting by heating the blend to the disordered micelle (DM) phase followed by cooling for micelle re-ordering. We demonstrated that HCP phase developed from the supercooled micellar liquid phase below TODT, and this lattice structure persisted throughout the entire temperature range in the cooling process, indicating that HCP was the more stable packing lattice than FCC. HCP phase was also found for the PEO-b-PB/h-PEO blend. The better thermodynamic stability of HCP than that of FCC was attributed to the higher translational entropy of the homopolymer chains localized into the octahedron voids due to the extended connectivity of these voids in the lattice.
We further analyzed the thermodynamic stability of CPS phase relative to that of BCC for the PEO-b-PB/homopolymer blends studied through calculating the distributions of the distances from the surface of the microdomain to the walls of the Voronoi cells of FCC, HCP and BCC lattices. The results showed that the majority of the coronal blocks would have been compressed if they were confined within the Voronoi cells, which was entropically unfavorable. We proposed that the coronal blocks tended to extend out of the Voronoi cell and intruded into the adjacent cells, leading to intermicellar overlap to release the entropic penalty arising from the chain compression. In this case, the close-packed lattice was favored over BCC for attaining higher overlap fraction and also for even distribution of the overlap fraction around a given micelle.
Finally, with the aid of the calculated SAXS profiles of the CPS phase containing different degrees of stacking fault, we observed that the amount of stacking fault in HCP lattice increased with decreasing temperature and the variation was thermally reversible. We proposed that the degree of stacking fault was governed by the uniformity of homopolymer solubilization in the micellar corona, where the enrichment of homopolymer near the micelle boundary at lower temperature effectively reduced the intermicellar correlation and hence increased the degree of stacking fault.

Abstract.........................................................I
摘要...........................................................III
Table of Contents................................................V
List of Figures................................................VII
Chapter 1. Introduction..........................................1
1.1 Background of Reasearch......................................1
1.2 Basic Phase Behavior of Neat Diblock Copolymer...............3
1.3 Basic Phase Behavior of Block Copolymer/Homopolymer Blends..........................................................14
1.4 Close-Packed Sphere (CPS) Phase of Block Copolymer and Block Copolymer/Homopolymer Blends....................................20
1.4.1 CPS Phase of Crystallographically Equivalent Microdomains: FCC and HCP Packing.............................................20
1.4.2 CPS Phase of Crystallographically Inequivalent Spheres: Frank-Kasper Phase..............................................23
1.4.3 CPS Phase in Block Copolymer/Homopolymer Blends...........26
1.5 Objectives of Research and Overview of Thesis...............30
1.6 References and Notes........................................34
Chapter 2. Discovery of Hexagonal Close-packed (HCP) Phase of Block Copolymer/Homopolymer Blends..............................41
2.1 Introduction................................................41
2.2 Experimental Section........................................46
2.2.1 Materials.................................................46
2.2.2 SAXS Measurement..........................................46
2.3 Results and Discussion......................................48
2.4 Conclusions.................................................67
2.5 References and Notes........................................68
Chapter 3. Thermodynamic Stability and Temperature-Dependent Degree of Stacking Fault of the CPS Phase of Block Copolymer/Homopolymer Blends....................................72
3.1 Introduction................................................72
3.2 Experimental Section........................................74
3.2.1 Materials.................................................74
3.2.2 SAXS Measurement..........................................74
3.3 Results.....................................................76
3.3.1 SAXS Profiles of CPS Phase Containing Stacking Fault......76
3.3.2 The SAXS Results of PEO-Rich Blends Showing Temperature-Dependent Degree of Stacking Fault..............................95
3.4 Discussion.................................................104
3.4.1. Thermodynamic Reasoning on the Relative Stabilities of the Packing Lattices of Block Copolymer Micelles in Quiescent Melt...........................................................105
3.4.2 Quantitative Characterization of the Voronoi Cells of BCC, FCC and HCP Lattice of the PEO-b-PB/Homopolymer Blends Studied........................................................112
3.4.3 Thermally Driven Variation of Stacking Fault in HCP Lattice........................................................119
3.5 Conclusions................................................123
3.6 References and Notes.......................................125
Chapter 4 Overall Summery......................................127
List of Publications...........................................129

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