嵌段共聚物自組裝可利用調整排斥力強度及組成的方式提供我們得到不同規則排列的奈米結構之方法。然而，在wet brush的條件下，將一個能均勻混到其中一微相結構中的均聚物混摻至嵌段共聚物中是一個能有效調控自組裝結構的方式。在高度不對稱的組成中，嵌段共聚物會形成微胞，這些微胞會進而排列成一個三維向度的結構，而這些立體結構中以體心立方結構最為對稱。近年的理論研究發現，當構型高度不對稱且主成分鏈鍛的Kuhn length較小時，若嵌段共聚物系統可形成微胞，則這些微胞會趨向形成Frank-Kasper相。此時，為了減少冠狀區域的高分子鏈鍛產生packing frustration，微胞中的球核區與冠狀區域之介面會形變成Voronoi cell的形狀。

在此研究中，我們利用強排斥力嵌段共聚物:聚苯乙烯-共-聚二甲基矽氧烷混摻聚苯乙烯均聚物，將系統調控在組成不對稱的區域來系統性的探討其自組裝結構及相行為。從先前文獻的結果得知，聚苯乙烯-共-聚二甲基矽氧烷屬於構型對稱的系統，此系統不應形成Frank-Kasper相。然而，聚苯乙烯與聚二甲基矽氧烷之間有極大的排斥力，因此趨向形成微胞來降低介面自由能。然而，我們發現即使在高度組成不對稱的情況下，由於純的嵌段共聚物擁有較強的排斥力，使得介面自由能主導整體自組裝行為，而形成六方堆積柱狀結構。若混摻一種比共聚物之聚苯乙烯鏈鍛還小分子量的聚苯乙烯均聚物，此時系統會形成微胞結構，代表聚苯乙烯均聚物與共聚物之聚苯乙烯在冠狀區域中相互混合。於此系統中，聚二甲基矽氧烷所形成之球核主要會以體心立方結構的方式排列。有趣的是，在靠近六方堆積柱狀結構的附近，我們發現當均聚物分子量較小時，微胞將排列成Frank-Kasper σ 相。在升溫過程中，由於lattice fluctuation的緣故，使得微胞從近似準晶結構轉變成體心立方結構。此研究說明，即便在構型對稱的系統中，仍可利用混摻均聚物的方式來得到Frank-Kasper σ 相。

Self-assembly of block copolymer offers a fascinating process of producing a variety of ordered nanostructures governed by the segregation strength (χN, with χ and N being the Flory-Huggins interaction parameter and the degree of polymerization of the bcp, respectively) and composition of the constituting blocks. Blending with homopolymer is an effective strategy to tailor the morphology of a given bcp, provided that the homopolymer is uniformly solubilized in one of the microphases under the wet-brush condition. At highly asymmetric composition, the bcp system forms the spherical micelles that pack into three-dimensionally ordered lattices, where body-centred cubic (bcc) is the most common packing symmetry. It has been demonstrated theoretically for neat bcp that Frank-Kasper (FK) phase can be accessed for the micelles when the conformational asymmetry of the constituent blocks is sufficiently large, with the majority block bearing a smaller Kuhn length. In this case, the core-corona interface approaches the polyhedral interface limit (PIL) with the core adopting the polyhedral geometry that is the affinely shrunk copy of the Voronoi cell to minimize the packing frustration of the coronal block.
The present study systematically investigates the self-assembled structure and phase transition behavior of a common high-χ bcp, polystyrene-block-poly (dimethylsiloxane) (PS-b-PDMS), and its blends with PS homopolymer (h-PS) in the compositionally asymmetric regime. The formation of FK phase in PS-b-PDMS should be highly unfavored considering its conformational symmetry and the strong repulsion between PS and PDMS blocks so as to favor spherical core geometry for minimizing the interfacial free energy. The neat PS-b-PDMS was found to form hexagonally packed cylinders (HEXc) structure in spite of its highly asymmetric composition because of the significant role of the interfacial free energy for large χ. Blending with h-PS with lower molecular weight than that of the PS block transformed the morphology to spherical micelles, indicating that h-PS and PS block formed wet-brush mixture in the micelle corona. The PDMS core of the micelle was found to pack in bcc lattice over the major composition window. Intriguingly, in the vicinity of the boundary of HEXc phase, the micelles were found to organize into FK σ phase when h-PS molecular weight was sufficiently low. This quasicrystalline approximant underwent an order-order transition to bcc phase on heating, which can be attributed to the influence of the lattice fluctuations. The present study demonstrates that blending with homopolymer offers a facile approach for creating FK σ phase even for conformationally symmetric block copolymers.

1 Chapter 1 Introduction and Literature Review 1
1.1 Phase Behavior of the diblock copolymer 1
1.1.1 Microphase-separated morphology of diblock copolymers 1
1.1.2 Self-consistent Mean Field Theory: 4
1.2 Classical Phases in diblock copolymers 6
1.3 Spherical phase lattice structures of block copolymers 7
1.3.1 Body centered cubic (bcc) lattice 7
1.3.2 Closed packed spheres (CPS) Lattices: 8
1.4 Phase Behavior of diblock copolymer /homopolymer blends: 9
1.4.1 Frank-Kasper phase of sphere-forming diblock Copolymers 12
1.4.2 Conformational asymmetry effect on complex phases 15
1.4.3 Features of sigma phase 16
1.5 Research Motivation 19
2 Chapter 2 Frank-Kasper σ Phase and Its Formation Mechanism in Polystyrene-block-Poly (dimethyl siloxane) /Polystyrene Homopolymer Blends. 20
2.1 Introduction: 20
2.2 Experimental Section: 23
2.2.1 Material Preparation 23
2.2.2 Characterization 24
2.3 Results and Discussion 27
2.3.1 Equilibrium structure of PS-b-PDMS and PS-b-PDMS/h-PS blends 27
2.3.2 Equilibrium Phase behavior of the blends 29
2.3.3 Effect of annealing temperature on the formation of the ordered spherical phase 44
2.3.4 Evolution of σ phase from LLP phase via Ostwald’s step rule 47
Chapter 3 Conclusions 49
References 51

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