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研究生: 巴克諾理
Nouri, Babak
論文名稱: 嵌段共聚物微胞於類膠體粒子領域之自組裝行為研究
Self-assembly of block copolymer micelles in the fuzzy colloid regime
指導教授: 陳信龍
Chen, Hsin-Lung
口試委員: 蘇安仲
Su, An-Chung
蔣酉旺
Chiang, Yeo-Wan
孫亞賢
Sun, Ya-Sen
朱哲毅
Chu, Che-Yi
學位類別: 博士
Doctor
系所名稱: 工學院 - 化學工程學系
Department of Chemical Engineering
論文出版年: 2022
畢業學年度: 111
語文別: 英文
論文頁數: 137
中文關鍵詞: 嵌段共聚物微胞拉維斯C14相晶格排列尺寸分散性
外文關鍵詞: block copolymer, micelle, Laves C14 phase, lattice packing, size polysispersity
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  • 組成高度不對稱的嵌段共聚物可以微相分離成球狀的微胞結構,微胞之間互斥作用力誘導微胞排列形成晶格結構。近年Frank-Kasper (FK) 相以及準晶結構的發現,嵌段共聚物微胞的堆積結構與機制引起了高度關注,FK相含有至少兩種以上配位數的Voronoi cell。因此,嵌段共聚物微胞在無序排列之微胞相過形成FK相的過程中,微胞尺寸應由單一分佈轉變為多重分佈,此程序需由微胞間的分子質量傳遞來達成。
    本研究開創了一種「模糊膠體粒子」的觀念來建構嵌段共聚物之FK相,我們在低於P2VP以的玻璃轉化溫度(T¬gcore)的條件下,限制共聚物分子的質量傳遞,透過長時間退火誘導P2VP-b-PDMS由類液態堆積相(LLP)轉化為Laves C14相。我們使用數種熱處理條件來產生不同平均尺寸及尺寸分散性的P2VP-b-PDMS微胞,形成各種LLP結構,我們發現,經過低於Tgcore的長時間退火可以誘導不同的LLP相轉化為體心立方結構(BCC)或C14結構可,即尺寸分布較均一的微胞傾向堆積成由單一種Voronoi cell構成的BCC結構;而尺寸分布較寬廣的微胞則傾向形成由三種Voronoi cell構成的Laves C14相。
    我們進一步針對微胞周遭局部環境進行實空間的分析,發現C14相可以容納較廣泛的粒子間距,並具有較不均一的局部環境。尺寸分布較廣的微胞形成C14相可使外圍之PDMS鏈段的熵損耗較為緩和。原則上,適當的微胞尺寸分散性有利於Laves C14相的形成。我們認為,尺寸分餾是LLP相轉化為C14相的關鍵,即為尺寸分布較廣的粒子可以分餾成三種尺寸次分佈,而排列成C14晶格,這些晶格結構的有序-無序轉化溫度(TODT)與LLP的結構息息相關。 最後,我們發現P2VP-b-PDMS的相轉化行為有高度的記憶效應,將樣品升溫到無序微胞結構後淬火,可以回復到原始LLP相的特性。而後在模糊膠體粒子區域進行退火後,即可得到原始的有序結構。


    Microphase separation between the constituent blocks of block copolymer (bcp) can generate spherical micelles at large compositional asymmetry. The interaction between the micelles, which is usually repulsive in nature, leads to their organization into long-range ordered lattices. The packing problem of bcp micelles has triggered considerable attention recently by the discovery of Frank-Kasper (FK) phase and quasicrystals. FK phase is the tetrahedrally close packed structure constructed by the distorted icosahedra with the coordination number of 12, 14, 15 or 16 in the unit cell, where each FK phase composes of at least two types of these motifs. In principle, the formation of FK phase from the supercooled liquid phase of bcp micelles should involve the mass transport of the constituent molecules to transform the unimodal distribution of micelle size into the multimodal distribution prescribed by the volume asymmetry of the Voronoi cells in the FK phase. Here we present a so-called “fuzzy colloid regime” in which the Laves C14 phase of a pol(2-vinyl pyridine)-block-poly(dimethyl siloxane) (P2VP-b-PDMS) developed from the liquidlike packing phase (LLP) below the glass transition temperature of the micelle core (T¬gcore) formed by P2VP block, where the mass transport mechanism was inaccessible.
    Several thermal processing conditions were adopted to produce the P2VP-b-PDMS micelles forming various LLP structures with different average micelle sizes and size dispersity. Prolonged annealing of these LLP phases at T < Tgcore was found to yield body-centered cubic (BCC) or C14 phase depending on the LLP structure. Micelles with narrow size dispersity tended to pack into BCC lattice composed of one type of Voronoi cell, while the broadly distributed micelles were found to pack into Laves C14 phase comprising three types of Voronoi cells. The real-space analysis of the local environments of the particles revealed that C14 phase can accommodate the particles with a broader range of interparticle distance and less uniform local environment, such that the PDMS coronal blocks of the micelles with greater size dispersity suffered a lower degree of packing frustration when they organized into C14 lattice. In principle, polydispersity destabilizes the classical lattice structure; however, a modest degree of polydispersity causes symmetry breaking, leading to the formation of Laves C14 phase.
    We propose that a self-sorting process via size fractionation was operative to direct the effective development of C14 phase from the LLP phase with sufficiently large size dispersity. The fractionation took place to yield three fractions of particles from the parent distribution with their relative populations approximately followed the stoichiometry of the particles in the C14 unit cell. Due to the metastable nature of the ordered phases, their order-disorder transition temperatures (TODTs) were found to depend strongly on the structures of the LLP phases from which they developed. Finally, we revealed a strong memory effect underlying the phase transitions. Heating the samples to the DM phase followed by quenching effectively recovered the characteristics of the original LLP phase from which the ordered phase evolved. The subsequent annealing in the fuzzy colloid regime led to the formation of the ordered phase identical to the original one. The present research lands a new paradigm of bcp metallurgy where the micelles can find their optimum ordered packing under a predetermined state of distribution without adjusting their sizes.

    Table of content Abstract...........................................................................................................I Table of content.............................................................................................III List of figures..................................................................................................V List of tables....................................................................................................X Chapter 1. Introduction ....................................................................................1 1.1 Background of Research ..................................................................................1 1.2. Quasicrystal and FK phases of one-component linear block copolymers......5 1.2.1. Conformational asymmetry effect on the stability of Frank-Kasper phase .....................................................................................7 1.2.2. Frank-Kasper phase of block copolymer with architectural asymmetry ...........................................................................13 1.3. Frank- Kasper phase of block copolymer blend systems..............................16 1.3.1. Block copolymer/block copolymer blends forming Frank-Kasper phase ...................................................................................17 1.3.2. Frank-Kasper phase of block copolymer /homopolymer blends......18 1.4. Self-assembly of colloidal suspension..........................................................22 1.4.1. Nanoparticle interactions .........................................................23 1.4.2. Hard-core van der Waals interaction ..........................................23 1.5. Self-assembly of binary hard particle suspension: effect of polydispersity .31 1.5.1. Size disparity effect of ligand-coated hard particles......................34 1.6. Conclusions and outlook...............................................................................36 1.6. Objectives of research and overview of thesis..............................................38 1.7. References and notes.....................................................................................42 Chapter 2. Emergence of a metastable Laves C14 phase of block copolymer micelle bearing glassy core .........................................................................................63 2.1. Introduction...................................................................................................63 IV 2.2. Experimental Section....................................................................................66 2.2.1. Sample preparation .................................................................66 2.2.2. Rheological measurement ........................................................67 2.2.3. Synchrotron small angle X-ray scattering (SAXS) measurements...68 2.3. Results and Discussion .................................................................................69 2.3.1. Glass transition temperature and the conformational asymmetry parameter of the P2VP-b-PDMS..............................................69 2.3.2. Micelle ordering resolved by SAXS...........................................71 2.3.3. Thermodynamic argument of the micelle ordering from the LLP phases ...........................................................................................79 2.3.4. Order-disorder transition of the metastable C14 phase ..................82 2.4. Conclusion ....................................................................................................84 2.5. References and notes.....................................................................................86 Chapter 3 Phase control of colloid-like block copolymer micelles by tuning size distribution via thermal processing..................................................................95 3.1. Introduction...................................................................................................95 3.2. Results and discussion ..................................................................................99 3.2.1. The LLP phases generated by different thermal processing conditions and the impact of LLP structure on the micelle ordering behavior in the fuzzy colloid regime .........................................................99 3.2.2. The local environment and the particle size dispersity of the LLP phases that favor the formation of Laves phase ........................106 3.2.3. The self-sorting mechanism leading to the development of C14 phase from the LLP phase .............................................................111 3.2.4 The order-disorder transition of the metastable ordered phases......118 3.3. Conclusions.................................................................................................122 3.4. References and notes...................................................................................125 Chapter 4 Overall Summery and Suggestion for Future Work .........................132 List of Publications.......................................................................................136

    Chapter 1
    (1) F., S. R. How Far Can We Push Chemical Self-Assembly? Science 2005, 309 (5731), 95.
    (2) Goodfellow, B. W.; Rasch, M. R.; Hessel, C. M.; Patel, R. N.; Smilgies, D.-M.; Korgel, B. A. Ordered Structure Rearrangements in Heated Gold Nanocrystal Superlattices. Nano Lett. 2013, 13 (11), 5710–5714.
    (3) Baez-Cotto, C. M.; Mahanthappa, M. K. Micellar Mimicry of Intermetallic C14 and C15 Laves Phases by Aqueous Lyotropic Self-Assembly. ACS Nano 2018, 12 (4), 3226–3234.
    (4) Zhao, Y.; Xie, Z.; Gu, H.; Jin, L.; Zhao, X.; Wang, B.; Gu, Z. Multifunctional Photonic Crystal Barcodes from Microfluidics. NPG Asia Mater. 2012, 4 (9), e25–e25.
    (5) A., D. K.; L., M. J. The Protein-Folding Problem, 50 Years On. Science 2012, 338 (6110), 1042–1046.
    (6) Tian, L.; Qian, K.; Qi, J.; Liu, Q.; Yao, C.; Song, W.; Wang, Y. Gold Nanoparticles Superlattices Assembly for Electrochemical Biosensor Detection of MicroRNA-21. Biosens. Bioelectron. 2018, 99, 564–570.
    (7) Kamien, R. D. Soap Froths and Crystal Structures. Ann. Henri Poincaré 2003, 4 (2), 679–681.
    (8) Grason, G. M.; DiDonna, B. A.; Kamien, R. D. Geometric Theory of Diblock Copolymer Phases. Phys. Rev. Lett. 2003, 91 (5), 58304..
    (9) Bates, F. S.; Schulz, M. F.; Khandpur, A. K.; Förster, S.; Rosedale, J. H.; Almdal, K.; Mortensen, K. Fluctuations, Conformational Asymmetry and Block Copolymer Phase Behaviour. Faraday Discuss. 1994, 98 (0), 7–18.
    (10) Castelli, A.; de Graaf, J.; Marras, S.; Brescia, R.; Goldoni, L.; Manna, L.; Arciniegas, M. P. Understanding and Tailoring Ligand Interactions in the Self-Assembly of Branched Colloidal Nanocrystals into Planar Superlattices. Nat. Commun. 2018, 9 (1), 1141.
    (11) Lifshitz, R.; Diamant, H. Soft Quasicrystals–Why Are They Stable? Philos. Mag. 2007, 87 (18–21), 3021–3030.
    (12) Palberg, T. Colloidal Crystallization Dynamics. Curr. Opin. Colloid Interface Sci. 1997, 2 (6), 607–614.
    (13) Frank, F. C.; Kasper, J. S. Complex Alloy Structures Regarded as Sphere Packings. I. Definitions and Basic Principles. Acta Crystallogr. 1958, 11 (3), 184–190.
    (14) Frank, F. C.; Kasper, J. S. Complex Alloy Structures Regarded as Sphere Packings. II. Analysis and Classification of Representative Structures. Acta Crystallogr. 1959, 12 (7), 483–499.
    (15) Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. Metallic Phase with Long-Range Orientational Order and No Translational Symmetry. Phys. Rev. Lett. 1984, 53 (20), 1951–1953.
    (16) Lawson, A. C.; Olsen, C. E.; Richardson Jnr, J. W.; Mueller, M. H.; Lander, G. H. Structure of β-Uranium. Acta Crystallogr. Sect. B 1988, 44 (2), 89–96.
    (17) Huang, M.; Yue, K.; Wang, J.; Hsu, C.-H.; Wang, L.; Cheng, S. Z. D. Frank-Kasper and Related Quasicrystal Spherical Phases in Macromolecules. Sci. China Chem. 2018, 61 (1), 33–45.
    (18) Talapin, D. V; Shevchenko, E. V; Bodnarchuk, M. I.; Ye, X.; Chen, J.; Murray, C. B. Quasicrystalline Order in Self-Assembled Binary Nanoparticle Superlattices. Nature 2009, 461 (7266), 964–967.
    (19) Zeng, X.; Ungar, G.; Liu, Y.; Percec, V.; Dulcey, A. E.; Hobbs, J. K. Supramolecular Dendritic Liquid Quasicrystals. Nature 2004, 428 (6979), 157–160.
    (20) Goran, U.; Yongsong, L.; Xiangbing, Z.; Virgil, P.; Wook-Dong, C. Giant Supramolecular Liquid Crystal Lattice. Science 2003, 299 (5610), 1208–1211.
    (21) Ungar, G.; Zeng, X. Frank–Kasper, Quasicrystalline and Related Phases in Liquid Crystals. Soft Matter 2005, 1 (2), 95–106.
    (22) Liew, C. Y.; Salim, M.; Zahid, N. I.; Hashim, R. Biomass Derived Xylose Guerbet Surfactants: Thermotropic and Lyotropic Properties from Small-Angle X-Ray Scattering. RSC Adv. 2015, 5 (120), 99125–99132.
    (23) Kim, S. A.; Jeong, K.-J.; Yethiraj, A.; Mahanthappa, M. K. Low-Symmetry Sphere Packings of Simple Surfactant Micelles Induced by Ionic Sphericity. Proc. Natl. Acad. Sci. 2017, 114 (16), 4072 – 4077.
    (24) Sun, H.-J.; Zhang, S.; Percec, V. From Structure to Function via Complex Supramolecular Dendrimer Systems. Chem. Soc. Rev. 2015, 44 (12), 3900–3923.
    (25) D., H. S.; H.-T., J.; V., P.; W.-D., C.; G., J.; G., U.; K., B. V. S. Direct Visualization of Individual Cylindrical and Spherical Supramolecular Dendrimers. Science 1997, 278 (5337), 449–452.
    (26) Lee, S.; Bluemle, M. J.; Bates, F. S. Discovery of a Frank-Kasper σ Phase in Sphere-Forming Block Copolymer Melts. Science 2010, 330 (6002), 349 – 353.
    (27) Kim, K.; Schulze, M. W.; Arora, A.; Lewis, R. M.; Hillmyer, M. A.; Dorfman, K. D.; Bates, F. S. Thermal Processing of Diblock Copolymer Melts Mimics Metallurgy. Science 2017, 356 (6337), 520 – 523.
    (28) Takagi, H.; Yamamoto, K. Phase Boundary of Frank–Kasper σ Phase in Phase Diagrams of Binary Mixtures of Block Copolymers and Homopolymers. Macromolecules 2019, 52 (5), 2007–2014.
    (29) Barbon, S. M.; Song, J.-A.; Chen, D.; Zhang, C.; Lequieu, J.; Delaney, K. T.; Anastasaki, A.; Rolland, M.; Fredrickson, G. H.; Bates, M. W.; Hawker, C. J.; Bates, C. M. Architecture Effects in Complex Spherical Assemblies of (AB)n-Type Block Copolymers. ACS Macro Lett. 2020, 9 (12), 1745–1752.
    (30) Lachmayr, K. K.; Wentz, C. M.; Sita, L. R. An Exceptionally Stable and Scalable Sugar–Polyolefin Frank–Kasper A15 Phase. Angew. Chemie Int. Ed. 2020, 59 (4), 1521–1526.
    (31) Jeon, S.; Jun, T.; Jo, S.; Ahn, H.; Lee, S.; Lee, B.; Ryu, D. Y. Frank–Kasper Phases Identified in PDMS-b-PTFEA Copolymers with High Conformational Asymmetry. Macromol. Rapid Commun. 2019, 40 (19), 1900259.
    (32) Bates, M. W.; Lequieu, J.; Barbon, S. M.; Lewis, R. M.; Delaney, K. T.; Anastasaki, A.; Hawker, C. J.; Fredrickson, G. H.; Bates, C. M. Stability of the A15 Phase in Diblock Copolymer Melts. Proc. Natl. Acad. Sci. 2019, 116 (27), 13194 – 13199.
    (33) Lindsay, A. P.; Jayaraman, A.; Peterson, A. J.; Mueller, A. J.; Weigand, S.; Almdal, K.; Mahanthappa, M. K.; Lodge, T. P.; Bates, F. S. Reevaluation of Poly(Ethylene-Alt-Propylene)-Block-Polydimethylsiloxane Phase Behavior Uncovers Topological Close-Packing and Epitaxial Quasicrystal Growth. ACS Nano 2021.
    (34) Nouri, B.; Chen, C.-Y.; Huang, Y.-S.; Mansel, B. W.; Chen, H.-L. Emergence of a Metastable Laves C14 Phase of Block Copolymer Micelle Bearing a Glassy Core. Macromolecules 2021.
    (35) Mueller, A. J.; Lindsay, A. P.; Jayaraman, A.; Lodge, T. P.; Mahanthappa, M. K.; Bates, F. S. Emergence of a C15 Laves Phase in Diblock Polymer/Homopolymer Blends. ACS Macro Lett. 2020, 9 (4), 576–582.
    (36) Huang, M.; Hsu, C.-H.; Wang, J.; Mei, S.; Dong, X.; Li, Y.; Li, M.; Liu, H.; Zhang, W.; Aida, T.; Zhang, W.-B.; Yue, K.; Cheng, S. Z. D. Selective Assemblies of Giant Tetrahedra via Precisely Controlled Positional Interactions. Science 2015, 348 (6233), 424 – 428.
    (37) Yue, K.; Huang, M.; Marson, R. L.; He, J.; Huang, J.; Zhou, Z.; Wang, J.; Liu, C.; Yan, X.; Wu, K.; Guo, Z.; Liu, H.; Zhang, W.; Ni, P.; Wesdemiotis, C.; Zhang, W.-B.; Glotzer, S. C.; Cheng, S. Z. D. Geometry Induced Sequence of Nanoscale Frank–Kasper and Quasicrystal Mesophases in Giant Surfactants. Proc. Natl. Acad. Sci. 2016, 113 (50), 14195 – 14200.
    (38) Montis, R.; Fusaro, L.; Falqui, A.; Hursthouse, M. B.; Tumanov, N.; Coles, S. J.; Threlfall, T. L.; Horton, P. N.; Sougrat, R.; Lafontaine, A.; Coquerel, G.; Rae, A. D. Complex Structures Arising from the Self-Assembly of a Simple Organic Salt. Nature 2021, 590 (7845), 275–278.
    (39) Dotera, T. Quasicrystals in Soft Matter. Isr. J. Chem. 2011, 51 (11–12), 1197–1205.
    (40) Lindsay, A. P.; Lewis, R. M.; Lee, B.; Peterson, A. J.; Lodge, T. P.; Bates, F. S. A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends. ACS Macro Lett. 2020, 9 (2), 197–203.
    (41) Ziherl, P.; Kamien, R. D. Maximizing Entropy by Minimizing Area:  Towards a New Principle of Self-Organization. J. Phys. Chem. B 2001, 105 (42), 10147–10158.
    (42) Pansu, B.; Sadoc, J.-F. Metallurgy of Soft Spheres with Hard Core: From BCC to Frank-Kasper Phases. Eur. Phys. J. E 2017, 40 (11), 102.
    (43) Grason, G. M. The Packing of Soft Materials: Molecular Asymmetry, Geometric Frustration and Optimal Lattices in Block Copolymer Melts. Phys. Rep. 2006, 433 (1), 1–64.
    (44) Matsen, M. W.; Bates, F. S. Unifying Weak- and Strong-Segregation Block Copolymer Theories. Macromolecules 1996, 29 (4), 1091–1098.
    (45) Matsen, M. W.; Schick, M. Stable and Unstable Phases of a Diblock Copolymer Melt. Phys. Rev. Lett. 1994, 72 (16), 2660–2663.
    (46) Gillard, T. M.; Lee, S.; Bates, F. S. Dodecagonal Quasicrystalline Order in a Diblock Copolymer Melt. Proc. Natl. Acad. Sci. 2016, 113 (19), 5167– 5172.
    (47) Xie, N.; Li, W.; Qiu, F.; Shi, A.-C. σ Phase Formed in Conformationally Asymmetric AB-Type Block Copolymers. ACS Macro Lett. 2014, 3 (9), 906–910.
    (48) Bates, M. W.; Barbon, S. M.; Levi, A. E.; Lewis, R. M.; Beech, H. K.; Vonk, K. M.; Zhang, C.; Fredrickson, G. H.; Hawker, C. J.; Bates, C. M. Synthesis and Self-Assembly of ABn Miktoarm Star Polymers. ACS Macro Lett. 2020, 9 (3), 396–403.
    (49) Schulze, M. W.; Lewis, R. M.; Lettow, J. H.; Hickey, R. J.; Gillard, T. M.; Hillmyer, M. A.; Bates, F. S. Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers. Phys. Rev. Lett. 2017, 118 (20), 207801.
    (50) Lee, S.; Gillard, T. M.; Bates, F. S. Fluctuations, Order, and Disorder in Short Diblock Copolymers. AIChE J. 2013, 59 (9), 3502–3513.
    (51) Reddy, A.; Buckley, M. B.; Arora, A.; Bates, F. S.; Dorfman, K. D.; Grason, G. M. Stable Frank–Kasper Phases of Self-Assembled, Soft Matter Spheres. Proc. Natl. Acad. Sci. 2018, 115 (41), 10233– 10238.
    (52) Lee, S.; Leighton, C.; Bates, F. S. Sphericity and Symmetry Breaking in the Formation of Frank–Kasper Phases from One Component Materials. Proc. Natl. Acad. Sci. 2014, 111 (50), 17723-17731.
    (53) Li, W.; Duan, C.; Shi, A.-C. Nonclassical Spherical Packing Phases Self-Assembled from AB-Type Block Copolymers. ACS Macro Lett. 2017, 6 (11), 1257–1262.
    (54) Qiang, Y.; Li, W.; Shi, A.-C. Stabilizing Phases of Block Copolymers with Gigantic Spheres via Designed Chain Architectures. ACS Macro Lett. 2020, 9 (5), 668–673.
    (55) Zhao, M.; Li, W. Laves Phases Formed in the Binary Blend of AB4 Miktoarm Star Copolymer and A-Homopolymer. Macromolecules 2019, 52 (4), 1832–1842.
    (56) Xie, Q.; Qiang, Y.; Chen, L.; Xia, Y.; Li, W. Synergistic Effect of Stretched Bridging Block and Released Packing Frustration Leads to Exotic Nanostructures. ACS Macro Lett. 2020, 9 (7), 980–984.
    (57) Chen, L.; Qiang, Y.; Li, W. Tuning Arm Architecture Leads to Unusual Phase Behaviors in a (BAB)5 Star Copolymer Melt. Macromolecules 2018, 51 (23), 9890–9900.
    (58) Sun, Y.; Tan, R.; Ma, Z.; Gan, Z.; Li, G.; Zhou, D.; Shao, Y.; Zhang, W.-B.; Zhang, R.; Dong, X.-H. Discrete Block Copolymers with Diverse Architectures: Resolving Complex Spherical Phases with One Monomer Resolution. ACS Cent. Sci. 2020, 6 (8), 1386–1393.
    (59) Chang, A. B.; Bates, F. S. Impact of Architectural Asymmetry on Frank–Kasper Phase Formation in Block Polymer Melts. ACS Nano 2020, 14 (9), 11463–11472.
    (60) Liu, M.; Li, W.; Qiu, F.; Shi, A.-C. Stability of the Frank–Kasper σ-Phase in BABC Linear Tetrablock Terpolymers. Soft Matter 2016, 12 (30), 6412–6421.
    (61) Lewis, R. M.; Arora, A.; Beech, H. K.; Lee, B.; Lindsay, A. P.; Lodge, T. P.; Dorfman, K. D.; Bates, F. S. Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers. Phys. Rev. Lett. 2018, 121 (20), 208002.
    (62) Cheong, G. K.; Bates, F. S.; Dorfman, K. D. Symmetry Breaking in Particle-Forming Diblock Polymer/Homopolymer Blends. Proc. Natl. Acad. Sci. 2020, 117 (29), 16764 – 16769.
    (63) Xie, J.; Shi, A.-C. Formation of Complex Spherical Packing Phases in Diblock Copolymer/Homopolymer Blends. Giant 2021, 5, 100043.
    (64) Liu, M.; Qiang, Y.; Li, W.; Qiu, F.; Shi, A.-C. Stabilizing the Frank-Kasper Phases via Binary Blends of AB Diblock Copolymers. ACS Macro Lett. 2016, 5 (10), 1167–1171.
    (65) Yamamoto, K.; Takagi, H. Frank-Kasper σ and A-15 Phases Formed in Symmetry and Asymmetry Block Copolymer Blend System. Mater. Trans. 2020, advpub.
    (66) Lindsay, A. P.; Cheong, G. K.; Peterson, A. J.; Weigand, S.; Dorfman, K. D.; Lodge, T. P.; Bates, F. S. Complex Phase Behavior in Particle-Forming AB/AB′ Diblock Copolymer Blends with Variable Core Block Lengths. Macromolecules 2021, 54 (15), 7088–7101.
    (67) Yanagioka, M.; Frank, C. Structure, Stability and Applications of Colloidal Crystals. Korea Aust. Rheol. J. 2008, 20, 97–107.
    (68) Gasser, U.; Weeks, E. R.; Schofield, A.; Pusey, P. N.; Weitz, D. A. Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization. Science 2001, 292 (5515), 258– 262.
    (69) Boles, M. A.; Engel, M.; Talapin, D. V. Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials. Chem. Rev. 2016, 116 (18), 11220–11289.
    (70) Ascolani, H.; van der Meijden, M. W.; Cristina, L. J.; Gayone, J. E.; Kellogg, R. M.; Fuhr, J. D.; Lingenfelder, M. Van Der Waals Interactions in the Self-Assembly of 5-Amino[6]Helicene on Cu(100) and Au(111). Chem. Commun. 2014, 50 (90), 13907–13909.
    (71) Gurvinder, S.; Henry, C.; Artem, B.; Elijah, G.; Nikita, R.; Petr, K.; Rafal, K. Self-Assembly of Magnetite Nanocubes into Helical Superstructures. Science 2014, 345 (6201), 1149–1153.
    (72) Lv, Z.-P.; Kapuscinski, M.; Bergström, L. Tunable Assembly of Truncated Nanocubes by Evaporation-Driven Poor-Solvent Enrichment. Nat. Commun. 2019, 10 (1), 4228.
    (73) Sau, T. K.; Murphy, C. J. Self-Assembly Patterns Formed upon Solvent Evaporation of Aqueous Cetyltrimethylammonium Bromide-Coated Gold Nanoparticles of Various Shapes. Langmuir 2005, 21 (7), 2923–2929.
    (74) Shevchenko, E. V; Talapin, D. V. Self-Assembly of Semiconductor Nanocrystals into Ordered Superstructures BT - Semiconductor Nanocrystal Quantum Dots: Synthesis, Assembly, Spectroscopy and Applications; Rogach, A. L., Ed.; Springer Vienna: Vienna, 2008; pp 119–169.
    (75) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Synthesis and Characterization of Monodisperse Nanocrystals and Close-Packed Nanocrystal Assemblies. Annu. Rev. Mater. Sci. 2000, 30 (1), 545–610.
    (76) B., M. C.; R., K. C.; G., B. M. Self-Organization of CdSe Nanocrystallites into Three-Dimensional Quantum Dot Superlattices. Science 1995, 270 (5240), 1335–1338.
    (77) Bruel, C.; Davies, T. S.; Carreau, P. J.; Tavares, J. R.; Heuzey, M.-C. Self-Assembly Behaviors of Colloidal Cellulose Nanocrystals: A Tale of Stabilization Mechanisms. J. Colloid Interface Sci. 2020, 574, 399–409.
    (78) Bigioni, T. P.; Lin, X.-M.; Nguyen, T. T.; Corwin, E. I.; Witten, T. A.; Jaeger, H. M. Kinetically Driven Self Assembly of Highly Ordered Nanoparticle Monolayers. Nat. Mater. 2006, 5 (4), 265–270.
    (79) Lee, B.; Littrell, K.; Sha, Y.; Shevchenko, E. V. Revealing the Effects of the Non-Solvent on the Ligand Shell of Nanoparticles and Their Crystallization. J. Am. Chem. Soc. 2019, 141 (42), 16651–16662.
    (80) Lu, P. J.; Zaccarelli, E.; Ciulla, F.; Schofield, A. B.; Sciortino, F.; Weitz, D. A. Gelation of Particles with Short-Range Attraction. Nature 2008, 453 (7194), 499–503.
    (81) Ge, G.; Brus, L. Evidence for Spinodal Phase Separation in Two-Dimensional Nanocrystal Self-Assembly. J. Phys. Chem. B 2000, 104 (41), 9573–9575.
    (82) Witten, T. A.; Sander, L. M. Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon. Phys. Rev. Lett. 1981, 47 (19), 1400–1403.
    (83) Wang, L.; Albouy, P.-A.; Pileni, M.-P. Synthesis and Self-Assembly Behavior of Charged Au Nanocrystals in Aqueous Solution. Chem. Mater. 2015, 27 (12), 4431–4440.
    (84) Bian, T.; Gardin, A.; Gemen, J.; Houben, L.; Perego, C.; Lee, B.; Elad, N.; Chu, Z.; Pavan, G. M.; Klajn, R. Electrostatic Co-Assembly of Nanoparticles with Oppositely Charged Small Molecules into Static and Dynamic Superstructures. Nat. Chem. 2021, 13 (10), 940–949.
    (85) Curk, T.; Luijten, E. Charge Regulation Effects in Nanoparticle Self-Assembly. Phys. Rev. Lett. 2021, 126 (13), 138003.
    (86) Kazes, M.; Udayabhaskararao, T.; Dey, S.; Oron, D. Effect of Surface Ligands in Perovskite Nanocrystals: Extending in and Reaching Out. Acc. Chem. Res. 2021, 54 (6), 1409–1418.
    (87) Luo, Y.; Zhao, R.; Pendry, J. B. Van Der Waals Interactions at the Nanoscale: The Effects of Nonlocality. Proc. Natl. Acad. Sci. 2014, 111 (52), 18422 LP – 18427.
    (88) Parsegian, V. A. Van Der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists; Cambridge University Press: Cambridge, 2005.
    (89) Alberto, A.; Nicola, F.; A., D. R.; Alexandre, T. Wavelike Charge Density Fluctuations and van Der Waals Interactions at the Nanoscale. Science 2016, 351 (6278), 1171–1176.
    (90) Hamaker, H. C. The London—van Der Waals Attraction between Spherical Particles. Physica 1937, 4 (10), 1058–1072.
    (91) Intermolecular and Surface Forces; Israelachvili, J. N. B. T.-I. and S. F. (Third E., Ed.; Academic Press: Boston, 2011.
    (92) Napper, D. H. Steric Stabilization. J. Colloid Interface Sci. 1977, 58 (2), 390–407.
    (93) Hajiw, S.; Pansu, B.; Sadoc, J.-F. Evidence for a C14 Frank–Kasper Phase in One-Size Gold Nanoparticle Superlattices. ACS Nano 2015, 9 (8), 8116–8121.
    (94) Schmitt, J.; Hajiw, S.; Lecchi, A.; Degrouard, J.; Salonen, A.; Impéror-Clerc, M.; Pansu, B. Formation of Superlattices of Gold Nanoparticles Using Ostwald Ripening in Emulsions: Transition from Fcc to Bcc Structure. J. Phys. Chem. B 2016, 120 (25), 5759–5766.
    (95) Boles, M. A.; Talapin, D. V. Self-Assembly of Tetrahedral CdSe Nanocrystals: Effective “Patchiness” via Anisotropic Steric Interaction. J. Am. Chem. Soc. 2014, 136 (16), 5868–5871.
    (96) Yang, W.; Zhong, Y.; He, C.; Peng, S.; Yang, Y.; Qi, F.; Feng, P.; Shuai, C. Electrostatic Self-Assembly of PFe3O4 Nanoparticles on Graphene Oxide: A Co-Dispersed Nanosystem Reinforces PLLA Scaffolds. J. Adv. Res. 2020, 24, 191–203.
    (97) Mau, S.-C.; Huse, D. A. Stacking Entropy of Hard-Sphere Crystals. Phys. Rev. E 1999, 59 (4), 4396–4401.
    (98) Hone, D.; Alexander, S.; Chaikin, P. M.; Pincus, P. The Phase Diagram of Charged Colloidal Suspensions. J. Chem. Phys. 1983, 79 (3), 1474–1479.
    (99) Kremer, K.; Robbins, M. O.; Grest, G. S. Phase Diagram of Yukawa Systems: Model for Charge-Stabilized Colloids. Phys. Rev. Lett. 1986, 57 (21), 2694–2697.
    (100) Cochran, T. W.; Chiew, Y. C. Thermodynamic and Structural Properties of Repulsive Hard-Core Yukawa Fluid: Integral Equation Theory, Perturbation Theory and Monte Carlo Simulations. J. Chem. Phys. 2004, 121 (3), 1480–1486.
    (101) Ziherl, P.; Kamien, R. D. Soap Froths and Crystal Structures. Phys. Rev. Lett. 2000, 85 (16), 3528–3531.
    (102) Weaire, D.; Phelan, R. A Counter-Example to Kelvin’s Conjecture on Minimal Surfaces. Philos. Mag. Lett. 1994, 69 (2), 107–110.
    (103) Goodfellow, B. W.; Yu, Y.; Bosoy, C. A.; Smilgies, D.-M.; Korgel, B. A. The Role of Ligand Packing Frustration in Body-Centered Cubic (Bcc) Superlattices of Colloidal Nanocrystals. J. Phys. Chem. Lett. 2015, 6 (13), 2406–2412.
    (104) Yun, H.; Paik, T. Colloidal Self-Assembly of Inorganic Nanocrystals into Superlattice Thin-Films and Multiscale Nanostructures. Nanomaterials . 2019.
    (105) Goodfellow, B. W.; Korgel, B. A. Reversible Solvent Vapor-Mediated Phase Changes in Nanocrystal Superlattices. ACS Nano 2011, 5 (4), 2419–2424.
    (106) Bian, K.; Choi, J. J.; Kaushik, A.; Clancy, P.; Smilgies, D.-M.; Hanrath, T. Shape-Anisotropy Driven Symmetry Transformations in Nanocrystal Superlattice Polymorphs. ACS Nano 2011, 5 (4), 2815–2823.
    (107) Schulz, F.; Pavelka, O.; Lehmkühler, F.; Westermeier, F.; Okamura, Y.; Mueller, N. S.; Reich, S.; Lange, H. Structural Order in Plasmonic Superlattices. Nat. Commun. 2020, 11 (1), 3821.
    (108) Evers, W. H.; Nijs, B. De; Filion, L.; Castillo, S.; Dijkstra, M.; Vanmaekelbergh, D. Entropy-Driven Formation of Binary Semiconductor-Nanocrystal Superlattices. Nano Lett. 2010, 10 (10), 4235–4241.
    (109) Whetten, R. L.; Shafigullin, M. N.; Khoury, J. T.; Schaaff, T. G.; Vezmar, I.; Alvarez, M. M.; Wilkinson, A. Crystal Structures of Molecular Gold Nanocrystal Arrays. Acc. Chem. Res. 1999, 32 (5), 397–406.
    (110) Korgel, B. A.; Fitzmaurice, D. Small-Angle x-Ray-Scattering Study of Silver-Nanocrystal Disorder-Order Phase Transitions. Phys. Rev. B 1999, 59 (22), 14191–14201.
    (111) Pusey, P. Liquids, Freezing and Glass Transition. Les Houches Sess. 51, 1989 1991, 765–942.
    (112) Zaccarelli, E.; Valeriani, C.; Sanz, E.; Poon, W. C. K.; Cates, M. E.; Pusey, P. N. Crystallization of Hard-Sphere Glasses. Phys. Rev. Lett. 2009, 103 (13), 135704.
    (113) Hermes, M.; Dijkstra, M. Jamming of Polydisperse Hard Spheres: The Effect of Kinetic Arrest. EPL (Europhysics Lett. 2010, 89 (3), 38005.
    (114) Mari, R.; Krzakala, F.; Kurchan, J. Jamming versus Glass Transitions. Phys. Rev. Lett. 2009, 103 (2), 25701.
    (115) Sollich, P.; Wilding, N. B. Crystalline Phases of Polydisperse Spheres. Phys. Rev. Lett. 2010, 104 (11), 118302.
    (116) Fasolo, M.; Sollich, P. Fractionation Effects in Phase Equilibria of Polydisperse Hard-Sphere Colloids. Phys. Rev. E 2004, 70 (4), 41410.
    (117) Kose, A.; Ozaki, M.; Takano, K.; Kobayashi, Y.; Hachisu, S. Direct Observation of Ordered Latex Suspension by Metallurgical Microscope. J. Colloid Interface Sci. 1973, 44 (2), 330–338.
    (118) Pusey, P. N.; van Megen, W. Phase Behaviour of Concentrated Suspensions of Nearly Hard Colloidal Spheres. Nature 1986, 320 (6060), 340–342.
    (119) Yethiraj, A.; van Blaaderen, A. A Colloidal Model System with an Interaction Tunable from Hard Sphere to Soft and Dipolar. Nature 2003, 421 (6922), 513–517.
    (120) Sear, R. P. Phase Separation and Crystallisation of Polydisperse Hard Spheres. Europhys. Lett. 1998, 44 (4), 531–535.
    (121) Bartlett, P. Fractionated Crystallization in a Polydisperse Mixture of Hard Spheres. J. Chem. Phys. 1998, 109 (24), 10970–10975.
    (122) Wang, K.; Li, F.; Jin, S.-M.; Wang, K.; Tian, D.; Hussain, M.; Xu, J.; Zhang, L.; Liao, Y.; Lee, E.; Yi, G.-R.; Xie, X.; Zhu, J. Chain-Length Effect on Binary Superlattices of Polymer-Tethered Nanoparticles. Mater. Chem. Front. 2020, 4 (7), 2089–2095.
    (123) Wei, J.; Schaeffer, N.; Pileni, M.-P. Ligand Exchange Governs the Crystal Structures in Binary Nanocrystal Superlattices. J. Am. Chem. Soc. 2015, 137 (46), 14773–14784.
    (124) Yoshimura, S.; Hachisu, S. Order Formation in Binary Mixtures of Monodisperse Latices BT - Frontiers in Colloid Science In Memoriam Professor Dr. Bun-Ichi Tamamushi; Nakagaski, M., Shinoda, K., Matijević, E., Eds.; Steinkopff: Darmstadt, 1983; 59–70.
    (125) Bartlett, P.; Ottewill, R. H.; Pusey, P. N. Superlattice Formation in Binary Mixtures of Hard-Sphere Colloids. Phys. Rev. Lett. 1992, 68 (25), 3801–3804.
    (126) TRIZAC, B. E.; MADDEN, M. D. E. and P. A. Stability of the AB Crystal for Asymmetric Binary Hard Sphere Mixtures. Mol. Phys. 1997, 90 (4), 675–678.
    (127) Shevchenko, E. V; Talapin, D. V; Murray, C. B.; O’Brien, S. Structural Characterization of Self-Assembled Multifunctional Binary Nanoparticle Superlattices. J. Am. Chem. Soc. 2006, 128 (11), 3620–3637.
    (128) Shevchenko, E. V; Talapin, D. V; Kotov, N. A.; O’Brien, S.; Murray, C. B. Structural Diversity in Binary Nanoparticle Superlattices. Nature 2006, 439 (7072), 55–59.
    (129) Ye, X.; Zhu, C.; Ercius, P.; Raja, S. N.; He, B.; Jones, M. R.; Hauwiller, M. R.; Liu, Y.; Xu, T.; Alivisatos, A. P. Structural Diversity in Binary Superlattices Self-Assembled from Polymer-Grafted Nanocrystals. Nat. Commun. 2015, 6 (1), 10052.
    (130) Hynninen, A.-P.; Filion, L.; Dijkstra, M. Stability of LS and LS2 Crystal Structures in Binary Mixtures of Hard and Charged Spheres. J. Chem. Phys. 2009, 131 (6), 64902.
    (131) Hopkins, A. B.; Stillinger, F. H.; Torquato, S. Densest Binary Sphere Packings. Phys. Rev. E 2012, 85 (2), 21130.
    (132) Lindquist, B. A.; Jadrich, R. B.; Truskett, T. M. Communication: From Close-Packed to Topologically Close-Packed: Formation of Laves Phases in Moderately Polydisperse Hard-Sphere Mixtures. J. Chem. Phys. 2018, 148 (19), 191101.
    (133) Sollich, P.; Warren, P. B.; Cates, M. E. Moment Free Energies for Polydisperse Systems. Advances in Chemical Physics. January 1, 2001, 265–336.
    (134) Bareigts, G.; Kiatkirakajorn, P.-C.; Li, J.; Botet, R.; Sztucki, M.; Cabane, B.; Goehring, L.; Labbez, C. Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters. Phys. Rev. Lett. 2020, 124 (5), 58003.
    (135) Cabane, B.; Li, J.; Artzner, F.; Botet, R.; Labbez, C.; Bareigts, G.; Sztucki, M.; Goehring, L. Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations. Phys. Rev. Lett. 2016, 116 (20), 208001.
    (136) Fasolo, M.; Sollich, P. Equilibrium Phase Behavior of Polydisperse Hard Spheres. Phys. Rev. Lett. 2003, 91 (6), 68301.
    (137) Botet, R.; Cabane, B.; Goehring, L.; Li, J.; Artzner, F. How Do Polydisperse Repulsive Colloids Crystallize? Faraday Discuss. 2016, 186 (0), 229–240.
    (138) Leff, D. V; Brandt, L.; Heath, J. R. Synthesis and Characterization of Hydrophobic, Organically-Soluble Gold Nanocrystals Functionalized with Primary Amines. Langmuir 1996, 12 (20), 4723–4730.
    (139) Murray, C. B.; Norris, D. J.; Bawendi, M. G. Synthesis and Characterization of Nearly Monodisperse CdE (E = Sulfur, Selenium, Tellurium) Semiconductor Nanocrystallites. J. Am. Chem. Soc. 1993, 115 (19), 8706–8715.
    (140) Boles, M. A.; Talapin, D. V. Many-Body Effects in Nanocrystal Superlattices: Departure from Sphere Packing Explains Stability of Binary Phases. J. Am. Chem. Soc. 2015, 137 (13), 4494–4502.
    (141) Salerno, K. M.; Ismail, A. E.; Lane, J. M. D.; Grest, G. S. Coating Thickness and Coverage Effects on the Forces between Silica Nanoparticles in Water. J. Chem. Phys. 2014, 140 (19), 194904.
    (142) Kaushik, A. P.; Clancy, P. Explicit All-Atom Modeling of Realistically Sized Ligand-Capped Nanocrystals. J. Chem. Phys. 2012, 136 (11), 114702.
    (143) Zha, X.; Travesset, A. Thermodynamic Equilibrium of Binary Nanocrystal Superlattices. J. Phys. Chem. C 2021, 125 (34), 18936–18945.
    (144) Djebaili, T.; Richardi, J.; Abel, S.; Marchi, M. Atomistic Simulations of the Surface Coverage of Large Gold Nanocrystals. J. Phys. Chem. C 2013, 117 (34), 17791–17800.
    (145) Landman, U.; Luedtke, W. D. Small Is Different: Energetic, Structural, Thermal, and Mechanical Properties of Passivated Nanocluster Assemblies. Faraday Discuss. 2004, 125 (0), 1–22.
    (146) Schapotschnikow, P.; Vlugt, T. J. H. Understanding Interactions between Capped Nanocrystals: Three-Body and Chain Packing Effects. J. Chem. Phys. 2009, 131 (12), 124705.
    (147) Travesset, A. Topological Structure Prediction in Binary Nanoparticle Superlattices. Soft Matter 2017, 13 (1), 147–157.
    (148) Coropceanu, I.; Boles, M. A.; Talapin, D. V. Systematic Mapping of Binary Nanocrystal Superlattices: The Role of Topology in Phase Selection. J. Am. Chem. Soc. 2019, 141 (14), 5728–5740.
    (149) Travesset, A. Soft Skyrmions, Spontaneous Valence and Selection Rules in Nanoparticle Superlattices. ACS Nano 2017, 11 (6), 5375–5382.
    (150) Waltmann, T.; Waltmann, C.; Horst, N.; Travesset, A. Many Body Effects and Icosahedral Order in Superlattice Self-Assembly. J. Am. Chem. Soc. 2018, 140 (26), 8236–8245.

    Chapter 2

    (1) Yanagioka, M.; Frank, C. Structure, Stability and Applications of Colloidal Crystals. Korea Aust. Rheol. J. 2008, 20, 97–107.
    (2) Boles, M. A.; Engel, M.; Talapin, D. V. Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials. Chem. Rev. 2016, 116 (18), 11220–11289.
    (3) Gasser, U.; Weeks, E. R.; Schofield, A.; Pusey, P. N.; Weitz, D. A. Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization. Science 2001, 292 (5515), 258 – 262.
    (4) Frenkel, D.; Ladd, A. J. C. New Monte Carlo Method to Compute the Free Energy of Arbitrary Solids. Application to the Fcc and Hcp Phases of Hard Spheres. J. Chem. Phys. 1984, 81 (7), 3188–3193.
    (5) Woodcock, L. V. Entropy Difference between the Face-Centred Cubic and Hexagonal Close-Packed Crystal Structures. Nature 1997, 385 (6612), 141–143.
    (6) Mau, S.-C.; Huse, D. A. Stacking Entropy of Hard-Sphere Crystals. Phys. Rev. E 1999, 59 (4), 4396–4401.
    (7) Singh, J. P.; Walsh, S. D. C.; Koch, D. L. Brownian Dynamics of a Suspension of Particles with Constrained Voronoi Cell Volumes. Langmuir 2015, 31 (24), 6829–6841.
    (8) Deza, M.; Sikirić, M. D. Voronoi Polytopes for Polyhedral Norms on Lattices. Discret. Appl. Math. 2015, 197, 42–52.
    (9) Lucarini, V. Symmetry-Break in Voronoi Tessellations. Symmetry, 2009, 1(1), 21-54.
    (10) Lifshitz, R.; Diamant, H. Soft Quasicrystals–Why Are They Stable? Philos. Mag. 2007, 87 (18–21), 3021–3030.
    (11) Huang, M.; Yue, K.; Wang, J.; Hsu, C.-H.; Wang, L.; Cheng, S. Z. D. Frank-Kasper and Related Quasicrystal Spherical Phases in Macromolecules. Sci. China Chem. 2018, 61 (1), 33–45.
    (12) Liu, Y.; Liu, T.; Yan, X.; Guo, Q.-Y.; Wang, J.; Zhang, R.; Zhang, S.; Su, Z.; Huang, J.; Liu, G.-X.; Zhang, W.; Zhang, W.; Aida, T.; Yue, K.; Huang, M.; Cheng, S. Z. D. Mesoatom Alloys via Self-Sorting Approach of Giant Molecules Blends. Giant 2020, 4, 100031.
    (13) Frank, F. C.; Kasper, J. S. Complex Alloy Structures Regarded as Sphere Packings. I. Definitions and Basic Principles. Acta Crystallogr. 1958, 11 (3), 184–190.
    (14) Talapin, D. V; Shevchenko, E. V; Bodnarchuk, M. I.; Ye, X.; Chen, J.; Murray, C. B. Quasicrystalline Order in Self-Assembled Binary Nanoparticle Superlattices. Nature 2009, 461 (7266), 964–967.
    (15) Huang, M.; Hsu, C.-H.; Wang, J.; Mei, S.; Dong, X.; Li, Y.; Li, M.; Liu, H.; Zhang, W.; Aida, T.; Zhang, W.-B.; Yue, K.; Cheng, S. Z. D. Selective Assemblies of Giant Tetrahedra via Precisely Controlled Positional Interactions. Science 2015, 348 (6233), 424 – 428.
    (16) Yue, K.; Huang, M.; Marson, R. L.; He, J.; Huang, J.; Zhou, Z.; Wang, J.; Liu, C.; Yan, X.; Wu, K.; Guo, Z.; Liu, H.; Zhang, W.; Ni, P.; Wesdemiotis, C.; Zhang, W.-B.; Glotzer, S. C.; Cheng, S. Z. D. Geometry Induced Sequence of Nanoscale Frank–Kasper and Quasicrystal Mesophases in Giant Surfactants. Proc. Natl. Acad. Sci. 2016, 113 (50), 14195 – 14200.
    (17) Su, Z.; Hsu, C.-H.; Gong, Z.; Feng, X.; Huang, J.; Zhang, R.; Wang, Y.; Mao, J.; Wesdemiotis, C.; Li, T.; Seifert, S.; Zhang, W.; Aida, T.; Huang, M.; Cheng, S. Z. D. Identification of a Frank–Kasper Z Phase from Shape Amphiphile Self-Assembly. Nat. Chem. 2019, 11 (10), 899–905.
    (18) Lee, S.; Bluemle, M. J.; Bates, F. S. Discovery of a Frank-Kasper σ Phase in Sphere-Forming Block Copolymer Melts. Science 2010, 330 (6002), 349 LP – 353.
    (19) Kim, K.; Schulze, M. W.; Arora, A.; Lewis, R. M.; Hillmyer, M. A.; Dorfman, K. D.; Bates, F. S. Thermal Processing of Diblock Copolymer Melts Mimics Metallurgy. Science (80-. ). 2017, 356 (6337), 520 LP – 523.
    (20) Jeon, S.; Jun, T.; Jo, S.; Ahn, H.; Lee, S.; Lee, B.; Ryu, D. Y. Frank–Kasper Phases Identified in PDMS-b-PTFEA Copolymers with High Conformational Asymmetry. Macromol. Rapid Commun. 2019, 40 (19), 1900259.
    (21) Schulze, M. W.; Lewis, R. M.; Lettow, J. H.; Hickey, R. J.; Gillard, T. M.; Hillmyer, M. A.; Bates, F. S. Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers. Phys. Rev. Lett. 2017, 118 (20), 207801.
    (22) Lachmayr, K. K.; Wentz, C. M.; Sita, L. R. An Exceptionally Stable and Scalable Sugar–Polyolefin Frank–Kasper A15 Phase. Angew. Chemie Int. Ed. 2020, 59 (4), 1521–1526.
    (23) Liew, C. Y.; Salim, M.; Zahid, N. I.; Hashim, R. Biomass Derived Xylose Guerbet Surfactants: Thermotropic and Lyotropic Properties from Small-Angle X-Ray Scattering. RSC Adv. 2015, 5 (120), 99125–99132.
    (24) Kim, S. A.; Jeong, K.-J.; Yethiraj, A.; Mahanthappa, M. K. Low-Symmetry Sphere Packings of Simple Surfactant Micelles Induced by Ionic Sphericity. Proc. Natl. Acad. Sci. 2017, 114 (16), 4072 – 4077.
    (25) Lee, S.; Leighton, C.; Bates, F. S. Sphericity and Symmetry Breaking in the Formation of Frank–Kasper Phases from One Component Materials. Proc. Natl. Acad. Sci. 2014, 111 (50), 17723-17731.
    (26) Lindquist, B. A.; Jadrich, R. B.; Piñeros, W. D.; Truskett, T. M. Inverse Design of Self-Assembling Frank-Kasper Phases and Insights Into Emergent Quasicrystals. J. Phys. Chem. B 2018, 122 (21), 5547–5556.
    (27) Kim, K.; Arora, A.; Lewis, R. M.; Liu, M.; Li, W.; Shi, A.-C.; Dorfman, K. D.; Bates, F. S. Origins of Low-Symmetry Phases in Asymmetric Diblock Copolymer Melts. Proc. Natl. Acad. Sci. 2018, 115 (5), 847 – 854.
    (28) Reddy, A.; Buckley, M. B.; Arora, A.; Bates, F. S.; Dorfman, K. D.; Grason, G. M. Stable Frank–Kasper Phases of Self-Assembled, Soft Matter Spheres. Proc. Natl. Acad. Sci. 2018, 115 (41), 10233 – 10238.
    (29) Ziherl, P.; Kamien, R. D. Maximizing Entropy by Minimizing Area:  Towards a New Principle of Self-Organization. J. Phys. Chem. B 2001, 105 (42), 10147–10158.
    (30) James E. Mark. Polymer Data Handbook; Oxford University Press Inc, 1999.
    (31) Zha, W.; Han, C. D.; Lee, D. H.; Han, S. H.; Kim, J. K.; Kang, J. H.; Park, C. Origin of the Difference in Order−Disorder Transition Temperature between Polystyrene-Block-Poly(2-Vinylpyridine) and Polystyrene-Block-Poly(4-Vinylpyridine) Copolymers. Macromolecules 2007, 40 (6), 2109–2119.
    (32) Lindsay, A. P.; Jayaraman, A.; Peterson, A. J.; Mueller, A. J.; Weigand, S.; Almdal, K.; Mahanthappa, M. K.; Lodge, T. P.; Bates, F. S. Reevaluation of Poly(Ethylene-Alt-Propylene)-Block-Polydimethylsiloxane Phase Behavior Uncovers Topological Close-Packing and Epitaxial Quasicrystal Growth. ACS Nano 2021.
    (33) Chanpuriya, S.; Kim, K.; Zhang, J.; Lee, S.; Arora, A.; Dorfman, K. D.; Delaney, K. T.; Fredrickson, G. H.; Bates, F. S. Cornucopia of Nanoscale Ordered Phases in Sphere-Forming Tetrablock Terpolymers. ACS Nano 2016, 10 (5), 4961–4972.
    (34) Mueller, A. J.; Lindsay, A. P.; Jayaraman, A.; Lodge, T. P.; Mahanthappa, M. K.; Bates, F. S. Quasicrystals and Their Approximants in a Crystalline–Amorphous Diblock Copolymer. Macromolecules 2021, 54 (6), 2647–2660.
    (35) Timothy P. Lodge, P. C. H. Polymer Chemistry, 3rd ed.; Taylor & Francis Group, 2020.
    (36) Zhang, J.; Bates, F. S. Dodecagonal Quasicrystalline Morphology in a Poly(Styrene-b-Isoprene-b-Styrene-b-Ethylene Oxide) Tetrablock Terpolymer. J. Am. Chem. Soc. 2012, 134 (18), 7636–7639.
    (37) Gillard, T. M.; Lee, S.; Bates, F. S. Dodecagonal Quasicrystalline Order in a Diblock Copolymer Melt. Proc. Natl. Acad. Sci. 2016, 113 (19), 5167 – 5172.
    (38) Bates, M. W.; Lequieu, J.; Barbon, S. M.; Lewis, R. M.; Delaney, K. T.; Anastasaki, A.; Hawker, C. J.; Fredrickson, G. H.; Bates, C. M. Stability of the A15 Phase in Diblock Copolymer Melts. Proc. Natl. Acad. Sci. 2019, 116 (27), 13194 – 13199.
    (39) Takagi, H.; Yamamoto, K. Phase Boundary of Frank–Kasper σ Phase in Phase Diagrams of Binary Mixtures of Block Copolymers and Homopolymers. Macromolecules 2019, 52 (5), 2007–2014.
    (40) Stukowski, A. Visualization and Analysis of Atomistic Simulation Data with OVITO-the Open Visualization Tool. Model. Simul. Mater. Sci. Eng. 2010, 18 (1).
    (41) Hajiw, S.; Pansu, B.; Sadoc, J.-F. Evidence for a C14 Frank–Kasper Phase in One-Size Gold Nanoparticle Superlattices. ACS Nano 2015, 9 (8), 8116–8121.
    (42) Pansu, B.; Sadoc, J.-F. Metallurgy of Soft Spheres with Hard Core: From BCC to Frank-Kasper Phases. Eur. Phys. J. E 2017, 40 (11), 102.
    (43) Grieser, F.; Healy, T. W.; Hsu, W. P.; Kratohvil, J. P.; Warr, G. G. The Micelle Size Distribution of Nonionic Surfactants Determined by Ultrafiltration. Colloids and Surfaces 1989, 42 (1), 97–112.
    (44) Takagi, H.; Sugino, Y.; Hara, S.; Yamamoto, K.; Shimada, S. Non-Equilibrium Disordered Micelles Observed after Melting of Crystalline-Amorphous Alternating Lamellar Structure in Crystalline-Amorphous Block Copolymers Forming Spherical Morphology. Colloid Polym. Sci. 2016, 294 (6), 993–999.
    (45) Tanford, C. Thermodynamics of Micelle Formation: Prediction of Micelle Size and Size Distribution. Proc. Natl. Acad. Sci. 1974, 71 (5), 1811 – 1815.
    (46) Kakde, D.; Taresco, V.; Bansal, K. K.; Magennis, E. P.; Howdle, S. M.; Mantovani, G.; Irvine, D. J.; Alexander, C. Amphiphilic Block Copolymers from a Renewable ε-Decalactone Monomer: Prediction and Characterization of Micellar Core Effects on Drug Encapsulation and Release. J. Mater. Chem. B 2016, 4 (44), 7119–7129.
    (47) Grason, G. M. The Packing of Soft Materials: Molecular Asymmetry, Geometric Frustration and Optimal Lattices in Block Copolymer Melts. Phys. Rep. 2006, 433 (1), 1–64.
    (48) Cui, L.; Wang, H.; Ding, Y.; Han, Y. Tunable Ordered Droplets Induced by Convection in Phase-Separating P2VP/PS Blend Film. Polymer (Guildf). 2004, 45 (24), 8139–8146.
    (49) Jeong, J. W.; Park, W. I.; Kim, M.-J.; Ross, C. A.; Jung, Y. S. Highly Tunable Self-Assembled Nanostructures from a Poly(2-Vinylpyridine-b-Dimethylsiloxane) Block Copolymer. Nano Lett. 2011, 11 (10), 4095–4101.
    (50) Jeong, S.-J.; Kim, J. Y.; Kim, B. H.; Moon, H.-S.; Kim, S. O. Directed Self-Assembly of Block Copolymers for next Generation Nanolithography. Mater. Today 2013, 16 (12), 468–476.
    (51) Mieczkowski, R. The Determination of the Solubility Parameter Components of Polystyrene by Partial Specific Volume Measurements. Eur. Polym. J. 1988, 24 (12), 1185–1189.
    (52) Mieczkowski, R. Solubility Parameter Components of Some Polyols. Eur. Polym. J. 1991, 27 (4), 377–379.
    (53) Lindquist, B. A.; Jadrich, R. B.; Truskett, T. M. Communication: From Close-Packed to Topologically Close-Packed: Formation of Laves Phases in Moderately Polydisperse Hard-Sphere Mixtures. J. Chem. Phys. 2018, 148 (19), 191101.
    (54) Hasaka, M.; Nakashima, H.; Oki, K. Structure of the Laves Phase Observed in Polystyrene Latexes. Trans. Japan Inst. Met. 1984, 25 (2), 65–72.
    (55) Cabane, B.; Li, J.; Artzner, F.; Botet, R.; Labbez, C.; Bareigts, G.; Sztucki, M.; Goehring, L. Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations. Phys. Rev. Lett. 2016, 116 (20), 208001.
    (56) Xie, J.; Shi, A.-C. Formation of Complex Spherical Packing Phases in Diblock Copolymer/Homopolymer Blends. Giant 2021, 5, 100043.
    (57) Liu, M.; Qiang, Y.; Li, W.; Qiu, F.; Shi, A.-C. Stabilizing the Frank-Kasper Phases via Binary Blends of AB Diblock Copolymers. ACS Macro Lett. 2016, 5 (10), 1167–1171.
    (58) Cheong, G. K.; Bates, F. S.; Dorfman, K. D. Symmetry Breaking in Particle-Forming Diblock Polymer/Homopolymer Blends. Proc. Natl. Acad. Sci. 2020, 117 (29), 16764 – 16769.
    (59) Mueller, A. J.; Lindsay, A. P.; Jayaraman, A.; Lodge, T. P.; Mahanthappa, M. K.; Bates, F. S. Emergence of a C15 Laves Phase in Diblock Polymer/Homopolymer Blends. ACS Macro Lett. 2020, 9 (4), 576–582.

    Chapter 3
    (1) Huang, M.; Yue, K.; Wang, J.; Hsu, C.-H.; Wang, L.; Cheng, S. Z. D. Frank-Kasper and Related Quasicrystal Spherical Phases in Macromolecules. Sci. China Chem. 2018, 61 (1), 33–45.
    (2) Lee, S.; Bluemle, M. J.; Bates, F. S. Discovery of a Frank-Kasper σ Phase in Sphere-Forming Block Copolymer Melts. Science 2010, 330 (6002), 349 – 353.
    (3) Frank, F. C.; Kasper, J. S. Complex Alloy Structures Regarded as Sphere Packings. II. Analysis and Classification of Representative Structures. Acta Crystallogr. 1959, 12 (7), 483–499.
    (4) Frank, F. C.; Kasper, J. S. Complex Alloy Structures Regarded as Sphere Packings. I. Definitions and Basic Principles. Acta Crystallogr. 1958, 11 (3), 184–190.
    (5) Cabane, B.; Li, J.; Artzner, F.; Botet, R.; Labbez, C.; Bareigts, G.; Sztucki, M.; Goehring, L. Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations. Phys. Rev. Lett. 2016, 116 (20), 208001.
    (6) Bareigts, G.; Kiatkirakajorn, P.-C.; Li, J.; Botet, R.; Sztucki, M.; Cabane, B.; Goehring, L.; Labbez, C. Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters. Phys. Rev. Lett. 2020, 124 (5), 58003.
    (7) Goran, U.; Yongsong, L.; Xiangbing, Z.; Virgil, P.; Wook-Dong, C. Giant Supramolecular Liquid Crystal Lattice. Science 2003, 299 (5610), 1208–1211.
    (8) Kim, S. A.; Jeong, K.-J.; Yethiraj, A.; Mahanthappa, M. K. Low-Symmetry Sphere Packings of Simple Surfactant Micelles Induced by Ionic Sphericity. Proc. Natl. Acad. Sci. 2017, 114 (16), 4072 – 4077.
    (9) Kim, K.; Schulze, M. W.; Arora, A.; Lewis, R. M.; Hillmyer, M. A.; Dorfman, K. D.; Bates, F. S. Thermal Processing of Diblock Copolymer Melts Mimics Metallurgy. Science (80-. ). 2017, 356 (6337), 520 – 523.
    (10) Mueller, A. J.; Lindsay, A. P.; Jayaraman, A.; Lodge, T. P.; Mahanthappa, M. K.; Bates, F. S. Quasicrystals and Their Approximants in a Crystalline–Amorphous Diblock Copolymer. Macromolecules 2021, 54 (6), 2647–2660.
    (11) Jeon, S.; Jun, T.; Jeon, H. Il; Ahn, H.; Lee, S.; Lee, B.; Ryu, D. Y. Various Low-Symmetry Phases in High-χ and Conformationally Asymmetric PDMS- b -PTFEA Copolymers . Macromolecules 2021.
    (12) Takagi, H.; Yamamoto, K. Phase Boundary of Frank–Kasper σ Phase in Phase Diagrams of Binary Mixtures of Block Copolymers and Homopolymers. Macromolecules 2019, 52 (5), 2007–2014.
    (13) Lachmayr, K. K.; Wentz, C. M.; Sita, L. R. An Exceptionally Stable and Scalable Sugar–Polyolefin Frank–Kasper A15 Phase. Angew. Chemie Int. Ed. 2020, 59 (4), 1521–1526.
    (14) Montis, R.; Fusaro, L.; Falqui, A.; Hursthouse, M. B.; Tumanov, N.; Coles, S. J.; Threlfall, T. L.; Horton, P. N.; Sougrat, R.; Lafontaine, A.; Coquerel, G.; Rae, A. D. Complex Structures Arising from the Self-Assembly of a Simple Organic Salt. Nature 2021, 590 (7845), 275–278.
    (15) Lee, S.; Leighton, C.; Bates, F. S. Sphericity and Symmetry Breaking in the Formation of Frank–Kasper Phases from One Component Materials. Proc. Natl. Acad. Sci. 2014, 111 (50), 17723-17731.
    (16) Dutour Sikirić, M.; Delgado-Friedrichs, O.; Deza, M. Space Fullerenes: A Computer Search for New Frank-Kasper Structures. Acta Crystallogr. Sect. A 2010, 66 (5), 602–615.
    (17) Su, Z.; Hsu, C.-H.; Gong, Z.; Feng, X.; Huang, J.; Zhang, R.; Wang, Y.; Mao, J.; Wesdemiotis, C.; Li, T.; Seifert, S.; Zhang, W.; Aida, T.; Huang, M.; Cheng, S. Z. D. Identification of a Frank–Kasper Z Phase from Shape Amphiphile Self-Assembly. Nat. Chem. 2019, 11 (10), 899–905.
    (18) Xie, N.; Li, W.; Qiu, F.; Shi, A.-C. σ Phase Formed in Conformationally Asymmetric AB-Type Block Copolymers. ACS Macro Lett. 2014, 3 (9), 906–910.
    (19) Liu, M.; Qiang, Y.; Li, W.; Qiu, F.; Shi, A.-C. Stabilizing the Frank-Kasper Phases via Binary Blends of AB Diblock Copolymers. ACS Macro Lett. 2016, 5 (10), 1167–1171.
    (20) Grason, G. M. The Packing of Soft Materials: Molecular Asymmetry, Geometric Frustration and Optimal Lattices in Block Copolymer Melts. Phys. Rep. 2006, 433 (1), 1–64.
    (21) Schulze, M. W.; Lewis, R. M.; Lettow, J. H.; Hickey, R. J.; Gillard, T. M.; Hillmyer, M. A.; Bates, F. S. Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers. Phys. Rev. Lett. 2017, 118 (20), 207801.
    (22) Lindsay, A. P.; Lewis, R. M.; Lee, B.; Peterson, A. J.; Lodge, T. P.; Bates, F. S. A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends. ACS Macro Lett. 2020, 9 (2), 197–203.
    (23) Reddy, A.; Buckley, M. B.; Arora, A.; Bates, F. S.; Dorfman, K. D.; Grason, G. M. Stable Frank–Kasper Phases of Self-Assembled, Soft Matter Spheres. Proc. Natl. Acad. Sci. 2018, 115 (41), 10233– 10238.
    (24) Qiang, Y.; Li, W.; Shi, A.-C. Stabilizing Phases of Block Copolymers with Gigantic Spheres via Designed Chain Architectures. ACS Macro Lett. 2020, 9 (5), 668–673.
    (25) Chang, A. B.; Bates, F. S. Impact of Architectural Asymmetry on Frank − Kasper Phase Formation in Block Polymer Melts. 2020,14 (9), 11463–11472
    (26) Yamamoto, K.; Takagi, H. Frank-Kasper σ and A-15 Phases Formed in Symmetry and Asymmetry Block Copolymer Blend System. Mater. Trans. 2020, advpub.
    (27) Lindsay, A. P.; Cheong, G. K.; Peterson, A. J.; Weigand, S.; Dorfman, K. D.; Lodge, T. P.; Bates, F. S. Complex Phase Behavior in Particle-Forming AB/AB′ Diblock Copolymer Blends with Variable Core Block Lengths. Macromolecules 2021, 54 (15), 7088–7101.
    (28) Hajiw, S.; Pansu, B.; Sadoc, J.-F. Evidence for a C14 Frank–Kasper Phase in One-Size Gold Nanoparticle Superlattices. ACS Nano 2015, 9 (8), 8116–8121.
    (29) Pansu, B.; Sadoc, J.-F. Metallurgy of Soft Spheres with Hard Core: From BCC to Frank-Kasper Phases. Eur. Phys. J. E 2017, 40 (11), 102.
    (30) Goodfellow, B. W.; Rasch, M. R.; Hessel, C. M.; Patel, R. N.; Smilgies, D.-M.; Korgel, B. A. Ordered Structure Rearrangements in Heated Gold Nanocrystal Superlattices. Nano Lett. 2013, 13 (11), 5710–5714.
    (31) Jeon, S.; Jun, T.; Jo, S.; Ahn, H.; Lee, S.; Lee, B.; Ryu, D. Y. Frank–Kasper Phases Identified in PDMS-b-PTFEA Copolymers with High Conformational Asymmetry. Macromol. Rapid Commun. 2019, 40 (19), 1900259.
    (32) Olmsted, P. D.; Milner, S. T. Strong-Segregation Theory of Bicontinuous Phases in Block Copolymers. Phys. Rev. Lett. 1994, 72 (6), 936–939.
    (33) Olmsted, P. D.; Milner, S. T. Strong Segregation Theory of Bicontinuous Phases in Block Copolymers. Macromolecules 1998, 31 (12), 4011–4022.
    (34) Kim, K.; Arora, A.; Lewis, R. M.; Liu, M.; Li, W.; Shi, A.-C.; Dorfman, K. D.; Bates, F. S. Origins of Low-Symmetry Phases in Asymmetric Diblock Copolymer Melts. Proc. Natl. Acad. Sci. 2018, 115 (5), 847 – 854.
    (35) Magruder, B. R.; Park, S. J.; Collanton, R. P.; Bates, F. S.; Dorfman, K. D. Laves Phase Field in a Diblock Copolymer Alloy. Macromolecules 2022, 55 (7), 2991–2998.
    (36) Dorfman, K. D. Frank–Kasper Phases in Block Polymers. Macromolecules 2021, 54 (22), 10251–10270.
    (37) Alfons, van B.; Pierre, W. Real-Space Structure of Colloidal Hard-Sphere Glasses. Science 1995, 270 (5239), 1177–1179.
    (38) Liu, Y.; Liu, T.; Yan, X.; Guo, Q.-Y.; Wang, J.; Zhang, R.; Zhang, S.; Su, Z.; Huang, J.; Liu, G.-X.; Zhang, W.; Zhang, W.; Aida, T.; Yue, K.; Huang, M.; Cheng, S. Z. D. Mesoatom Alloys via Self-Sorting Approach of Giant Molecules Blends. Giant 2020, 4, 100031.
    (39) Hynninen, A.-P.; Thijssen, J. H. J.; Vermolen, E. C. M.; Dijkstra, M.; van Blaaderen, A. Self-Assembly Route for Photonic Crystals with a Bandgap in the Visible Region. Nat. Mater. 2007, 6 (3), 202–205.
    (40) Lindquist, B. A.; Jadrich, R. B.; Truskett, T. M. Communication: From Close-Packed to Topologically Close-Packed: Formation of Laves Phases in Moderately Polydisperse Hard-Sphere Mixtures. J. Chem. Phys. 2018, 148 (19), 191101.
    (41) Hasaka, M.; Nakashima, H.; Oki, K. Structure of the Laves Phase Observed in Polystyrene Latexes. Trans. Japan Inst. Met. 1984, 25 (2), 65–72.
    (42) Abbas, S.; Lodge, T. P. Superlattice Formation in a Binary Mixture of Block Copolymer Micelles. Phys. Rev. Lett. 2006, 97 (9), 97803.
    (43) Coropceanu, I.; Boles, M. A.; Talapin, D. V. Systematic Mapping of Binary Nanocrystal Superlattices: The Role of Topology in Phase Selection. J. Am. Chem. Soc. 2019, 141 (14), 5728–5740.
    (44) Hynninen, A.-P.; Filion, L.; Dijkstra, M. Stability of LS and LS2 Crystal Structures in Binary Mixtures of Hard and Charged Spheres. J. Chem. Phys. 2009, 131 (6), 64902.
    (45) Sollich, P.; Wilding, N. B. Crystalline Phases of Polydisperse Spheres. Phys. Rev. Lett. 2010, 104 (11), 118302.
    (46) Bommineni, P. K.; Varela-Rosales, N. R.; Klement, M.; Engel, M. Complex Crystals from Size-Disperse Spheres. Phys. Rev. Lett. 2019, 122 (12), 128005.
    (47) Lindsay, A. P.; Jayaraman, A.; Peterson, A. J.; Mueller, A. J.; Weigand, S.; Almdal, K.; Mahanthappa, M. K.; Lodge, T. P.; Bates, F. S. Reevaluation of Poly(Ethylene-Alt-Propylene)-Block-Polydimethylsiloxane Phase Behavior Uncovers Topological Close-Packing and Epitaxial Quasicrystal Growth. ACS Nano 2021.
    (48) Botet, R.; Cabane, B.; Goehring, L.; Li, J.; Artzner, F. How Do Polydisperse Repulsive Colloids Crystallize? Faraday Discuss. 2016, 186 (0), 229–240.
    (49) Fasolo, M.; Sollich, P. Fractionation Effects in Phase Equilibria of Polydisperse Hard-Sphere Colloids. Phys. Rev. E 2004, 70 (4), 41410.
    (50) Evans, R. M. L.; Holmes, C. B. Diffusive Growth of Polydisperse Hard-Sphere Crystals. Phys. Rev. E 2001, 64 (1), 11404

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