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Building blocks of order: block copolymer micelles and colloidal particles in complex packing structures

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Abstract

The self-assembly of polymeric micelles and colloidal dispersions into intricate structures represents a transformative approach in contrast to traditional fabrication methods for creating new functional materials. Despite remarkable advancements in the field, there exists substantial potential for further progress. In the past two decades, scientists have innovated and applied sophisticated methods for synthesizing nanocrystals of diverse geometries and polymeric materials with varying molecular characteristics. These synthetic pathways play a pivotal role in the facile fabrication of a multitude of nanostructures, which also greatly facilitates our understanding of the governing principles of meso and nano object self-assembly. This review focuses on the complex packing structures of block copolymer micelles and colloidal particles, with a particular emphasis on the Frank-Kasper phase. A comprehensive exploration of the recent theoretical and experimental advances in this interdisciplinary field is presented. By drawing parallels between the self-organized formation of both hard particles and soft micelles, this review aims to provide a fundamental understanding of the underlying physics and chemistry that contribute to the emergence of complex packing behavior. This knowledge is instrumental in the design and engineering of structures tailored to specific applications, fostering further innovation in the realm of nanomaterials.

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References

  1. Robert F. Service (2005) How Far Can We Push Chemical Self-Assembly? Science 309:95. https://doi.org/10.1126/science.309.5731.95

    Article  PubMed  Google Scholar 

  2. Baez-Cotto CM, Mahanthappa MK (2018) Micellar Mimicry of Intermetallic C14 and C15 Laves Phases by Aqueous Lyotropic Self-Assembly. ACS Nano 12:3226–3234. https://doi.org/10.1021/acsnano.7b07475

    Article  CAS  PubMed  Google Scholar 

  3. Zhao Y, Xie Z, Gu H, Jin L, Zhao X, Wang B, Gu Z (2012) Multifunctional photonic crystal barcodes from microfluidics. NPG Asia Mater 4:e25–e25. https://doi.org/10.1038/am.2012.46

    Article  CAS  Google Scholar 

  4. Dill KA, MacCallum JL (2012) The Protein-Folding Problem, 50 Years On. Science 338:1042–1046. https://doi.org/10.1126/science.1219021

    Article  CAS  PubMed  Google Scholar 

  5. Tian L, Qian K, Qi J, Liu Q, Yao C, Song W, Wang Y (2018) Gold nanoparticles superlattices assembly for electrochemical biosensor detection of microRNA-21. Biosens Bioelectron 99:564–570. https://doi.org/10.1016/j.bios.2017.08.035

    Article  CAS  PubMed  Google Scholar 

  6. Kamien RD (2003) Soap Froths and Crystal Structures. Ann Henri Poincaré 4:679–681. https://doi.org/10.1007/s00023-003-0953-7

    Article  CAS  Google Scholar 

  7. Grason GM, DiDonna BA, Kamien RD (2003) Geometric Theory of Diblock Copolymer Phases. Phys Rev Lett 91:58304. https://doi.org/10.1103/PhysRevLett.91.058304

    Article  CAS  Google Scholar 

  8. Bates FS, Schulz MF, Khandpur AK, Förster S, Rosedale JH, Almdal K, Mortensen K (1994) Fluctuations, conformational asymmetry and block copolymer phase behaviour. Faraday Discuss 98:7–18. https://doi.org/10.1039/FD9949800007

    Article  CAS  Google Scholar 

  9. Castelli A, de Graaf J, Marras S, Brescia R, Goldoni L, Manna L, Arciniegas MP (2018) Understanding and tailoring ligand interactions in the self-assembly of branched colloidal nanocrystals into planar superlattices. Nat Commun 9:1141. https://doi.org/10.1038/s41467-018-03550-z

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Lifshitz R, Diamant H (2007) Soft quasicrystals–Why are they stable? Philos Mag 87:3021–3030. https://doi.org/10.1080/14786430701358673

    Article  CAS  Google Scholar 

  11. Palberg T (1997) Colloidal crystallization dynamics. Curr Opin Colloid Interface Sci 2:607–614. https://doi.org/10.1016/S1359-0294(97)80053-2

    Article  CAS  Google Scholar 

  12. Frank FC, Kasper JS (1958) Complex alloy structures regarded as sphere packings. I. Definitions and basic principles Acta Crystallogr 11:184–190. https://doi.org/10.1107/S0365110X58000487

    Article  CAS  Google Scholar 

  13. Frank FC, Kasper JS (1959) Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures. Acta Crystallogr 12:483–499. https://doi.org/10.1107/S0365110X59001499

    Article  CAS  Google Scholar 

  14. Shechtman D, Blech I, Gratias D, Cahn JW (1984) Metallic Phase with Long-Range Orientational Order and No Translational Symmetry. Phys Rev Lett 53:1951–1953. https://doi.org/10.1103/PhysRevLett.53.1951

    Article  CAS  Google Scholar 

  15. Lawson AC, Olsen CE, Richardson Jnr JW, Mueller MH, Lander GH (1988) Structure of β-uranium. Acta Crystallogr Sect B 44:89–96. https://doi.org/10.1107/S0108768187009406

    Article  Google Scholar 

  16. Huang M, Yue K, Wang J, Hsu CH, Wang L, Cheng SZD (2018) Frank-Kasper and related quasicrystal spherical phases in macromolecules. Sci China Chem 61:33–45. https://doi.org/10.1007/s11426-017-9140-8

    Article  CAS  Google Scholar 

  17. Talapin DV, Shevchenko EV, Bodnarchuk MI, Ye X, Chen J, Murray CB (2009) Quasicrystalline order in self-assembled binary nanoparticle superlattices. Nature 461:964–967. https://doi.org/10.1038/nature08439

    Article  CAS  PubMed  Google Scholar 

  18. Zeng X, Ungar G, Liu Y, Percec V, Dulcey AD, Hobbs JK (2004) Supramolecular dendritic liquid quasicrystals. Nature 428:157–160. https://doi.org/10.1038/nature02368

    Article  CAS  PubMed  Google Scholar 

  19. Ungar G, Liu Y, Zeng X, Percec V, Cho WD (2003) Giant Supramolecular Liquid Crystal Lattice. Science 299:1208–1211. https://doi.org/10.1126/science.1078849

    Article  CAS  PubMed  Google Scholar 

  20. Ungar G, Zeng X (2005) Frank-Kasper, quasicrystalline and related phases in liquid crystals. Soft Matter 1:95–106. https://doi.org/10.1039/B502443A

    Article  CAS  PubMed  Google Scholar 

  21. Liew CY, Salim M, Zahid NI, Hashim R (2015) Biomass derived xylose Guerbet surfactants: thermotropic and lyotropic properties from small-angle X-ray scattering. RSC Adv 5:99125–99132. https://doi.org/10.1039/C5RA17828B

    Article  CAS  Google Scholar 

  22. Kim SA, Jeong K-J, Yethiraj A, Mahanthappa MK (2017) Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity. Proc Natl Acad Sci 114:4072–4077. https://doi.org/10.1073/pnas.1701608114

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Sun H-J, Zhang S, Percec V (2015) From structure to function via complex supramolecular dendrimer systems. Chem Soc Rev 44:3900–3923. https://doi.org/10.1039/C4CS00249K

    Article  CAS  PubMed  Google Scholar 

  24. Hudson SD, Jung HT, Percec V, Cho WD, Johansson G, Ungar G, Balagurusamy VSK (1997) Direct Visualization of Individual Cylindrical and Spherical Supramolecular Dendrimers. Science 278:449–452. https://doi.org/10.1126/science.278.5337.449

    Article  CAS  Google Scholar 

  25. Lee S, Bluemle MJ, Bates FS (2010) Discovery of a Frank-Kasper σ Phase in Sphere-Forming Block Copolymer Melts. Science 330:349–353. https://doi.org/10.1126/science.1195552

    Article  CAS  PubMed  Google Scholar 

  26. Kim K, Schulze MW, Arora A, Lewis RM III, Hillmyer MA, Dorfman KD, Bates FS (2017) Thermal processing of diblock copolymer melts mimics metallurgy. Science 356:520–523. https://doi.org/10.1126/science.aam7212

    Article  CAS  PubMed  Google Scholar 

  27. Takagi H, Yamamoto K (2019) Phase Boundary of Frank-Kasper σ Phase in Phase Diagrams of Binary Mixtures of Block Copolymers and Homopolymers. Macromolecules 52:2007–2014. https://doi.org/10.1021/acs.macromol.8b02356

    Article  CAS  Google Scholar 

  28. Barbon SM, Song JA, Chen D, Zhang C, Lequieu J, Delaney KT, Anastasaki A, Rolland M, Fredrickson GH, Bates MW, Hawker CJ, Bates CM (2020) Architecture Effects in Complex Spherical Assemblies of (AB)n-Type Block Copolymers. ACS Macro Lett 9:1745–1752. https://doi.org/10.1021/acsmacrolett.0c00704

    Article  CAS  PubMed  Google Scholar 

  29. Lachmayr KK, Wentz CM, Sita LR (2020) An Exceptionally Stable and Scalable Sugar-Polyolefin Frank–Kasper A15 Phase. Angew Chemie Int Ed 59:1521–1526. https://doi.org/10.1002/anie.201912648

    Article  CAS  Google Scholar 

  30. Jeon S, Jun T, Jo S, Ahn H, Lee S, Lee B, Ryu DY (2019) Frank-Kasper Phases Identified in PDMS-b-PTFEA Copolymers with High Conformational Asymmetry. Macromol Rapid Commun 40:1900259. https://doi.org/10.1002/marc.201900259

    Article  CAS  Google Scholar 

  31. Bates MW, Lequieu J, Barbon SM, Lewis RM III, Delaney KT, Anastasaki A, Hawker CJ, Fredrickson GH, Bates CM (2019) Stability of the A15 phase in diblock copolymer melts. Proc Natl Acad Sci 116:13194–13199. https://doi.org/10.1073/pnas.1900121116

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Lindsay AP, Jayaraman A, Peterson AJ, Mueller AJ, Weigand S, Almdal K, Mahanthappa MK, Lodge TP, Bates FS (2021) Reevaluation of Poly(ethylene-alt-propylene)-block-Polydimethylsiloxane Phase Behavior Uncovers Topological Close-Packing and Epitaxial Quasicrystal Growth. ACS Nano 15(6):9453–9468. https://doi.org/10.1021/acsnano.1c02420

    Article  CAS  PubMed  Google Scholar 

  33. Nouri B, Chen CY, Huang YS, Mansel BW, Chen HL (2021) Emergence of a Metastable Laves C14 Phase of Block Copolymer Micelle Bearing a Glassy Core. Macromolecules 54(19):9195–9203. https://doi.org/10.1021/acs.macromol.1c01385

    Article  CAS  Google Scholar 

  34. Mueller AJ, Lindsay AP, Jayaraman A, Lodge TP, Mahanthappa MK, Bates FS (2020) Emergence of a C15 Laves Phase in Diblock Polymer/Homopolymer Blends. ACS Macro Lett 9:576–582. https://doi.org/10.1021/acsmacrolett.0c00124

    Article  CAS  PubMed  Google Scholar 

  35. Huang M, Hsu CH, Wang J, Mei S, Dong X, Li Y, Li M, Liu H, Zhang W, Aida T, Zhang WB, Yue K, Cheng SZD (2015) Selective assemblies of giant tetrahedra via precisely controlled positional interactions. Science 348:424–428. https://doi.org/10.1126/science.aaa2421

    Article  CAS  PubMed  Google Scholar 

  36. Yue K, Huang M, Marson RL, 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 WB, Glotzer SC, Cheng SZD (2016) Geometry induced sequence of nanoscale Frank-Kasper and quasicrystal mesophases in giant surfactants. Proc Natl Acad Sci 113:14195–14200. https://doi.org/10.1073/pnas.1609422113

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Montis R, Fusaro L, Falqui A, Hursthouse MB, Tumanov N, Coles SJ, Threlfall TL, Horton PN, Sougrat R, Lafontaine A, Coquerel G, Rae AD (2021) Complex structures arising from the self-assembly of a simple organic salt. Nature 590:275–278. https://doi.org/10.1038/s41586-021-03194-y

    Article  CAS  PubMed  Google Scholar 

  38. Dotera T (2011) Quasicrystals in Soft Matter. Isr J Chem 51:1197–1205. https://doi.org/10.1002/ijch.201100146

    Article  CAS  Google Scholar 

  39. Lucarini V (2009) Three-Dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes. J Stat Phys 134:185–206. https://doi.org/10.1007/s10955-008-9668-y

    Article  Google Scholar 

  40. Dorfman KD (2021) Frank-Kasper Phases in Block Polymers. Macromolecules 54:10251–10270. https://doi.org/10.1021/acs.macromol.1c01650

    Article  CAS  Google Scholar 

  41. Ziherl P, Kamien RD (2001) Maximizing Entropy by Minimizing Area: Towards a New Principle of Self-Organization. J Phys Chem B 105:10147–10158. https://doi.org/10.1021/jp010944q

    Article  CAS  Google Scholar 

  42. Pansu B, Sadoc J-F (2017) Metallurgy of soft spheres with hard core: From BCC to Frank-Kasper phases. Eur Phys J E 40:102. https://doi.org/10.1140/epje/i2017-11592-6

    Article  CAS  PubMed  Google Scholar 

  43. Grason GM (2006) The packing of soft materials: Molecular asymmetry, geometric frustration and optimal lattices in block copolymer melts. Phys Rep 433:1–64. https://doi.org/10.1016/j.physrep.2006.08.001

    Article  CAS  Google Scholar 

  44. Matsen MW, Bates FS (1996) Unifying Weak- and Strong-Segregation Block Copolymer Theories. Macromolecules 29:1091–1098. https://doi.org/10.1021/ma951138i

    Article  CAS  Google Scholar 

  45. Matsen MW, Schick M (1994) Stable and unstable phases of a diblock copolymer melt. Phys Rev Lett 72:2660–2663. https://doi.org/10.1103/PhysRevLett.72.2660

    Article  CAS  PubMed  Google Scholar 

  46. Gillard TM, Lee S, Bates FS (2016) Dodecagonal quasicrystalline order in a diblock copolymer melt. Proc Natl Acad Sci 113:5167–5172. https://doi.org/10.1073/pnas.1601692113

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Xie N, Li W, Qiu F, Shi AC (2014) σ Phase Formed in Conformationally Asymmetric AB-Type Block Copolymers. ACS Macro Lett 3:906–910. https://doi.org/10.1021/mz500445v

    Article  CAS  PubMed  Google Scholar 

  48. Bates MW, Barbon SM, Levi AE, Lewis RM, Beech HK, Vonk KM, Zhang C, Fredrickson GH, Hawker CJ, Bates CM (2020) Synthesis and Self-Assembly of ABn Miktoarm Star Polymers. ACS Macro Lett 9:396–403. https://doi.org/10.1021/acsmacrolett.0c00061

    Article  CAS  PubMed  Google Scholar 

  49. Schulze MW, Lewis RM, Lettow JH, Hickey RJ, Gillard TM, Hillmyer MA, Bates FS (2017) Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers. Phys Rev Lett 118:207801. https://doi.org/10.1103/PhysRevLett.118.207801

    Article  PubMed  Google Scholar 

  50. Lee S, Gillard TM, Bates FS (2013) Fluctuations, Order, and Disorder in Short Diblock Copolymers. AIChE J 59:3502–3513. https://doi.org/10.1002/aic.14023

    Article  CAS  Google Scholar 

  51. Reddy A, Buckley MB, Arora A, Bates FS, Dorfman KD, Grason GM (2018) Stable Frank-Kasper phases of self-assembled, soft matter spheres. Proc Natl Acad Sci 115:10233–10238. https://doi.org/10.1073/pnas.1809655115

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Lee S, Leighton C, Bates FS (2014) Sphericity and symmetry breaking in the formation of Frank-Kasper phases from one component materials. Proc Natl Acad Sci 111:17723–17731. https://doi.org/10.1073/pnas.1408678111

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Kim K, Arora A, Lewis RM, Liu M, Li W, Shi AC, Dorfman KD, Bates FS (2018) Origins of low-symmetry phases in asymmetric diblock copolymer melts. Proc Natl Acad Sci 115:847–854. https://doi.org/10.1073/pnas.1717850115

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Nouri B, Chen CY, Lin JM, Chen HL (2022) Phase Control of Colloid-like Block Copolymer Micelles by Tuning Size Distribution via Thermal Processing. Macromolecules 55:9820–9832. https://doi.org/10.1021/acs.macromol.2c01387

    Article  CAS  Google Scholar 

  55. Li W, Duan C, Shi AC (2017) Nonclassical Spherical Packing Phases Self-Assembled from AB-Type Block Copolymers. ACS Macro Lett 6:1257–1262. https://doi.org/10.1021/acsmacrolett.7b00756

    Article  CAS  PubMed  Google Scholar 

  56. Qiang Y, Li W, Shi AC (2020) Stabilizing Phases of Block Copolymers with Gigantic Spheres via Designed Chain Architectures. ACS Macro Lett 9:668–673. https://doi.org/10.1021/acsmacrolett.0c00193

    Article  CAS  PubMed  Google Scholar 

  57. Zhao M, Li W (2019) Laves Phases Formed in the Binary Blend of AB4 Miktoarm Star Copolymer and A-Homopolymer. Macromolecules 52:1832–1842. https://doi.org/10.1021/acs.macromol.8b02407

    Article  CAS  Google Scholar 

  58. Xie Q, Qiang Y, Chen L, Xia Y, Li W (2020) Synergistic Effect of Stretched Bridging Block and Released Packing Frustration Leads to Exotic Nanostructures. ACS Macro Lett 9:980–984. https://doi.org/10.1021/acsmacrolett.0c00313

    Article  CAS  PubMed  Google Scholar 

  59. Chen L, Qiang Y, Li W (2018) Tuning Arm Architecture Leads to Unusual Phase Behaviors in a (BAB)5 Star Copolymer Melt. Macromolecules 51:9890–9900. https://doi.org/10.1021/acs.macromol.8b01484

    Article  CAS  Google Scholar 

  60. Sun Y, Tan R, Ma Z, Gan Z, Li G, Zhou D, Shao Y, Zhang WB, Zhang R, Dong XH (2020) Discrete Block Copolymers with Diverse Architectures: Resolving Complex Spherical Phases with One Monomer Resolution. ACS Cent Sci 6:1386–1393. https://doi.org/10.1021/acscentsci.0c00798

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Chang AB, Bates FS (2020) Impact of Architectural Asymmetry on Frank-Kasper Phase Formation in Block Polymer Melts. ACS Nano 14:11463–11472. https://doi.org/10.1021/acsnano.0c03846

    Article  CAS  PubMed  Google Scholar 

  62. Liu M, Li W, Qiu F, Shi AC (2016) Stability of the Frank-Kasper σ-phase in BABC linear tetrablock terpolymers. Soft Matter 12:6412–6421. https://doi.org/10.1039/C6SM00798H

    Article  CAS  PubMed  Google Scholar 

  63. Lewis RM, Arora A, Beech HK, Lee B, Lindsay AP, Lodge TP, Dorfman KD, Bates FS (2018) Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers. Phys Rev Lett 121:208002. https://doi.org/10.1103/PhysRevLett.121.208002

    Article  PubMed  Google Scholar 

  64. Cheong GK, Bates FS, Dorfman KD (2020) Symmetry breaking in particle-forming diblock polymer/homopolymer blends. Proc Natl Acad Sci 117:16764–16769. https://doi.org/10.1073/pnas.2006079117

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  65. Xie J, Shi AC (2021) Formation of complex spherical packing phases in diblock copolymer/homopolymer blends. Giant 5:100043. https://doi.org/10.1016/j.giant.2020.100043

    Article  CAS  Google Scholar 

  66. Magruder BR, Park SJ, Collanton RP, Bates FS, Dorfman KD (2022) Laves Phase Field in a Diblock Copolymer Alloy. Macromolecules 55:2991–2998. https://doi.org/10.1021/acs.macromol.2c00346

    Article  CAS  Google Scholar 

  67. Park SJ, Bates FS, Dorfman KD (2023) Complex Phase Behavior in Binary Blends of AB Diblock Copolymer and ABC Triblock Terpolymer. Macromolecules 56:1278–1288. https://doi.org/10.1021/acs.macromol.2c02216

    Article  CAS  Google Scholar 

  68. He W, Wang F, Qiang Y, Pan Y, Li W, Liu M (2023) Asymmetric Binary Spherical Phases Self-Assembled by Mixing AB Diblock/ABC Triblock Copolymers. Macromolecules 56:719–729. https://doi.org/10.1021/acs.macromol.2c02217

    Article  CAS  Google Scholar 

  69. Chen MZ, Huang YT, Chen CY, Chen HL (2022) Accessing the Frank-Kasper σ Phase of Block Copolymer with Small Conformational Asymmetry via Selective Solvent Solubilization in the Micellar Corona. Macromolecules 55:10812–10820. https://doi.org/10.1021/acs.macromol.2c01757

    Article  CAS  Google Scholar 

  70. Chen MZ, Tung CH, Chen CY, Chen HL (2023) Expanding the window of the Frank-Kasper σ phase of block copolymer/homopolymer blend by selective incorporation of metal salt. Phys Rev Mater 7:115604. https://doi.org/10.1103/PhysRevMaterials.7.115604

    Article  CAS  Google Scholar 

  71. Xie J, Shi AC (2023) Theory of Complex Spherical Packing Phases in Diblock Copolymer/Homopolymer Blends. Macromolecules 56(24):10296–10312. https://doi.org/10.1021/acs.macromol.3c01973

    Article  CAS  Google Scholar 

  72. Zhao F, Dong Q, Li Q, Liu M, Li W (2022) Emergence and Stability of Exotic “Binary” HCP-Type Spherical Phase in Binary AB/AB Blends. Macromolecules 55:10005–10013. https://doi.org/10.1021/acs.macromol.2c01957

    Article  CAS  Google Scholar 

  73. Liu M, Qiang Y, Li W, Qiu F, Shi AC (2016) Stabilizing the Frank-Kasper Phases via Binary Blends of AB Diblock Copolymers. ACS Macro Lett 5:1167–1171. https://doi.org/10.1021/acsmacrolett.6b00685

    Article  CAS  PubMed  Google Scholar 

  74. Lindsay AP, Lewis RM, Lee B, Peterson AJ, Lodge TP, Bates FS (2020) A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends. ACS Macro Lett 9:197–203. https://doi.org/10.1021/acsmacrolett.9b01026

    Article  CAS  PubMed  Google Scholar 

  75. Yamamoto K, Takagi H (2020) Frank-Kasper σ and A-15 Phases Formed in Symmetry and Asymmetry Block Copolymer Blend System. Mater Trans advpub 62:325–328. https://doi.org/10.2320/matertrans.MT-MB2020002

    Article  Google Scholar 

  76. Lindsay AP, Cheong GK, Peterson AJ, Weigand S, Dorfman KD, Lodge TP, Bates FS (2021) Complex Phase Behavior in Particle-Forming AB/AB′ Diblock Copolymer Blends with Variable Core Block Lengths. Macromolecules 54:7088–7101. https://doi.org/10.1021/acs.macromol.1c01290

    Article  CAS  Google Scholar 

  77. Yanagioka M, Frank C (2008) Structure, stability and applications of colloidal crystals. Korea Aust Rheol J 20:97–107

    Google Scholar 

  78. Gasser U, Weeks ER, Schofield A, Pusey PN, Weitz DA (2001) Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization. Science 292:258–262. https://doi.org/10.1126/science.1058457

    Article  CAS  PubMed  Google Scholar 

  79. Boles MA, Engel M, Talapin DV (2016) Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials. Chem Rev 116:11220–11289. https://doi.org/10.1021/acs.chemrev.6b00196

    Article  CAS  PubMed  Google Scholar 

  80. Ascolani H, van der Meijden MW, Cristina LJ, Gayone JE, Kellogg RM, Fuhr JD, Lingenfelder M (2014) Van der Waals interactions in the self-assembly of 5-amino [6]helicene on Cu(100) and Au(111). Chem Commun 50:13907–13909. https://doi.org/10.1039/C4CC04338C

    Article  CAS  Google Scholar 

  81. Gurvinder S, Henry C, Artem B, Gelman E, Repnin N, Král P, Klajn R (2014) Self-assembly of magnetite nanocubes into helical superstructures. Science 345:1149–1153. https://doi.org/10.1126/science.1254132

    Article  CAS  Google Scholar 

  82. Lv Z-P, Kapuscinski M, Bergström L (2019) Tunable assembly of truncated nanocubes by evaporation-driven poor-solvent enrichment. Nat Commun 10:4228. https://doi.org/10.1038/s41467-019-12237-y

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Sau TK, Murphy CJ (2005) Self-Assembly Patterns Formed upon Solvent Evaporation of Aqueous Cetyltrimethylammonium Bromide-Coated Gold Nanoparticles of Various Shapes. Langmuir 21:2923–2929. https://doi.org/10.1021/la047488s

    Article  CAS  PubMed  Google Scholar 

  84. Shevchenko EV, Talapin DV (2008) Self-assembly of semiconductor nanocrystals into ordered superstructures BT. In: Rogach AL (ed) Semiconductor Nanocrystal Quantum Dots: Synthesis. Assembly, Spectroscopy and Applications. Springer Vienna, Vienna

    Google Scholar 

  85. Murray CB, Kagan CR, Bawendi MG (2000) Synthesis and Characterization of Monodisperse Nanocrystals and Close-Packed Nanocrystal Assemblies. Annu Rev Mater Sci 30:545–610. https://doi.org/10.1146/annurev.matsci.30.1.545

    Article  CAS  Google Scholar 

  86. Murray CB, Kagan CR, Bawendi MG (1995) Self-Organization of CdSe Nanocrystallites into Three-Dimensional Quantum Dot Superlattices. Science 270:1335–1338. https://doi.org/10.1126/science.270.5240.1335

    Article  CAS  Google Scholar 

  87. Bruel C, Davies TS, Carreau PJ, Tavares JR, Heuzey MC (2020) Self-assembly behaviors of colloidal cellulose nanocrystals: A tale of stabilization mechanisms. J Colloid Interface Sci 574:399–409. https://doi.org/10.1016/j.jcis.2020.04.049

    Article  CAS  PubMed  Google Scholar 

  88. Bigioni TP, Lin XM, Nguyen TT, Corwin EI, Witten TA, Jaeger HM (2006) Kinetically driven self assembly of highly ordered nanoparticle monolayers. Nat Mater 5:265–270. https://doi.org/10.1038/nmat1611

    Article  CAS  PubMed  Google Scholar 

  89. Lee B, Littrell K, Sha Y, Shevchenko EV (2019) Revealing the Effects of the Non-solvent on the Ligand Shell of Nanoparticles and Their Crystallization. J Am Chem Soc 141:16651–16662. https://doi.org/10.1021/jacs.9b06010

    Article  CAS  PubMed  Google Scholar 

  90. Lu PJ, Zaccarelli E, Ciulla F, Schofield AB, Sciortino F, Weitz DA (2008) Gelation of particles with short-range attraction. Nature 453:499–503. https://doi.org/10.1038/nature06931

    Article  CAS  PubMed  Google Scholar 

  91. Ge G, Brus L (2000) Evidence for Spinodal Phase Separation in Two-Dimensional Nanocrystal Self-Assembly. J Phys Chem B 104:9573–9575. https://doi.org/10.1021/jp002280a

    Article  CAS  Google Scholar 

  92. Witten TA, Sander LM (1981) Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon. Phys Rev Lett 47:1400–1403. https://doi.org/10.1103/PhysRevLett.47.1400

    Article  CAS  Google Scholar 

  93. Wang L, Albouy P-A, Pileni M-P (2015) Synthesis and Self-Assembly Behavior of Charged Au Nanocrystals in Aqueous Solution. Chem Mater 27:4431–4440. https://doi.org/10.1021/acs.chemmater.5b01370

    Article  CAS  Google Scholar 

  94. Bian T, Gardin A, Gemen J, Lothar Houben L, Perego C, Lee B, Elad N, Chu Z, Pavan GM, Klajn R (2021) Electrostatic co-assembly of nanoparticles with oppositely charged small molecules into static and dynamic superstructures. Nat Chem 13:940–949. https://doi.org/10.1038/s41557-021-00752-9

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  95. Curk T, Luijten E (2021) Charge Regulation Effects in Nanoparticle Self-Assembly. Phys Rev Lett 126:138003. https://doi.org/10.1103/PhysRevLett.126.138003

    Article  CAS  PubMed  Google Scholar 

  96. Kazes M, Udayabhaskararao T, Dey S, Oron D (2021) Effect of Surface Ligands in Perovskite Nanocrystals: Extending in and Reaching out. Acc Chem Res 54:1409–1418. https://doi.org/10.1021/acs.accounts.0c00712

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  97. Luo Y, Zhao R, Pendry JB (2014) van der Waals interactions at the nanoscale: The effects of nonlocality. Proc Natl Acad Sci 111:18422–18427. https://doi.org/10.1073/pnas.1420551111

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  98. Parsegian VA (2005) Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists. Cambridge University Press, Cambridge

    Book  Google Scholar 

  99. Ambrosetti A, Ferri N, DiStasio Jr RA, Tkatchenko A (2016) Wavelike charge density fluctuations and van der Waals interactions at the nanoscale. Science 351:1171–1176. https://doi.org/10.1126/science.aae0509

    Article  CAS  PubMed  Google Scholar 

  100. Hamaker HC (1937) The London—van der Waals attraction between spherical particles. Physica 4:1058–1072. https://doi.org/10.1016/S0031-8914(37)80203-7

    Article  CAS  Google Scholar 

  101. Israelachvili JNBT-I and SF Third E (2011) Intermolecular and Surface Forces. Academic Press, Boston, p iii

  102. Napper DH (1977) Steric stabilization. J Colloid Interface Sci 58:390–407. https://doi.org/10.1016/0021-9797(77)90150-3

    Article  CAS  Google Scholar 

  103. Hajiw S, Pansu B, Sadoc JF (2015) Evidence for a C14 Frank-Kasper Phase in One-Size Gold Nanoparticle Superlattices. ACS Nano 9:8116–8121. https://doi.org/10.1021/acsnano.5b02216

    Article  CAS  PubMed  Google Scholar 

  104. Schmitt J, Hajiw S, Lecchi A, Degrouard J, Salonen A, Impéror-Clerc M, Pansu B (2016) Formation of Superlattices of Gold Nanoparticles Using Ostwald Ripening in Emulsions: Transition from fcc to bcc Structure. J Phys Chem B 120:5759–5766. https://doi.org/10.1021/acs.jpcb.6b03287

    Article  CAS  PubMed  Google Scholar 

  105. Boles MA, Talapin DV (2014) Self-Assembly of Tetrahedral CdSe Nanocrystals: Effective “Patchiness” via Anisotropic Steric Interaction. J Am Chem Soc 136:5868–5871. https://doi.org/10.1021/ja501596z

    Article  CAS  PubMed  Google Scholar 

  106. Yang W, Zhong Y, He C, Peng S, Yang Y, Qi F, Feng P, Shuai C (2020) Electrostatic self-assembly of pFe3O4 nanoparticles on graphene oxide: A co-dispersed nanosystem reinforces PLLA scaffolds. J Adv Res 24:191–203. https://doi.org/10.1016/j.jare.2020.04.009

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  107. Mau SC, Huse DA (1999) Stacking entropy of hard-sphere crystals. Phys Rev E 59:4396–4401. https://doi.org/10.1103/PhysRevE.59.4396

    Article  CAS  Google Scholar 

  108. Hone D, Alexander S, Chaikin PM, Pincus P (1983) The phase diagram of charged colloidal suspensions. J Chem Phys 79:1474–1479. https://doi.org/10.1063/1.445937

    Article  CAS  Google Scholar 

  109. Kremer K, Robbins MO, Grest GS (1986) Phase Diagram of Yukawa Systems: Model for Charge-Stabilized Colloids. Phys Rev Lett 57:2694–2697. https://doi.org/10.1103/PhysRevLett.57.2694

    Article  CAS  PubMed  Google Scholar 

  110. Cochran TW, Chiew YC (2004) Thermodynamic and structural properties of repulsive hard-core Yukawa fluid: Integral equation theory, perturbation theory and Monte Carlo simulations. J Chem Phys 121:1480–1486. https://doi.org/10.1063/1.1759616

    Article  CAS  PubMed  Google Scholar 

  111. Ziherl P, Kamien RD (2000) Soap Froths and Crystal Structures. Phys Rev Lett 85:3528–3531. https://doi.org/10.1103/PhysRevLett.85.3528

    Article  CAS  PubMed  Google Scholar 

  112. Weaire D, Phelan R (1994) A counter-example to Kelvin’s conjecture on minimal surfaces. Philos Mag Lett 69:107–110. https://doi.org/10.1080/09500839408241577

    Article  CAS  Google Scholar 

  113. Goodfellow BW, Yu Y, Bosoy CA, Smilgies DM, Korgel BA (2015) The Role of Ligand Packing Frustration in Body-Centered Cubic (bcc) Superlattices of Colloidal Nanocrystals. J Phys Chem Lett 6:2406–2412. https://doi.org/10.1021/acs.jpclett.5b00946

    Article  CAS  PubMed  Google Scholar 

  114. Yun H, Paik T (2019) Colloidal Self-Assembly of Inorganic Nanocrystals into Superlattice Thin-Films and Multiscale Nanostructures. Nanomater 9

  115. Goodfellow BW, Korgel BA (2011) Reversible Solvent Vapor-Mediated Phase Changes in Nanocrystal Superlattices. ACS Nano 5:2419–2424. https://doi.org/10.1021/nn201273c

    Article  CAS  PubMed  Google Scholar 

  116. Bian K, Choi JJ, Kaushik A, Clancy P, Smilgies DM, Hanrath T (2011) Shape-Anisotropy Driven Symmetry Transformations in Nanocrystal Superlattice Polymorphs. ACS Nano 5:2815–2823. https://doi.org/10.1021/nn103303q

    Article  CAS  PubMed  Google Scholar 

  117. Schulz F, Pavelka O, Lehmkühler F, Westermeier F, Okamura Y, Mueller NS, Reich S, Lange H (2020) Structural order in plasmonic superlattices. Nat Commun 11:3821. https://doi.org/10.1038/s41467-020-17632-4

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  118. Evers WH, De NB, Filion L, Castillo S, Dijkstra M, Vanmaekelbergh D (2010) Entropy-Driven Formation of Binary Semiconductor-Nanocrystal Superlattices. Nano Lett 10:4235–4241. https://doi.org/10.1021/nl102705p

    Article  CAS  PubMed  Google Scholar 

  119. Whetten RL, Shafigullin MN, Khoury JT, Schaaff TG, Vezmar I, Alvarez MM, Angus Wilkinson A (1999) Crystal Structures of Molecular Gold Nanocrystal Arrays. Acc Chem Res 32:397–406. https://doi.org/10.1021/ar970239t

    Article  CAS  Google Scholar 

  120. Korgel BA, Fitzmaurice D (1999) Small-angle x-ray-scattering study of silver-nanocrystal disorder-order phase transitions. Phys Rev B 59:14191–14201. https://doi.org/10.1103/PhysRevB.59.14191

    Article  CAS  Google Scholar 

  121. Pusey P (1991) Liquids, Freezing and Glass Transition. Les Houches Sess 51(1989):765–942

    Google Scholar 

  122. Zaccarelli E, Valeriani C, Sanz E, Poon WCK, Cates ME, Pusey PN (2009) Crystallization of Hard-Sphere Glasses. Phys Rev Lett 103:135704. https://doi.org/10.1103/PhysRevLett.103.135704

    Article  CAS  PubMed  Google Scholar 

  123. Hermes M, Dijkstra M (2010) Jamming of polydisperse hard spheres: The effect of kinetic arrest. EPL Europhysics Lett 89:38005. https://doi.org/10.1209/0295-5075/89/38005

    Article  CAS  Google Scholar 

  124. Mari R, Krzakala F, Kurchan J (2009) Jamming versus Glass Transitions. Phys Rev Lett 103:25701. https://doi.org/10.1103/PhysRevLett.103.025701

    Article  CAS  Google Scholar 

  125. Sollich P, Wilding NB (2010) Crystalline Phases of Polydisperse Spheres. Phys Rev Lett 104:118302. https://doi.org/10.1103/PhysRevLett.104.118302

    Article  CAS  PubMed  Google Scholar 

  126. Fasolo M, Sollich P (2004) Fractionation effects in phase equilibria of polydisperse hard-sphere colloids. Phys Rev E 70:41410. https://doi.org/10.1103/PhysRevE.70.041410

    Article  CAS  Google Scholar 

  127. Kose A, Ozaki M, Takano K, Kobayashi Y, Hachisu S (1973) Direct observation of ordered latex suspension by metallurgical microscope. J Colloid Interface Sci 44:330–338. https://doi.org/10.1016/0021-9797(73)90224-5

    Article  CAS  Google Scholar 

  128. Pusey PN, van Megen W (1986) Phase behaviour of concentrated suspensions of nearly hard colloidal spheres. Nature 320:340–342. https://doi.org/10.1038/320340a0

    Article  CAS  Google Scholar 

  129. Yethiraj A, van Blaaderen A (2003) A colloidal model system with an interaction tunable from hard sphere to soft and dipolar. Nature 421:513–517. https://doi.org/10.1038/nature01328

    Article  CAS  PubMed  Google Scholar 

  130. Sear RP (1998) Phase separation and crystallisation of polydisperse hard spheres. Europhys Lett 44:531–535. https://doi.org/10.1209/epl/i1998-00500-3

    Article  CAS  Google Scholar 

  131. Bartlett P (1998) Fractionated crystallization in a polydisperse mixture of hard spheres. J Chem Phys 109:10970–10975. https://doi.org/10.1063/1.477753

    Article  CAS  Google Scholar 

  132. Kalapurakal RAM, Rocha BC, Vashisth H (2023) Self-Assembly in an Experimentally Realistic Model of Lobed Patchy Colloids. ACS Appl Bio Mater. https://doi.org/10.1021/acsabm.2c00910

    Article  PubMed  PubMed Central  Google Scholar 

  133. Wang K, Li F, Jin S-M, Kui Wang K, Tian D, Hussain M, Xu J, Zhang L, Liao Y, Lee E, Yi GR, Xiea X, Zhu J (2020) Chain-length effect on binary superlattices of polymer-tethered nanoparticles. Mater Chem Front 4:2089–2095. https://doi.org/10.1039/D0QM00194E

    Article  CAS  Google Scholar 

  134. Wei J, Schaeffer N, Pileni MP (2015) Ligand Exchange Governs the Crystal Structures in Binary Nanocrystal Superlattices. J Am Chem Soc 137:14773–14784. https://doi.org/10.1021/jacs.5b09959

    Article  CAS  PubMed  Google Scholar 

  135. Yoshimura S, Hachisu S (1983) Order formation in binary mixtures of monodisperse latices BT. In: Nakagaski M, Shinoda K, Matijević E (eds) Frontiers in Colloid Science In Memoriam Professor Dr. Bun-ichi Tamamushi. Steinkopff, Darmstadt

    Google Scholar 

  136. Bartlett P, Ottewill RH, Pusey PN (1992) Superlattice formation in binary mixtures of hard-sphere colloids. Phys Rev Lett 68:3801–3804. https://doi.org/10.1103/PhysRevLett.68.3801

    Article  CAS  PubMed  Google Scholar 

  137. Trizac E, Eldridge MD, Madden PA (1997) Stability of the AB crystal for asymmetric binary hard sphere mixtures. Mol Phys 90:675–678. https://doi.org/10.1080/002689797172408

    Article  CAS  Google Scholar 

  138. Shevchenko EV, Talapin DV, Murray CB, O’Brien S (2006) Structural Characterization of Self-Assembled Multifunctional Binary Nanoparticle Superlattices. J Am Chem Soc 128:3620–3637. https://doi.org/10.1021/ja0564261

    Article  CAS  PubMed  Google Scholar 

  139. Shevchenko EV, Talapin DV, Kotov NA, O’Brien S, Murray CB (2006) Structural diversity in binary nanoparticle superlattices. Nature 439:55–59. https://doi.org/10.1038/nature04414

    Article  CAS  PubMed  Google Scholar 

  140. Ye X, Zhu C, Ercius P, Raja SN, He B, Jones MR, Hauwiller MR, Liu Y, Xu T, Alivisatos AP (2015) Structural diversity in binary superlattices self-assembled from polymer-grafted nanocrystals. Nat Commun 6:10052. https://doi.org/10.1038/ncomms10052

    Article  CAS  PubMed  Google Scholar 

  141. Hynninen A-P, Filion L, Dijkstra M (2009) Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres. J Chem Phys 131:64902. https://doi.org/10.1063/1.3182724

    Article  CAS  Google Scholar 

  142. Hopkins AB, Stillinger FH, Torquato S (2012) Densest binary sphere packings. Phys Rev E 85:21130. https://doi.org/10.1103/PhysRevE.85.021130

    Article  CAS  Google Scholar 

  143. Luo B, Kim A, Smith JW, Ou Z, Wu Z, Kim J, Chen Q (2019) Hierarchical self-assembly of 3D lattices from polydisperse anisometric colloids. Nat Commun 10:1815. https://doi.org/10.1038/s41467-019-09787-6

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  144. Xia Y, Nguyen TD, Yang M, Lee B, Santos A, Podsiadlo P, Tang Z, Glotzer SC, Kotov NA (2011) Self-assembly of self-limiting monodisperse supraparticles from polydisperse nanoparticles. Nat Nanotechnol 6:580–587. https://doi.org/10.1038/nnano.2011.121

    Article  CAS  PubMed  Google Scholar 

  145. Lindquist BA, Jadrich RB, Truskett TM (2018) Communication: From close-packed to topologically close-packed: Formation of Laves phases in moderately polydisperse hard-sphere mixtures. J Chem Phys 148:191101. https://doi.org/10.1063/1.5028279

    Article  CAS  PubMed  Google Scholar 

  146. Sollich P, Warren PB, Cates ME (2001) Moment Free Energies for Polydisperse Systems. Adv Chem Phys 265–336. https://doi.org/10.1002/9780470141762.ch4

  147. Bareigts G, Kiatkirakajorn PC, Li J, Botet R, Sztucki M, Cabane B, Goehring L, Labbez C (2020) Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters. Phys Rev Lett 124:58003. https://doi.org/10.1103/PhysRevLett.124.058003

    Article  CAS  Google Scholar 

  148. Cabane B, Li J, Artzner F, Botet R, Labbez C, Bareigts G, Sztucki M, Lucas Goehring L (2016) Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations. Phys Rev Lett 116:208001. https://doi.org/10.1103/PhysRevLett.116.208001

    Article  CAS  PubMed  Google Scholar 

  149. Fasolo M, Sollich P (2003) Equilibrium Phase Behavior of Polydisperse Hard Spheres. Phys Rev Lett 91:68301. https://doi.org/10.1103/PhysRevLett.91.068301

    Article  CAS  Google Scholar 

  150. Botet R, Cabane B, Goehring L, Li J, Artzner F (2016) How do polydisperse repulsive colloids crystallize? Faraday Discuss 186:229–240. https://doi.org/10.1039/C5FD00145E

    Article  CAS  PubMed  Google Scholar 

  151. Leff DV, Brandt L, Heath JR (1996) Synthesis and Characterization of Hydrophobic, Organically-Soluble Gold Nanocrystals Functionalized with Primary Amines. Langmuir 12:4723–4730. https://doi.org/10.1021/la960445u

    Article  CAS  Google Scholar 

  152. Murray CB, Norris DJ, Bawendi MG (1993) Synthesis and characterization of nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor nanocrystallites. J Am Chem Soc 115:8706–8715. https://doi.org/10.1021/ja00072a025

    Article  CAS  Google Scholar 

  153. Lee S, Ngo A-T, Lisiecki I, Courty A (2022) Structural diversity in binary superlattices from Au and γ-Fe2O3 nanocrystals: towards fine tuning of dipolar interactions. Mater Chem Front 6:1814–1823. https://doi.org/10.1039/D2QM00139J

    Article  CAS  Google Scholar 

  154. Hensley A, Jacobs WM, Rogers WB (2022) Self-assembly of photonic crystals by controlling the nucleation and growth of DNA-coated colloids. Proc Natl Acad Sci 119:e2114050118. https://doi.org/10.1073/pnas.2114050118

    Article  CAS  PubMed  Google Scholar 

  155. Boles MA, Talapin DV (2015) Many-Body Effects in Nanocrystal Superlattices: Departure from Sphere Packing Explains Stability of Binary Phases. J Am Chem Soc 137:4494–4502. https://doi.org/10.1021/jacs.5b00839

    Article  CAS  PubMed  Google Scholar 

  156. Salerno KM, Ismail AE, Lane JMD, Grest GS (2014) Coating thickness and coverage effects on the forces between silica nanoparticles in water. J Chem Phys 140:194904. https://doi.org/10.1063/1.4874638

    Article  CAS  PubMed  Google Scholar 

  157. Kaushik AP, Clancy P (2012) Explicit all-atom modeling of realistically sized ligand-capped nanocrystals. J Chem Phys 136:114702. https://doi.org/10.1063/1.3689973

    Article  CAS  PubMed  Google Scholar 

  158. Zha X, Travesset A (2021) Thermodynamic Equilibrium of Binary Nanocrystal Superlattices. J Phys Chem C 125:18936–18945. https://doi.org/10.1021/acs.jpcc.1c05015

    Article  CAS  Google Scholar 

  159. Djebaili T, Richardi J, Abel S, Marchi M (2013) Atomistic Simulations of the Surface Coverage of Large Gold Nanocrystals. J Phys Chem C 117:17791–17800. https://doi.org/10.1021/jp403442s

    Article  CAS  Google Scholar 

  160. Landman U, Luedtke WD (2004) Small is different: energetic, structural, thermal, and mechanical properties of passivated nanocluster assemblies. Faraday Discuss 125:1–22. https://doi.org/10.1039/B312640B

    Article  CAS  PubMed  Google Scholar 

  161. Schapotschnikow P, Vlugt TJH (2009) Understanding interactions between capped nanocrystals: Three-body and chain packing effects. J Chem Phys 131:124705. https://doi.org/10.1063/1.3227043

    Article  CAS  PubMed  Google Scholar 

  162. Travesset A (2017) Topological structure prediction in binary nanoparticle superlattices. Soft Matter 13:147–157. https://doi.org/10.1039/C6SM00713A

    Article  CAS  Google Scholar 

  163. Coropceanu I, Boles MA, Talapin DV (2019) Systematic Mapping of Binary Nanocrystal Superlattices: The Role of Topology in Phase Selection. J Am Chem Soc 141:5728–5740. https://doi.org/10.1021/jacs.8b12539

    Article  CAS  PubMed  Google Scholar 

  164. Travesset A (2017) Soft Skyrmions, Spontaneous Valence and Selection Rules in Nanoparticle Superlattices. ACS Nano 11:5375–5382. https://doi.org/10.1021/acsnano.7b02219

    Article  CAS  PubMed  Google Scholar 

  165. Waltmann T, Waltmann C, Horst N, Travesset A (2018) Many Body Effects and Icosahedral Order in Superlattice Self-Assembly. J Am Chem Soc 140:8236–8245. https://doi.org/10.1021/jacs.8b03895

    Article  CAS  PubMed  Google Scholar 

  166. Goodfellow BW, Rasch MR, Hessel CM, Patel RN, Smilgies DM, Korgel BA (2013) Ordered Structure Rearrangements in Heated Gold Nanocrystal Superlattices. Nano Lett 13:5710–5714. https://doi.org/10.1021/nl403458q

    Article  CAS  PubMed  Google Scholar 

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This work is supported by the National Science and Technology Council (NSTC) Taiwan under grant No. 111-2221-E-007-013.

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    Babak Nouri & Hsin-Lung Chen

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Nouri, B., Chen, HL. Building blocks of order: block copolymer micelles and colloidal particles in complex packing structures. J Polym Res 31, 120 (2024). https://doi.org/10.1007/s10965-024-03958-w

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