Origin of polytypism in block copolymer materials

Lee, Sangwoo; Ahn, Juhong; Chen, Liwen; Wąsik, Patryk

doi:10.1103/physrevmaterials.7.110301

Title: Origin of polytypism in block copolymer materials

Journal Article · 16 November 2023 · Physical Review Materials

DOI: https://doi.org/10.1103/physrevmaterials.7.110301 · OSTI ID:2212797

^[1];

^[2];

^[3]

Rensselaer Polytechnic Institute, Troy, NY (United States)
University of Shanghai for Science and Technology (China)
Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)

Block copolymers have served as versatile model compounds to understand the self-assembly of inhomogeneous materials. However, the close-packed structures and relevant polytypic crystal systems in block copolymer materials still require a better understanding. In this research update, we review early and recent advancements in close-packed structures in block copolymer materials and attempts to present a framework to understand the origin of polytypism in polymeric and relevant systems. We propose a critical role of interstitial space as a structure director in polytypism and introduce the interstitial space distribution factor as a semiquantitative parameter to address the difference in the configurations of interstitial space distribution in polytypes of the same class. We also note that the random stacking of two-dimensional close-packed structures is a class of aperiodic crystals.

View Journal Article

Cite

Export

Save

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF); USDOE

Grant/Contract Number:: SC0012704; DESC0012704

OSTI ID:: 2212797

Alternate ID(s):: OSTI ID: 2267558

Report Number(s):: BNL-225115-2023-JAAM; TRN: US2407800

Journal Information:: Physical Review Materials, Vol. 7, Issue 11; ISSN 2475-9953

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (105)

Prediction of absolute crystal-nucleation rate in hard-sphere colloids Auer, Stefan; Frenkel, Daan Nature, Vol. 409, Issue 6823 https://doi.org/10.1038/35059035	journal	February 2001
How do Quasicrystals Grow? Keys, Aaron S.; Glotzer, Sharon C. Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.235503	journal	December 2007
Medial Packing, Frustration, and Competing Network Phases in Strongly Segregated Block Copolymers Dimitriyev, Michael S.; Reddy, Abhiram; Grason, Gregory M. Macromolecules, Vol. 56, Issue 17 https://doi.org/10.1021/acs.macromol.3c01098	journal	August 2023
Giant Supramolecular Liquid Crystal Lattice Ungar, G. Science, Vol. 299, Issue 5610 https://doi.org/10.1126/science.1078849	journal	February 2003
Expanding quasiperiodicity in soft matter: Supramolecular decagonal quasicrystals by binary giant molecule blends Liu, Yuchu; Liu, Tong; Yan, Xiao-Yun Proceedings of the National Academy of Sciences, Vol. 119, Issue 3 https://doi.org/10.1073/pnas.2115304119	journal	January 2022
Colloidal alloys with preassembled clusters and spheres Ducrot, Étienne; He, Mingxin; Yi, Gi-Ra Nature Materials, Vol. 16, Issue 6 https://doi.org/10.1038/nmat4869	journal	February 2017
Dodecagonal Quasicrystalline Morphology in a Poly(styrene- b -isoprene- b -styrene- b -ethylene oxide) Tetrablock Terpolymer Zhang, Jingwen; Bates, Frank S. Journal of the American Chemical Society, Vol. 134, Issue 18 https://doi.org/10.1021/ja301770v	journal	April 2012
Solidification in soft-core fluids: Disordered solids from fast solidification fronts Archer, A. J.; Walters, M. C.; Thiele, U. Physical Review E, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevE.90.042404	journal	October 2014
Experimental and Computational Evaluation of Self-Assembled Morphologies in Diblock Janus Bottlebrush Copolymers Liu, Runze; Sun, Zehao; Huang, Hejin Nano Letters, Vol. 23, Issue 1 https://doi.org/10.1021/acs.nanolett.2c03927	journal	December 2022
Stable Frank–Kasper phases of self-assembled, soft matter spheres Reddy, Abhiram; Buckley, Michael B.; Arora, Akash Proceedings of the National Academy of Sciences, Vol. 115, Issue 41 https://doi.org/10.1073/pnas.1809655115	journal	September 2018
Theory of Microphase Separation in Block Copolymers Leibler, Ludwik Macromolecules, Vol. 13, Issue 6 https://doi.org/10.1021/ma60078a047	journal	November 1980
The Physics of Neutron Stars Lattimer, J. M. Science, Vol. 304, Issue 5670 https://doi.org/10.1126/science.1090720	journal	April 2004
Silicon Carbide Microelectromechanical Systems for Harsh Environments Cheung, Rebecca https://doi.org/10.1142/p426	book	June 2006
Large Difference in the Elastic Properties of fcc and hcp Hard-Sphere Crystals Pronk, Sander; Frenkel, Daan Physical Review Letters, Vol. 90, Issue 25 https://doi.org/10.1103/PhysRevLett.90.255501	journal	June 2003
Superlattice Formation in a Binary Mixture of Block Copolymer Micelles Abbas, Sayeed; Lodge, Timothy P. Physical Review Letters, Vol. 97, Issue 9 https://doi.org/10.1103/PhysRevLett.97.097803	journal	August 2006
On measuring colloidal volume fractions Poon, Wilson C. K.; Weeks, Eric R.; Royall, C. Patrick Soft Matter, Vol. 8, Issue 1 https://doi.org/10.1039/C1SM06083J	journal	January 2012
What is a crystal? Lifshitz, Ron Zeitschrift für Kristallographie, Vol. 222, Issue 6 https://doi.org/10.1524/zkri.2007.222.6.313	journal	January 2007
Predictive Self-Assembly of Polyhedra into Complex Structures Damasceno, P. F.; Engel, M.; Glotzer, S. C. Science, Vol. 337, Issue 6093 https://doi.org/10.1126/science.1220869	journal	July 2012
Microphase separation in diblock-copolymer melts: ordering of micelles Semenov, A. N. Macromolecules, Vol. 22, Issue 6 https://doi.org/10.1021/ma00196a054	journal	November 1989
Imperfections in the structure of cobalt. I. Experimental work and proposed structure Edwards, Olive S.; Lipson, Henry Solomon Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 180, Issue 982, p. 268-277 https://doi.org/10.1098/rspa.1942.0039	journal	June 1942
Transformation of cubic symmetry for spherical microdomains from face-centred to body-centred cubic upon uniaxial elongation in an elastomeric triblock copolymer Imaizumi, K.; Ono, T.; Kota, T. Journal of Applied Crystallography, Vol. 36, Issue 4 https://doi.org/10.1107/S0021889803008471	journal	July 2003
Epitaxial Transitions among FCC, HCP, BCC, and Cylinder Phases in a Block Copolymer Solution Park, Moon Jeong; Bang, Joona; Harada, Tamotsu Macromolecules, Vol. 37, Issue 24 https://doi.org/10.1021/ma049285g	journal	November 2004
Almost Fooled Again: New Insights into Cesium Dodecyl Sulfate Micelle Structures Lee, Han Seung; Adhimoolam Arunagirinathan, Manickam; Vagias, Apostolos Langmuir, Vol. 30, Issue 43 https://doi.org/10.1021/la502809y	journal	October 2014
Reconstructive transitions between ordered phases: The martensitic fcc-hcp and the graphite-diamond transitions Dmitriev, V. P.; Rochal, S. B.; Gufan, Yu. M. Physical Review Letters, Vol. 62, Issue 21 https://doi.org/10.1103/PhysRevLett.62.2495	journal	May 1989
Crystallization kinetics of atomic crystals revealed by a single-shot and single-particle X-ray diffraction experiment Niozu, Akinobu; Kumagai, Yoshiaki; Hiraki, Toshiyuki Nishiyama Proceedings of the National Academy of Sciences, Vol. 118, Issue 51 https://doi.org/10.1073/pnas.2111747118	journal	December 2021
Phase Diagram of Star Polymer Solutions Watzlawek, M.; Likos, C. N.; Löwen, H. Physical Review Letters, Vol. 82, Issue 26 https://doi.org/10.1103/PhysRevLett.82.5289	journal	June 1999
Diffraction of Random Tilings: Some Rigorous Results Baake, Michael; Höffe, Moritz Journal of Statistical Physics, Vol. 99, Issue 1/2, p. 219-261 https://doi.org/10.1023/A:1018648707744	journal	April 2000
Effect of Architecture on the Phase Behavior of AB-Type Block Copolymer Melts Matsen, M. W. Macromolecules, Vol. 45, Issue 4 https://doi.org/10.1021/ma202782s	journal	February 2012
Mesoscale networks and corresponding transitions from self-assembly of block copolymers Chang, Cheng-Yen; Manesi, Gkreti-Maria; Yang, Chih-Ying Proceedings of the National Academy of Sciences, Vol. 118, Issue 11 https://doi.org/10.1073/pnas.2022275118	journal	March 2021
Mechanisms of Chain Diffusion in Lamellar Block Copolymers Lodge, T. P.; Dalvi, M. C. Physical Review Letters, Vol. 75, Issue 4 https://doi.org/10.1103/PhysRevLett.75.657	journal	July 1995
Tuning Arm Architecture Leads to Unusual Phase Behaviors in a (BAB) ₅ Star Copolymer Melt Chen, Lei; Qiang, Yicheng; Li, Weihua Macromolecules, Vol. 51, Issue 23 https://doi.org/10.1021/acs.macromol.8b01484	journal	November 2018
Small-angle neutron scattering study of block copolymer morphology Richards, Randal W.; Thomason, J. L. Macromolecules, Vol. 16, Issue 6 https://doi.org/10.1021/ma00240a031	journal	June 1983
Structural changes in block copolymer micelles induced by cosolvent mixtures Kelley, Elizabeth G.; Smart, Thomas P.; Jackson, Andrew J. Soft Matter, Vol. 7, Issue 15 https://doi.org/10.1039/c1sm05506b	journal	January 2011
Optics of photonic quasicrystals Vardeny, Z. Valy; Nahata, Ajay; Agrawal, Amit Nature Photonics, Vol. 7, Issue 3 https://doi.org/10.1038/nphoton.2012.343	journal	February 2013
Structure Direction of II−VI Semiconductor Quantum Dot Binary Nanoparticle Superlattices by Tuning Radius Ratio Chen, Zhuoying; O’Brien, Stephen ACS Nano, Vol. 2, Issue 6 https://doi.org/10.1021/nn800129s	journal	May 2008
Rational Design of the First Spherical Supramolecular Dendrimers Self-Organized in a Novel Thermotropic Cubic Liquid-Crystalline Phase and the Determination of Their Shape by X-ray Analysis Balagurusamy, V. S. K.; Ungar, G.; Percec, V. Journal of the American Chemical Society, Vol. 119, Issue 7 https://doi.org/10.1021/ja963295i	journal	February 1997
Thermodynamically Originated Stacking Fault in the Close-Packed Structure of Block Copolymer Micelles Chen, Li-Ting; Huang, Yu-Ting; Chen, Chun-Yu Macromolecules, Vol. 54, Issue 19 https://doi.org/10.1021/acs.macromol.1c00792	journal	September 2021
The Effects of Shape on the Interaction of Colloidal Particles Onsager, Lars Annals of the New York Academy of Sciences, Vol. 51, Issue 4 https://doi.org/10.1111/j.1749-6632.1949.tb27296.x	journal	May 1949
Order through entropy Frenkel, Daan Nature Materials, Vol. 14, Issue 1 https://doi.org/10.1038/nmat4178	journal	December 2014
Polydispersity-Induced Macrophase Separation in Diblock Copolymer Melts Matsen, M. W. Physical Review Letters, Vol. 99, Issue 14 https://doi.org/10.1103/PhysRevLett.99.148304	journal	October 2007
Existence of fcc-Packed Spherical Micelles in Diblock Copolymer Melt Huang, Yen-Yu; Hsu, Jen-Yung; Chen, Hsin-Lung Macromolecules, Vol. 40, Issue 3 https://doi.org/10.1021/ma062149m	journal	February 2007
Role of stacking disorder in ice nucleation Lupi, Laura; Hudait, Arpa; Peters, Baron Nature, Vol. 551, Issue 7679 https://doi.org/10.1038/nature24279	journal	November 2017
Should All Crystals Be bcc? Landau Theory of Solidification and Crystal Nucleation Alexander, S.; McTague, J. Physical Review Letters, Vol. 41, Issue 10 https://doi.org/10.1103/PhysRevLett.41.702	journal	September 1978
Structure of ice crystallized from supercooled water Malkin, T. L.; Murray, B. J.; Brukhno, A. V. Proceedings of the National Academy of Sciences, Vol. 109, Issue 4 https://doi.org/10.1073/pnas.1113059109	journal	January 2012
Origins of Complex Self-Assembly in Block Copolymers Matsen, M. W.; Bates, F. S. Macromolecules, Vol. 29, Issue 23 https://doi.org/10.1021/ma960744q	journal	January 1996
Statistical Mechanics of Phase Diagrams. I. Inverse Power Potentials and the Close‐Packed to Body‐Centered Cubic Transition Hoover, William G.; Young, David A.; Grover, Richard The Journal of Chemical Physics, Vol. 56, Issue 5 https://doi.org/10.1063/1.1677521	journal	March 1972
The standard Gaussian model for block copolymer melts Matsen, M. W. Journal of Physics: Condensed Matter, Vol. 14, Issue 2 https://doi.org/10.1088/0953-8984/14/2/201	journal	December 2001
Stability of the Gyroid Phase in Diblock Copolymers at Strong Segregation Cochran, Eric W.; Garcia-Cervera, Carlos J.; Fredrickson, Glenn H. Macromolecules, Vol. 39, Issue 7 https://doi.org/10.1021/ma0527707	journal	April 2006
Close-packed block copolymer micelles induced by temperature quenching Chen, Liwen; Lee, Han Seung; Lee, Sangwoo Proceedings of the National Academy of Sciences, Vol. 115, Issue 28 https://doi.org/10.1073/pnas.1801682115	journal	June 2018
Phase Behavior of Binary Blends of Diblock Copolymers: Progress and Opportunities Xie, Jiayu; Shi, An-Chang Langmuir, Vol. 39, Issue 33 https://doi.org/10.1021/acs.langmuir.3c01175	journal	August 2023
Structural diversity in binary nanoparticle superlattices Shevchenko, Elena V.; Talapin, Dmitri V.; Kotov, Nicholas A. Nature, Vol. 439, Issue 7072, p. 55-59 https://doi.org/10.1038/nature04414	journal	January 2006
Structural aging of crystals of hard-sphere colloids Martelozzo, V. C.; Schofield, A. B.; Poon, W. C. K. Physical Review E, Vol. 66, Issue 2 https://doi.org/10.1103/PhysRevE.66.021408	journal	August 2002
Large-Strain Mechanical Behavior of Model Block Copolymer Adhesives Creton, Costantino; Hu, Guangjun; Deplace, Fanny Macromolecules, Vol. 42, Issue 20 https://doi.org/10.1021/ma900821k	journal	October 2009
Multiblock Polymers: Panacea or Pandora's Box? Bates, F. S.; Hillmyer, M. A.; Lodge, T. P. Science, Vol. 336, Issue 6080 https://doi.org/10.1126/science.1215368	journal	April 2012
Cornucopia of Nanoscale Ordered Phases in Sphere-Forming Tetrablock Terpolymers Chanpuriya, Siddharth; Kim, Kyungtae; Zhang, Jingwen ACS Nano, Vol. 10, Issue 5 https://doi.org/10.1021/acsnano.6b00495	journal	April 2016
A proof of the Kepler conjecture Hales, Thomas Annals of Mathematics, Vol. 162, Issue 3 https://doi.org/10.4007/annals.2005.162.1065	journal	January 2005
Martensitic fcc-to-hcp Transformation Observed in Xenon at High Pressure Cynn, H.; Yoo, C. S.; Baer, B. Physical Review Letters, Vol. 86, Issue 20 https://doi.org/10.1103/PhysRevLett.86.4552	journal	May 2001
Phase diagrams of hard-core repulsive Yukawa particles Hynninen, Antti-Pekka; Dijkstra, Marjolein Physical Review E, Vol. 68, Issue 2 https://doi.org/10.1103/PhysRevE.68.021407	journal	August 2003
Emergence of Hexagonally Close-Packed Spheres in Linear Block Copolymer Melts Zhang, Cheng; Vigil, Daniel L.; Sun, Dan Journal of the American Chemical Society, Vol. 143, Issue 35 https://doi.org/10.1021/jacs.1c03647	journal	August 2021
Origins of low-symmetry phases in asymmetric diblock copolymer melts Kim, Kyungtae; Arora, Akash; Lewis, Ronald M. Proceedings of the National Academy of Sciences, Vol. 115, Issue 5 https://doi.org/10.1073/pnas.1717850115	journal	January 2018
Report of the Executive Committee for 1991 Acta Crystallographica Section A Foundations of Crystallography, Vol. 48, Issue 6, p. 922-946 https://doi.org/10.1107/S0108767392008328	journal	November 1992
Supramolecular dendritic liquid quasicrystals Zeng, Xiangbing; Ungar, Goran; Liu, Yongsong Nature, Vol. 428, Issue 6979 https://doi.org/10.1038/nature02368	journal	March 2004
In search of colloidal hard spheres Royall, C. Patrick; Poon, Wilson C. K.; Weeks, Eric R. Soft Matter, Vol. 9, Issue 1 https://doi.org/10.1039/C2SM26245B	journal	January 2013
Small-angle neutron scattering determination of macrolattice structure in a polystyrene-polybutadiene diblock copolymer Bates, F. S.; Cohen, R. E.; Berney, C. V. Macromolecules, Vol. 15, Issue 2 https://doi.org/10.1021/ma00230a073	journal	March 1982
Ordered phases of diblock copolymers in selective solvent Grason, Gregory M. The Journal of Chemical Physics, Vol. 126, Issue 11 https://doi.org/10.1063/1.2709646	journal	March 2007
Bragg Rods and Multiple X-Ray Scattering in Random-Stacking Colloidal Crystals Petukhov, A. V.; Dolbnya, I. P.; Aarts, D. G. A. L. Physical Review Letters, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRevLett.90.028304	journal	January 2003
Stacking entropy of hard-sphere crystals Mau, Siun-Chuon; Huse, David A. Physical Review E, Vol. 59, Issue 4 https://doi.org/10.1103/PhysRevE.59.4396	journal	April 1999
Continuous transition of colloidal crystals through stable random orders Ahn, Juhong; Chen, Liwen; Underhill, Patrick T. Soft Matter, Vol. 19, Issue 18 https://doi.org/10.1039/D3SM00199G	journal	January 2023
Discovery of a Frank-Kasper Phase in Sphere-Forming Block Copolymer Melts Lee, S.; Bluemle, M. J.; Bates, F. S. Science, Vol. 330, Issue 6002 https://doi.org/10.1126/science.1195552	journal	October 2010
FCC or HCP: The stable close-packed lattice of crystallographically equivalent spherical micelles in block copolymer/homopolymer blend Chen, Li-Ting; Chen, Chun-Yu; Chen, Hsin-Lung Polymer, Vol. 169 https://doi.org/10.1016/j.polymer.2019.02.041	journal	April 2019
Structure of the Cubic Phases of Lipid–Water Systems Luzzati, Vittorio; Tardieu, A.; Gulik-Krzywicki, T. Nature, Vol. 220, Issue 5166 https://doi.org/10.1038/220485a0	journal	November 1968
Unifying Weak- and Strong-Segregation Block Copolymer Theories Matsen, M. W.; Bates, F. S. Macromolecules, Vol. 29, Issue 4 https://doi.org/10.1021/ma951138i	journal	January 1996
Self-assembly of soft-matter quasicrystals and their approximants Iacovella, C. R.; Keys, A. S.; Glotzer, S. C. Proceedings of the National Academy of Sciences, Vol. 108, Issue 52 https://doi.org/10.1073/pnas.1019763108	journal	December 2011
Can stacking faults in hard-sphere crystals anneal out spontaneously? Pronk, Sander; Frenkel, Daan The Journal of Chemical Physics, Vol. 110, Issue 9 https://doi.org/10.1063/1.478339	journal	March 1999
Frank–Kasper Phases in Block Polymers Dorfman, Kevin D. Macromolecules, Vol. 54, Issue 22 https://doi.org/10.1021/acs.macromol.1c01650	journal	October 2021
σ Phase Formed in Conformationally Asymmetric AB-Type Block Copolymers Xie, Nan; Li, Weihua; Qiu, Feng ACS Macro Letters, Vol. 3, Issue 9 https://doi.org/10.1021/mz500445v	journal	August 2014
Phase Behaviour and Morphologies of Block Copolymers Abetz, Volker; Simon, Peter F. W. Block Copolymers I https://doi.org/10.1007/12_004	book	January 2005
Complex Phase Behavior in Particle-Forming AB/AB′ Diblock Copolymer Blends with Variable Core Block Lengths Lindsay, Aaron P.; Cheong, Guo Kang; Peterson, Austin J. Macromolecules, Vol. 54, Issue 15 https://doi.org/10.1021/acs.macromol.1c01290	journal	July 2021
Phase diagram of Hertzian spheres Pàmies, Josep C.; Cacciuto, Angelo; Frenkel, Daan The Journal of Chemical Physics, Vol. 131, Issue 4 https://doi.org/10.1063/1.3186742	journal	July 2009
Quasicrystalline order in self-assembled binary nanoparticle superlattices Talapin, Dmitri V.; Shevchenko, Elena V.; Bodnarchuk, Maryna I. Nature, Vol. 461, Issue 7266 https://doi.org/10.1038/nature08439	journal	October 2009
Phase behaviour of concentrated suspensions of nearly hard colloidal spheres Pusey, P. N.; van Megen, W. Nature, Vol. 320, Issue 6060 https://doi.org/10.1038/320340a0	journal	March 1986
Phase diagram and structural study of polystyrene — poly(ethylene oxide) block copolymers, 1. Systems polystyrene/poly(ethylene oxide)/diethyl phthalate Gervais, Monique; Gallot, Bernard Die Makromolekulare Chemie, Vol. 171, Issue 1, p. 157-178 https://doi.org/10.1002/macp.1973.021710116	journal	October 1973
Sphericity and symmetry breaking in the formation of Frank–Kasper phases from one component materials Lee, Sangwoo; Leighton, Chris; Bates, Frank S. Proceedings of the National Academy of Sciences, Vol. 111, Issue 50 https://doi.org/10.1073/pnas.1408678111	journal	November 2014
Nucleation of Ordered Phases in Block Copolymers Cheng, Xiuyuan; Lin, Ling; E., Weinan Physical Review Letters, Vol. 104, Issue 14 https://doi.org/10.1103/PhysRevLett.104.148301	journal	April 2010
Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres Wood, W. W.; Jacobson, J. D. The Journal of Chemical Physics, Vol. 27, Issue 5 https://doi.org/10.1063/1.1743956	journal	November 1957
Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing Matsen, M. W. The European Physical Journal E, Vol. 30, Issue 4 https://doi.org/10.1140/epje/i2009-10534-3	journal	December 2009
Phase Transition for a Hard Sphere System Alder, B. J.; Wainwright, T. E. The Journal of Chemical Physics, Vol. 27, Issue 5 https://doi.org/10.1063/1.1743957	journal	November 1957
Entropy difference between crystal phases Bolhuis, P. G.; Frenkel, D.; Mau, Siun-Choun Nature, Vol. 388, Issue 6639 https://doi.org/10.1038/40779	journal	July 1997
Phase Behavior of Block Copolymer/Homopolymer Blends Matsen, M. W. Macromolecules, Vol. 28, Issue 17 https://doi.org/10.1021/ma00121a011	journal	August 1995
Interplay between Cubic and Hexagonal Phases in Block Copolymer Solutions Park, Moon Jeong; Char, Kookheon; Bang, Joona Langmuir, Vol. 21, Issue 4 https://doi.org/10.1021/la048056k	journal	January 2005
Modification of the overlap potential to mimic a linear site–site potential Gay, J. G.; Berne, B. J. The Journal of Chemical Physics, Vol. 74, Issue 6 https://doi.org/10.1063/1.441483	journal	March 1981
Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures Frank, F. C.; Kasper, J. S. Acta Crystallographica, Vol. 12, Issue 7 https://doi.org/10.1107/S0365110X59001499	journal	July 1959
Understanding Interfacial Block Copolymer Structure and Dynamics Goswami, Monojoy; Iyiola, Oluwagbenga Oare; Lu, Wei Macromolecules, Vol. 56, Issue 3 https://doi.org/10.1021/acs.macromol.2c01814	journal	January 2023
Thermal processing of diblock copolymer melts mimics metallurgy Kim, Kyungtae; Schulze, Morgan W.; Arora, Akash Science, Vol. 356, Issue 6337 https://doi.org/10.1126/science.aam7212	journal	May 2017
Non-Equilibrium Block Copolymer Self-Assembly Based Porous Membrane Formation Processes Employing Multicomponent Systems Tsaur, Lieihn; Wiesner, Ulrich B. Polymers, Vol. 15, Issue 9 https://doi.org/10.3390/polym15092020	journal	April 2023
Stabilizing colloidal crystals by leveraging void distributions Mahynski, Nathan A.; Panagiotopoulos, Athanassios Z.; Meng, Dong Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5472	journal	July 2014
Stabilizing New Morphologies by Blending Homopolymer with Block Copolymer Matsen, M. W. Physical Review Letters, Vol. 74, Issue 21 https://doi.org/10.1103/PhysRevLett.74.4225	journal	May 1995
Spherical Packing Superlattices in Self-Assembly of Homogenous Soft Matter: Progresses and Potentials Liu, Yuchu; Lei, Huanyu; Guo, Qing-Yun Chinese Journal of Polymer Science, Vol. 41, Issue 5 https://doi.org/10.1007/s10118-023-2976-5	journal	March 2023
A thermally induced transition from a body-centred to a face-centred cubic lattice in a diblock copolymer gel Hamley, I. W.; Pople, J. A.; Diat, O. Colloid & Polymer Science, Vol. 276, Issue 5 https://doi.org/10.1007/s003960050265	journal	June 1998
Internal Microstructure Dictates Interactions of Polymer-grafted Nanoparticles in Solution Gury, Leo; Kamble, Samruddhi; Parisi, Daniele Macromolecules, Vol. 54, Issue 15 https://doi.org/10.1021/acs.macromol.1c00907	journal	July 2021
Polytypes and polytypism Angel, R. J. Zeitschrift für Kristallographie - Crystalline Materials, Vol. 176, Issue 1-2 https://doi.org/10.1524/zkri.1986.176.12.193	journal	October 1986
Hexagonal Close-Packed Sphere Phase of Conformationally Symmetric Block Copolymer Hsu, Nai-Wen; Nouri, Babak; Chen, Li-Ting Macromolecules, Vol. 53, Issue 21 https://doi.org/10.1021/acs.macromol.0c01445	journal	October 2020
Tuning Diblock Copolymer Particle Packing Symmetry with Variable Molecular Weight Core-Homopolymers Mueller, Andreas J.; Lindsay, Aaron P.; Jayaraman, Ashish Macromolecules, Vol. 55, Issue 18 https://doi.org/10.1021/acs.macromol.2c01267	journal	September 2022
Layer-stacking irregularities in C36-type Nb–Cr and Ti–Cr Laves phases and their relation with polytypic phase transformations Aufrecht, J.; Baumann, W.; Leineweber, A. Philosophical Magazine, Vol. 90, Issue 23 https://doi.org/10.1080/14786435.2010.482068	journal	August 2010
Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity Kim, Sung A.; Jeong, Kyeong-Jun; Yethiraj, Arun Proceedings of the National Academy of Sciences, Vol. 114, Issue 16 https://doi.org/10.1073/pnas.1701608114	journal	April 2017

Similar Records

Martensitic Transformation of Close-Packed Polytypes of Block Copolymer Micelles

Journal Article · 2019 · Macromolecules · OSTI ID:1570674

Chen, Liwen; Lee, Han Seung; Zhernenkov, Mikhail; +1 more

Block Copolymers beneath the Surface: Measuring and Modeling Complex Morphology at the Subdomain Scale

Journal Article · 2021 · Macromolecules · OSTI ID:1817808

Reddy, Abhiram; Feng, Xueyan; Thomas, Edwin L.; +1 more

Close-packed block copolymer micelles induced by temperature quenching

Journal Article · 2018 · Proceedings of the National Academy of Sciences of the United States of America · OSTI ID:1499538

Chen, Liwen; Lee, Han Seung; Lee, Sangwoo

Related Subjects

36 MATERIALS SCIENCE
Crystal structure
Block copolymers
Colloidal crystal
Colloids
Hexagonal close-packed
Condensed Matter
Materials & Applied Physics
Polymers & Soft Matter

Title: Origin of polytypism in block copolymer materials

Citation Formats

References (105)

Similar Records

Related Subjects