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Li L, Xu Z, Li W. Emergence of Connected Binary Spherical Structures from the Self-assembly of an AB 2C Four-Arm Star Terpolymer. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Luyang Li
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Zhanwen Xu
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Weihua Li
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
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2
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Liu Z, Wang Z, Yin Y, Jiang R, Li B. A simulation study of the self-assembly of ABC star terpolymers confined between two parallel surfaces. SOFT MATTER 2021; 17:5336-5348. [PMID: 33950058 DOI: 10.1039/d1sm00271f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The phase behavior of ABC star terpolymers confined between two identical parallel surfaces is systematically studied using a simulated annealing method. Several phase diagrams are constructed for systems with different bulk phases or with different interfacial interaction strength ratios in the space of surface distance (D) and surface preference for different arms, or in the space of D and the arm-length ratio x. Phases, including tiling patterns [6.6.6], [8.8.4], [8.6.6; 8.6.4], [8.6.6; 8.6.4; 10.6.6; 10.6.4] and hierarchical lamellar structures of lamella + cylinders and lamella + rods, are identified both in the bulk and in the films. Our results suggest that the self-assembled structure of a phase is largely controlled by x, while an increase of the interfacial interaction strength ratio shifts the x-window for each phase to the smaller x side. The orientation of a confined phase depends on the "effective surface preference" which is a combined effect of the interfacial interaction strength ratio, the surface preference, and the entropic preference. In the case of neutral or weak "effective surface preference", phases with a perpendicular orientation are usually observed, while in the case of strong "effective surface preference" phases with a perpendicular orientation or also with outermost wetting-layers can be frequently observed under some circumstances.
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Affiliation(s)
- Zhiyao Liu
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Zheng Wang
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Yuhua Yin
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Run Jiang
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Baohui Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
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3
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Hain TM, Schröder-Turk GE, Kirkensgaard JJK. Patchy particles by self-assembly of star copolymers on a spherical substrate: Thomson solutions in a geometric problem with a color constraint. SOFT MATTER 2019; 15:9394-9404. [PMID: 31595280 DOI: 10.1039/c9sm01460h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Confinement or geometric frustration is known to alter the structure of soft matter, including copolymeric melts, and can consequently be used to tune structure and properties. Here we investigate the self-assembly of ABC and ABB 3-miktoarm star copolymers confined to a spherical shell using coarse-grained dissipative particle dynamics simulations. In bulk and flat geometries the ABC stars form hexagonal tilings, but this is topologically prohibited in a spherical geometry which normally is alleviated by forming pentagonal tiles. However, the molecular architecture of the ABC stars implies an additional 'color constraint' which only allows even tilings (where all polygons have an even number of edges) and we study the effect of these simultaneous constraints. We find that both ABC and ABB systems form spherical tiling patterns, the type of which depends on the radius of the spherical substrate. For small spherical substrates, all solutions correspond to patterns solving the Thomson problem of placing mobile repulsive electric charges on a sphere. In ABC systems we find three coexisting, possibly different tilings, one in each color, each of them solving the Thomson problem simultaneously. For all except the smallest substrates, we find competing solutions with seemingly degenerate free energies that occur with different probabilities. Statistically, an observer who is blind to the differences between B and C can tell from the structure of the A domains if the system is an ABC or an ABB star copolymer system.
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Affiliation(s)
- Tobias M Hain
- College of Science, Health, Engineering and Education, Mathematics and Statistics, Murdoch University, 90 South Street, 6150 Murdoch, Western Australia, Australia.
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Kim H, Arras MML, Mahalik JP, Wang W, Yu DM, Chernyy S, Goswami M, Kumar R, Sumpter BG, Hong K, Smith GS, Russell TP. Studies on the 3-Lamellar Morphology of Miktoarm Terpolymers. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01548] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Hyeyoung Kim
- Department of Polymer Science and Engineering, University of Massachusetts Amherst, 120 Governors Drive, Amherst, Massachusetts 01003, United States
| | | | - J. P. Mahalik
- Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37916, United States
| | | | - Duk Man Yu
- Department of Polymer Science and Engineering, University of Massachusetts Amherst, 120 Governors Drive, Amherst, Massachusetts 01003, United States
| | - Sergey Chernyy
- Department of Micro- and Nanotechnology, Technical University of Denmark, Produktionstorvet, 2800 Lyngby, Denmark
| | | | - Rajeev Kumar
- Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37916, United States
| | | | | | | | - Thomas P. Russell
- Department of Polymer Science and Engineering, University of Massachusetts Amherst, 120 Governors Drive, Amherst, Massachusetts 01003, United States
- Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Bejing 100029, China
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Chernyy S, Kirkensgaard JJK, Mahalik JP, Kim H, Arras MML, Kumar R, Sumpter BG, Smith GS, Mortensen K, Russell TP, Almdal K. Bulk and Surface Morphologies of ABC Miktoarm Star Terpolymers Composed of PDMS, PI, and PMMA Arms. Macromolecules 2018. [DOI: 10.1021/acs.macromol.7b02485] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Sergey Chernyy
- DTU
Nanotech, Technical University of Denmark, Produktionstorvet, 2800 Lyngby, Denmark
| | | | | | - Hyeyoung Kim
- Department
of Polymer Science and Engineering, University of Massachusetts Amherst, 120 Governors Drive, Amherst, Massachusetts 01003, United States
| | | | | | | | | | - Kell Mortensen
- Niels
Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Thomas P. Russell
- Department
of Polymer Science and Engineering, University of Massachusetts Amherst, 120 Governors Drive, Amherst, Massachusetts 01003, United States
| | - Kristoffer Almdal
- DTU
Nanotech, Technical University of Denmark, Produktionstorvet, 2800 Lyngby, Denmark
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6
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Jiang K, Zhang J, Liang Q. Self-Assembly of Asymmetrically Interacting ABC Star Triblock Copolymer Melts. J Phys Chem B 2015; 119:14551-62. [PMID: 26492084 DOI: 10.1021/acs.jpcb.5b08187] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Kai Jiang
- Hunan Key
Laboratory for
Computation and Simulation in Science and Engineering, School of Mathematics
and Computational Science, Xiangtan University, Hunan 411105, China
| | - Juan Zhang
- Hunan Key
Laboratory for
Computation and Simulation in Science and Engineering, School of Mathematics
and Computational Science, Xiangtan University, Hunan 411105, China
| | - Qin Liang
- Hunan Key
Laboratory for
Computation and Simulation in Science and Engineering, School of Mathematics
and Computational Science, Xiangtan University, Hunan 411105, China
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7
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Kirkensgaard JJK, Pedersen MC, Hyde ST. Tiling patterns from ABC star molecules: 3-colored foams? SOFT MATTER 2014; 10:7182-7194. [PMID: 25026461 DOI: 10.1039/c4sm01052c] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present coarse-grained simulations of the self-assembly of 3-armed ABC star polyphiles. In systems of star polyphiles with two arms of equal length the simulations corroborate and expand previous findings from related miktoarm star terpolymer systems on the formation of patterns containing columnar domains whose sections are 2D planar tilings. However, the systematic variation of face topologies as the length of the third (unequal) arm is varied differs from earlier findings regarding the compositional dependence. We explore 2D 3-colored foams to establish the optimal patterns based on interfacial energy alone. A generic construction algorithm is described that accounts for all observed 2D tiling patterns and suggests other patterns likely to be found beyond the range of the simulations reported here. Patterns resulting from this algorithm are relaxed using Surface Evolver calculations to form 2D foams with minimal interfacial length as a function of composition. This allows us to estimate the interfacial enthalpic contributions to the free energy of related star molecular assemblies assuming strong segregation. We compare the resulting phase sequence with a number of theoretical results from particle-based simulations and field theory, allowing us to tease out relative enthalpic and entropic contributions as a function of the chain lengths making up the star molecules. Our results indicate that a richer polymorphism is to be expected in systems not dominated by chain entropy. Further, analysis of corresponding planar tiling patterns suggests that related two-periodic columnar structures are unlikely hypothetical phases in 4-arm star polyphile melts in the absence of sufficient arm configurational freedom for minor domains to form lens-shaped di-gons, which require higher molecular weight polymeric arms. Finally, we discuss the possibility of forming a complex tiling pattern that is a quasi-crystalline approximant for 3-arm star polyphiles with unequal arm lengths.
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Marson RL, Phillips CL, Anderson JA, Glotzer SC. Phase behavior and complex crystal structures of self-assembled tethered nanoparticle telechelics. NANO LETTERS 2014; 14:2071-2078. [PMID: 24641517 DOI: 10.1021/nl500236b] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Motivated by growing interest in the self-assembly of nanoparticles for applications such as photonics, organic photovoltaics, and DNA-assisted designer crystals, we explore the phase behavior of tethered spherical nanoparticles. Here, a polymer tether is used to geometrically constrain a pair of nanoparticles creating a tethered nanoparticle "telechelic". Using simulation, we examine how varying architectural features, such as the size ratio of the two end-group nanospheres and the length of the flexible tether, affects the self-assembled morphologies. We demonstrate not only that this hybrid building block maintains the same phase diversity as linear triblock copolymers, allowing for a variety of nanoparticle materials to replace polymer blocks, but also that new structures not previously reported are accessible. Our findings imply a robust underlying ordering mechanism is common among these systems, thus allowing flexibility in synthesis approaches to achieve a target morphology.
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Affiliation(s)
- Ryan L Marson
- Materials Science and Engineering, ‡Department of Applied Physics, and §Chemical Engineering, University of Michigan , Ann Arbor, Michigan 48109, United States
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Kirkensgaard JJK, Evans ME, de Campo L, Hyde ST. Hierarchical self-assembly of a striped gyroid formed by threaded chiral mesoscale networks. Proc Natl Acad Sci U S A 2014; 111:1271-6. [PMID: 24474747 PMCID: PMC3910609 DOI: 10.1073/pnas.1316348111] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Numerical simulations reveal a family of hierarchical and chiral multicontinuous network structures self-assembled from a melt blend of Y-shaped ABC and ABD three-miktoarm star terpolymers, constrained to have equal-sized A/B and C/D chains, respectively. The C and D majority domains within these patterns form a pair of chiral enantiomeric gyroid labyrinths (srs nets) over a broad range of compositions. The minority A and B components together define a hyperbolic film whose midsurface follows the gyroid minimal surface. A second level of assembly is found within the film, with the minority components also forming labyrinthine domains whose geometry and topology changes systematically as a function of composition. These smaller labyrinths are well described by a family of patterns that tile the hyperbolic plane by regular degree-three trees mapped onto the gyroid. The labyrinths within the gyroid film are densely packed and contain either graphitic hcb nets (chicken wire) or srs nets, forming convoluted intergrowths of multiple nets. Furthermore, each net is ideally a single chiral enantiomer, induced by the gyroid architecture. However, the numerical simulations result in defect-ridden achiral patterns, containing domains of either hand, due to the achiral terpolymeric starting molecules. These mesostructures are among the most topologically complex morphologies identified to date and represent an example of hierarchical ordering within a hyperbolic pattern, a unique mode of soft-matter self-assembly.
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Affiliation(s)
| | - Myfanwy E. Evans
- Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstrasse 7B, 91058 Erlangen, Germany; and
| | - Liliana de Campo
- Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra, ACT 0200, Australia
| | - Stephen T. Hyde
- Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra, ACT 0200, Australia
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Schröder-Turk GE, de Campo L, Evans ME, Saba M, Kapfer SC, Varslot T, Grosse-Brauckmann K, Ramsden S, Hyde ST. Polycontinuous geometries for inverse lipid phases with more than two aqueous network domains. Faraday Discuss 2013; 161:215-47; discussion 273-303. [DOI: 10.1039/c2fd20112g] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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