1
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Magruder BR, Ellison CJ, Dorfman KD. Equilibrium phase behavior of gyroid-forming diblock polymer thin films. J Chem Phys 2024; 161:084902. [PMID: 39171715 DOI: 10.1063/5.0224767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2024] [Accepted: 08/05/2024] [Indexed: 08/23/2024] Open
Abstract
Thin-film confinement of self-assembling block polymers results in materials with myriad potential applications-including membranes and optical devices-and provides design parameters for altering phase behavior that are not available in the bulk, namely, film thickness and preferential wetting. However, most research has been limited to lamella- and cylinder-forming polymers; three-dimensional phases, such as double gyroid (DG), have been observed in thin films, but their phase behavior under confinement is not yet well understood. We use self-consistent field theory to predict the equilibrium morphology of bulk-gyroid-forming AB diblock polymers under thin-film confinement. Phase diagrams reveal that the (211) orientation of DG, often observed in experiments, is stable between nonpreferential boundaries at thicknesses as small as 1.2 times the bulk DG lattice parameter. The (001) orientation is stable between modestly B-preferential boundaries, where B is the majority block, while a different (211)-oriented termination plane is stabilized by strongly B-preferential boundaries, neither of which has been observed experimentally. We then describe two particularly important phenomena for explaining the phase behavior of DG thin films at low film thicknesses. The first is "constructive interference," which arises when distortions due to the top and bottom boundaries overlap and is significant for certain DG orientations. The second is a symmetry-dependent, in-plane unit-cell distortion that arises because the distorted morphology near the boundary has a different preferred unit-cell size and shape than the bulk. These results provide a thermodynamic portrait of the phase behavior of DG thin films.
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Affiliation(s)
- Benjamin R Magruder
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Christopher J Ellison
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
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2
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Fan Z, Zimmermann J, Ciacchi LC, Fischlschweiger M. Lattice-Cluster-Theory-Informed Cross-Fractionation Chromatography Revealing Degree of Crystallinity of Single Macromolecular Species. ACS Macro Lett 2024; 13:1043-1049. [PMID: 39079010 PMCID: PMC11340020 DOI: 10.1021/acsmacrolett.4c00288] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2024] [Revised: 07/24/2024] [Accepted: 07/25/2024] [Indexed: 08/21/2024]
Abstract
The relationship between macromolecular architecture and crystallization properties is a relevant research topic in polymer science and technology. The average degree of crystallinity of disperse polymers is a well-studied quantity and is accessible by various experimental methods. However, how the different macromolecular species contribute to the degree of crystallinity and, in particular, the relationship between a certain macromolecular architecture and the degree of crystallinity are not accessible today, neither experimentally nor theoretically. Therefore, in this work, a lattice cluster theory (LCT)-informed cross-fractionation chromatography (CFC) approach is developed to access the degree of crystallinity of single and nonlinear macromolecular species crystallizing from solution. The method entangles high-throughput experimental data from CFC with the LCT for semicrystalline polymers to predict the degree of crystallinity of polymer species with different molecular weights and branching. The approach is applied to a linear low-density polyethylene (ethylene/1-octene copolymer) and a high-density polyethylene, which have specific and different bivariate distributions. The degree of crystallinity of individual macromolecular species of these polymer samples is calculated, and the predicted average degree of crystallinity is compared with experimental measurements, thus successfully validating the approach. Furthermore, the average segment length between branches is introduced as a characteristic molecular feature of branched polyethylene, and its relationship with the degree of crystallinity of certain species is established.
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Affiliation(s)
- Zengxuan Fan
- Chair
of Technical Thermodynamics and Energy Efficient Material Treatment,
Institute for Energy Process Engineering and Fuel Technology, Clausthal University of Technology, Agricolastraße 4, 38678 Clausthal-Zellerfeld, Germany
| | - Jana Zimmermann
- Chair
of Technical Thermodynamics and Energy Efficient Material Treatment,
Institute for Energy Process Engineering and Fuel Technology, Clausthal University of Technology, Agricolastraße 4, 38678 Clausthal-Zellerfeld, Germany
| | - Lucio Colombi Ciacchi
- Hybrid
Materials Interface Group, Faculty of Production Engineering, Bremen
Center for Computational Materials Science and MAPEX Center for Materials
and Processes, University of Bremen, 28359 Bremen, Germany
| | - Michael Fischlschweiger
- Chair
of Technical Thermodynamics and Energy Efficient Material Treatment,
Institute for Energy Process Engineering and Fuel Technology, Clausthal University of Technology, Agricolastraße 4, 38678 Clausthal-Zellerfeld, Germany
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3
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Ivancic RJS, Audus DJ. Predicting compatibilized polymer blend toughness. SCIENCE ADVANCES 2024; 10:eadk6165. [PMID: 38896612 PMCID: PMC11186489 DOI: 10.1126/sciadv.adk6165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 05/13/2024] [Indexed: 06/21/2024]
Abstract
Polymer blends can yield superior materials by merging the unique properties of their components. However, these mixtures often phase separate, leading to brittleness. While compatibilizers can toughen these blends, their vast design space makes optimization difficult. Here, we develop a model to predict the toughness of compatibilized glassy polymer mixtures. This theory reveals that compatibilizers increase blend toughness by creating molecular bridges that stitch the interface together. We validate this theory by directly comparing its predictions to extensive molecular dynamics simulations in which we vary polymer incompatibility, chain stiffness, compatibilizer areal density, and blockiness of copolymer compatibilizers. We then parameterize the model using self-consistent field theory and confirm its ability to make predictions for practical applications through comparison with simulations and experiments. These results suggest that the theory can optimize compatibilizer design for industrial glassy polymer blends in silico while providing microscopic insight, allowing for the development of next-generation mixtures.
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Affiliation(s)
- Robert J. S. Ivancic
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Debra J. Audus
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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4
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Magruder BR, Morse DC, Ellison CJ, Dorfman KD. Boundary Frustration in Double-Gyroid Thin Films. ACS Macro Lett 2024; 13:382-388. [PMID: 38478981 DOI: 10.1021/acsmacrolett.4c00026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2024]
Abstract
Self-consistent field theory for thin films of AB diblock polymers in the double-gyroid phase reveals that in the absence of preferential wetting of monomer species at the film boundaries, films with the (211) plane oriented parallel to the boundaries are more stable than other orientations, consistent with experimental results. This preferred orientation is explained in the context of boundary frustration. Specifically, the angle of intersection between the A/B interface and the film boundary, the wetting angle, is thermodynamically restricted to a narrow range of values. Most termination planes in the double gyroid cannot accommodate this narrow range of wetting angles without significant local distortion relative to the bulk morphology; the (211)-oriented termination plane with the "double-wave" pattern produces relatively minimal distortion, making it the least frustrated boundary. The principle of boundary frustration provides a framework to understand the relative stability of termination planes for complex ordered block polymer phases confined between flat, nonpreferential boundaries.
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Affiliation(s)
- Benjamin R Magruder
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
| | - David C Morse
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
| | - Christopher J Ellison
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
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5
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Dorfman KD, Wang ZG. Liquid-Like States in Micelle-Forming Diblock Copolymer Melts. ACS Macro Lett 2023:980-985. [PMID: 37399493 DOI: 10.1021/acsmacrolett.3c00259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/05/2023]
Abstract
Large cell self-consistent field theory (SCFT) solutions for a neat, micelle-forming diblock copolymer melt, initialized using the structure of a Lennard-Jones fluid, reveal the existence of a vast number of liquid-like states, with free energies of order 10-3 kBT per chain higher than the body-centered cubic (bcc) state near the order-disorder transition (ODT). Computation of the structure factor for these liquids at temperatures below the ODT indicates that their intermicellar distance is slightly swollen compared to bcc. In addition to providing a mean-field picture of the disordered micellar state, the number of liquid-like states and their near-degeneracy with the equilibrium bcc morphology suggest that self-assembly of micelle-forming diblock copolymers navigates a rugged free energy landscape with many local minima. This picture provides a basis for the anomalously slow ordering kinetics of particle-forming diblock copolymer melts observed in experiments.
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Affiliation(s)
- Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Twin-Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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6
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Lequieu J. Combining particle and field-theoretic polymer models with multi-representation simulations. J Chem Phys 2023; 158:244902. [PMID: 37377157 DOI: 10.1063/5.0153104] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Accepted: 05/30/2023] [Indexed: 06/29/2023] Open
Abstract
Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.
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Affiliation(s)
- Joshua Lequieu
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USA
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7
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Chen P, Bates FS, Dorfman KD. Alternating Gyroid Stabilized by Surfactant-like Triblock Terpolymers in IS/SO/ISO Ternary Blends. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c02485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/09/2023]
Affiliation(s)
- Pengyu Chen
- Department of Chemical Engineering and Materials Science, University of Minnesota−Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
| | - Frank S. Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota−Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota−Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
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8
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Practical compatibility between self-consistent field theory and dissipative particle dynamics. POLYMER 2023. [DOI: 10.1016/j.polymer.2023.125733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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9
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Case LJ, Bates FS, Dorfman KD. Tuning conformational asymmetry in particle-forming diblock copolymer alloys. SOFT MATTER 2022; 19:90-97. [PMID: 36472126 DOI: 10.1039/d2sm01332k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Self-consistent field theory is employed to compute the phase behavior of binary blends of conformationally asymmetric, micelle-forming diblock copolymers with miscible corona blocks and immiscible core blocks (a diblock copolymer "alloy"). The calculations focus on establishing conditions that promote the formation of Laves phases by tuning the relative softness of the cores of the two different Laves phase particles via independent control of their conformational asymmetries. Increasing the conformational asymmetry of the more spherical particles of the Laves structure has a stabilizing effect, consistent with the expectations of increased imprinting of the Wigner-Seitz cells on the core/corona interface as conformational asymmetry increases. The resulting phase diagram in the temperature-blend composition space features a more stable Laves phase field than that predicted for conformationally symmetric systems. The phase field closes at low temperatures in favor of macrophase separation between a hexagonally-packed cylinder (hex) phase and a body-centered cubic phase. Companion calculations, using an alloy whose components do not produce a hex phase in the neat melt state, suggest that the Laves phase field in such a blend will persist at strong segregation.
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Affiliation(s)
- Logan J Case
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, USA.
| | - Frank S Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, USA.
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, USA.
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10
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He J, Wang Q. Frank–Kasper Phases of Diblock Copolymer Melts Studied with the DPD Model: SCF Results. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00933] [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)
- Juntong He
- Department of Chemical and Biological Engineering, Colorado State University, 1370 Campus Delivery, Fort Collins, Colorado 80523-1370, United States
| | - Qiang Wang
- Department of Chemical and Biological Engineering, Colorado State University, 1370 Campus Delivery, Fort Collins, Colorado 80523-1370, United States
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11
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Hagita K, Murashima T, Kawakatsu T. Lamellar Domain Spacing of Symmetric Linear, Ring, and Four-Arm-Star Block Copolymer Blends. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00500] [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)
- Katsumi Hagita
- Department of Applied Physics, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan
| | - Takahiro Murashima
- Department of Physics, Tohoku University, 6-3 Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8578, Japan
| | - Toshihiro Kawakatsu
- Department of Physics, Tohoku University, 6-3 Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8578, Japan
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12
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Yong D, Kim JU. Accelerating Langevin Field-Theoretic Simulation of Polymers with Deep Learning. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00705] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Daeseong Yong
- Department of Physics, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Korea
| | - Jaeup U. Kim
- Department of Physics, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Korea
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13
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Shen Z, Luo K, Park SJ, Li D, Mahanthappa MK, Bates FS, Dorfman KD, Lodge TP, Siepmann JI. Stabilizing a Double Gyroid Network Phase with 2 nm Feature Size by Blending of Lamellar and Cylindrical Forming Block Oligomers. JACS AU 2022; 2:1405-1416. [PMID: 35783180 PMCID: PMC9241014 DOI: 10.1021/jacsau.2c00101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 04/20/2022] [Accepted: 05/13/2022] [Indexed: 06/15/2023]
Abstract
Molecular dynamics simulations are used to study binary blends of an AB-type diblock and an AB2-type miktoarm triblock amphiphiles (also known as high-χ block oligomers) consisting of sugar-based (A) and hydrocarbon (B) blocks. In their pure form, the AB diblock and AB2 triblock amphiphiles self-assemble into ordered lamellar (LAM) and cylindrical (CYL) structures, respectively. At intermediate compositions, however, the AB2-rich blend (0.2 ≤ x AB ≤ 0.4) forms a double gyroid (DG) network, whereas perforated lamellae (PL) are observed in the AB-rich blend (0.5 ≤ x AB ≤ 0.8). All of the ordered mesophases present domain pitches under 3 nm, with 1 nm feature sizes for the polar domains. Structural analyses reveal that the nonuniform interfacial curvatures of DG and PL structures are supported by local composition variations of the LAM- and CYL-forming amphiphiles. Self-consistent mean field theory calculations for blends of related AB and AB2 block polymers also show the DG network at intermediate compositions, when A is the minority block, but PL is not stable. This work provides molecular-level insights into how blending of shape-filling molecular architectures enables network phase formation with extremely small feature sizes over a wide composition range.
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Affiliation(s)
- Zhengyuan Shen
- Department
of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States
- Chemical
Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
| | - Ke Luo
- Chemical
Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
- Department
of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
| | - So Jung Park
- Department
of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States
| | - Daoyuan Li
- Department
of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States
- Chemical
Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
| | - Mahesh K. Mahanthappa
- Department
of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States
| | - Frank S. Bates
- Department
of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States
| | - Kevin D. Dorfman
- Department
of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States
| | - Timothy P. Lodge
- Department
of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States
- Department
of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
| | - J. Ilja Siepmann
- Department
of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, United States
- Chemical
Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
- Department
of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States
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14
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Magruder BR, Park SJ, Collanton RP, Bates FS, Dorfman KD. Laves Phase Field in a Diblock Copolymer Alloy. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00346] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Benjamin R. Magruder
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| | - So Jung Park
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| | - Ryan P. Collanton
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| | - Frank S. Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
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15
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Yong D, Kim Y, Jo S, Ryu DY, Kim JU. Order-to-Disorder Transition of Cylinder-Forming Block Copolymer Films Confined within Neutral Interfaces. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c02182] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daeseong Yong
- Department of Physics, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Korea
| | - Yeongsik Kim
- Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
| | - Seungyun Jo
- Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
| | - Du Yeol Ryu
- Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
| | - Jaeup U. Kim
- Department of Physics, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Korea
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16
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Cheong GK, Dorfman KD. Disordered Micelle Regime in a Conformationally Asymmetric Diblock Copolymer Melt. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01629] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota─Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota─Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
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17
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Dhamankar S, Webb MA. Chemically specific coarse‐graining of polymers: Methods and prospects. JOURNAL OF POLYMER SCIENCE 2021. [DOI: 10.1002/pol.20210555] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Satyen Dhamankar
- Department of Chemical and Biological Engineering Princeton University Princeton New Jersey USA
| | - Michael A. Webb
- Department of Chemical and Biological Engineering Princeton University Princeton New Jersey USA
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18
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Park SJ, Cheong GK, Bates FS, Dorfman KD. Stability of the Double Gyroid Phase in Bottlebrush Diblock Copolymer Melts. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01654] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- So Jung Park
- Department of Chemical Engineering and Materials Science, University of Minnesota—Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, United States
| | - Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota—Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, United States
| | - Frank S. Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota—Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, United States
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota—Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, United States
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19
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Case LJ, Delaney KT, Fredrickson GH, Bates FS, Dorfman KD. Open-source platform for block polymer formulation design using particle swarm optimization. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:115. [PMID: 34532757 DOI: 10.1140/epje/s10189-021-00123-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Accepted: 09/06/2021] [Indexed: 06/13/2023]
Abstract
Facile exploration of large design spaces is critical to the development of new functional soft materials, including self-assembling block polymers, and computational inverse design methodologies are a promising route to initialize this task. We present here an open-source software package coupling particle swarm optimization (PSO) with an existing open-source self-consistent field theory (SCFT) software for the inverse design of self-assembling block polymers to target bulk morphologies. To lower the barrier to use of the software and facilitate exploration of novel design spaces, the underlying SCFT calculations are seeded with algorithmically generated initial fields for four typical morphologies: lamellae, network phases, cylindrical phases, and spherical phases. In addition to its utility within PSO, the initial guess tool also finds generic applicability for stand-alone SCFT calculations. The robustness of the software is demonstrated with two searches for classical phases in the conformationally symmetric diblock system, as well as one search for the Frank-Kasper [Formula: see text] phase in conformationally asymmetric diblocks. The source code for both the initial guess generation and the PSO wrapper is publicly available.
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Affiliation(s)
- Logan J Case
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, MN, 55455, USA
| | - Kris T Delaney
- Department of Chemical Engineering and Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, CA, 93106, USA
| | - Glenn H Fredrickson
- Department of Chemical Engineering and Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, CA, 93106, USA
| | - Frank S Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, MN, 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, Minneapolis, MN, 55455, USA.
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20
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Matsen MW, Beardsley TM. Field-Theoretic Simulations for Block Copolymer Melts Using the Partial Saddle-Point Approximation. Polymers (Basel) 2021; 13:2437. [PMID: 34372040 PMCID: PMC8347900 DOI: 10.3390/polym13152437] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Revised: 07/16/2021] [Accepted: 07/20/2021] [Indexed: 11/16/2022] Open
Abstract
Field-theoretic simulations (FTS) provide an efficient technique for investigating fluctuation effects in block copolymer melts with numerous advantages over traditional particle-based simulations. For systems involving two components (i.e., A and B), the field-based Hamiltonian, Hf[W-,W+], depends on a composition field, W-(r), that controls the segregation of the unlike components and a pressure field, W+(r), that enforces incompressibility. This review introduces researchers to a promising variant of FTS, in which W-(r) fluctuates while W+(r) tracks its mean-field value. The method is described in detail for melts of AB diblock copolymer, covering its theoretical foundation through to its numerical implementation. We then illustrate its application for neat AB diblock copolymer melts, as well as ternary blends of AB diblock copolymer with its A- and B-type parent homopolymers. The review concludes by discussing the future outlook. To help researchers adopt the method, open-source code is provided that can be run on either central processing units (CPUs) or graphics processing units (GPUs).
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Affiliation(s)
- Mark W. Matsen
- Department of Chemical Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada
- Department of Physics & Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
- Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, ON N2L 3G1, Canada;
| | - Thomas M. Beardsley
- Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, ON N2L 3G1, Canada;
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RuSseL: A Self-Consistent Field Theory Code for Inhomogeneous Polymer Interphases. COMPUTATION 2021. [DOI: 10.3390/computation9050057] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, we publish the one-dimensional version of our in-house code, RuSseL, which has been developed to address polymeric interfaces through Self-Consistent Field calculations. RuSseL can be used for a wide variety of systems in planar and spherical geometries, such as free films, cavities, adsorbed polymer films, polymer-grafted surfaces, and nanoparticles in melt and vacuum phases. The code includes a wide variety of functional potentials for the description of solid–polymer interactions, allowing the user to tune the density profiles and the degree of wetting by the polymer melt. Based on the solution of the Edwards diffusion equation, the equilibrium structural properties and thermodynamics of polymer melts in contact with solid or gas surfaces can be described. We have extended the formulation of Schmid to investigate systems comprising polymer chains, which are chemically grafted on the solid surfaces. We present important details concerning the iterative scheme required to equilibrate the self-consistent field and provide a thorough description of the code. This article will serve as a technical reference for our works addressing one-dimensional polymer interphases with Self-Consistent Field theory. It has been prepared as a guide to anyone who wishes to reproduce our calculations. To this end, we discuss the current possibilities of the code, its performance, and some thoughts for future extensions.
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Affiliation(s)
- Russell K. W. Spencer
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Mark W. Matsen
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Qiang Y, Li W. Accelerated Pseudo-Spectral Method of Self-Consistent Field Theory via Crystallographic Fast Fourier Transform. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01974] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Yicheng Qiang
- 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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Abstract
This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.
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Affiliation(s)
- M W Matsen
- Department of Chemical Engineering, Department of Physics and Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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