1
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He J, Wang Q. Frank-Kasper Phases of Diblock Copolymer Melts: Self-Consistent Field Results of Two Commonly Used Models. Polymers (Basel) 2024; 16:372. [PMID: 38337261 DOI: 10.3390/polym16030372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2023] [Revised: 01/25/2024] [Accepted: 01/26/2024] [Indexed: 02/12/2024] Open
Abstract
We constructed phase diagrams of conformationally asymmetric diblock copolymer A-B melts using the polymer self-consistent field (SCF) calculations of both the dissipative particle dynamics chain (DPDC) model (i.e., compressible melts of discrete Gaussian chains with the DPD non-bonded potential) and the "standard" model (i.e., incompressible melts of continuous Gaussian chains with the Dirac δ-function non-bonded potential) in the χN-ε plane, where χN and ε characterize, respectively, the repulsion and conformational asymmetry between the A and B blocks, at the A-block volume fraction f = 0.2 and 0.3. Consistent with previous SCF calculations of the "standard" model, σ and A15 are the only stable Frank-Kasper (FK) phases among the five FK (i.e., σ, A15, C14, C15 and Z) phases considered. The stability of σ and A15 is due to their delicate balance between the energetic and entropic contributions to the Helmholtz free energy per chain of the system, which, within our parameter range, increases in the order of σ/A15, Z, and C14/C15. While in general the SCF phase diagrams of these two models are qualitatively consistent, A15 is not stable for the DPDC model at the copolymer chain length N = 10 and f = 0.3; any differences in the SCF phase diagrams are solely due to the differences between these two models.
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Affiliation(s)
- Juntong He
- Department of Chemical and Biological Engineering, Colorado State University, 1370 Campus Delivery, Fort Collins, CO 80523, USA
| | - Qiang Wang
- Department of Chemical and Biological Engineering, Colorado State University, 1370 Campus Delivery, Fort Collins, CO 80523, USA
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2
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Chen P, Dorfman KD. Gaming self-consistent field theory: Generative block polymer phase discovery. Proc Natl Acad Sci U S A 2023; 120:e2308698120. [PMID: 37922326 PMCID: PMC10636330 DOI: 10.1073/pnas.2308698120] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 09/25/2023] [Indexed: 11/05/2023] Open
Abstract
Block polymers are an attractive platform for uncovering the factors that give rise to self-assembly in soft matter owing to their relatively simple thermodynamic description, as captured in self-consistent field theory (SCFT). SCFT historically has found great success explaining experimental data, allowing one to construct phase diagrams from a set of candidate phases, and there is now strong interest in deploying SCFT as a screening tool to guide experimental design. However, using SCFT for phase discovery leads to a conundrum: How does one discover a new morphology if the set of candidate phases needs to be specified in advance? This long-standing challenge was surmounted by training a deep convolutional generative adversarial network (GAN) with trajectories from converged SCFT solutions, and then deploying the GAN to generate input fields for subsequent SCFT calculations. The power of this approach is demonstrated for network phase formation in neat diblock copolymer melts via SCFT. A training set of only five networks produced 349 candidate phases spanning known and previously unexplored morphologies, including a chiral network. This computational pipeline, constructed here entirely from open-source codes, should find widespread application in block polymer phase discovery and other forms of soft matter.
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Affiliation(s)
- Pengyu Chen
- Department of Chemical Engineering and Materials Science, University of Minnesota—Twin Cities, Minneapolis, MN55455
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota—Twin Cities, Minneapolis, MN55455
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3
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Quah T, Delaney KT, Fredrickson GH. Assessment of the partial saddle point approximation in field-theoretic polymer simulations. J Chem Phys 2023; 159:164103. [PMID: 37873956 DOI: 10.1063/5.0173047] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Accepted: 10/06/2023] [Indexed: 10/25/2023] Open
Abstract
Field-theoretic simulations are numerical treatments of polymer field theory models that go beyond the mean-field self-consistent field theory level and have successfully captured a range of mesoscopic phenomena. Inherent in molecularly-based field theories is a "sign problem" associated with complex-valued Hamiltonian functionals. One route to field-theoretic simulations utilizes the complex Langevin (CL) method to importance sample complex-valued field configurations to bypass the sign problem. Although CL is exact in principle, it can be difficult to stabilize in strongly fluctuating systems. An alternate approach for blends or block copolymers with two segment species is to make a "partial saddle point approximation" (PSPA) in which the stiff pressure-like field is constrained to its mean-field value, eliminating the sign problem in the remaining field theory, allowing for traditional (real) sampling methods. The consequences of the PSPA are relatively unknown, and direct comparisons between the two methods are limited. Here, we quantitatively compare thermodynamic observables, order-disorder transitions, and periodic domain sizes predicted by the two approaches for a weakly compressible model of AB diblock copolymers. Using Gaussian fluctuation analysis, we validate our simulation observations, finding that the PSPA incorrectly captures trends in fluctuation corrections to certain thermodynamic observables, microdomain spacing, and location of order-disorder transitions. For incompressible models with contact interactions, we find similar discrepancies between the predictions of CL and PSPA, but these can be minimized by regularization procedures such as Morse calibration. These findings mandate caution in applying the PSPA to broader classes of soft-matter models and systems.
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Affiliation(s)
- Timothy Quah
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Kris T Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Glenn H Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
- Materials Department, University of California, Santa Barbara, California 93106, USA
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4
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Saar KL, Qian D, Good LL, Morgunov AS, Collepardo-Guevara R, Best RB, Knowles TPJ. Theoretical and Data-Driven Approaches for Biomolecular Condensates. Chem Rev 2023; 123:8988-9009. [PMID: 37171907 PMCID: PMC10375482 DOI: 10.1021/acs.chemrev.2c00586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Indexed: 05/14/2023]
Abstract
Biomolecular condensation processes are increasingly recognized as a fundamental mechanism that living cells use to organize biomolecules in time and space. These processes can lead to the formation of membraneless organelles that enable cells to perform distinct biochemical processes in controlled local environments, thereby supplying them with an additional degree of spatial control relative to that achieved by membrane-bound organelles. This fundamental importance of biomolecular condensation has motivated a quest to discover and understand the molecular mechanisms and determinants that drive and control this process. Within this molecular viewpoint, computational methods can provide a unique angle to studying biomolecular condensation processes by contributing the resolution and scale that are challenging to reach with experimental techniques alone. In this Review, we focus on three types of dry-lab approaches: theoretical methods, physics-driven simulations and data-driven machine learning methods. We review recent progress in using these tools for probing biomolecular condensation across all three fields and outline the key advantages and limitations of each of the approaches. We further discuss some of the key outstanding challenges that we foresee the community addressing next in order to develop a more complete picture of the molecular driving forces behind biomolecular condensation processes and their biological roles in health and disease.
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Affiliation(s)
- Kadi L. Saar
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Cambridge CB2 1EW, United Kingdom
- Transition
Bio Ltd., Cambridge, United Kingdom
| | - Daoyuan Qian
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Lydia L. Good
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Cambridge CB2 1EW, United Kingdom
- Laboratory
of Chemical Physics, National Institute of Diabetes and Digestive
and Kidney Diseases, National Institutes
of Health, Bethesda, Maryland 20892, United States
| | - Alexey S. Morgunov
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Rosana Collepardo-Guevara
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Cambridge CB2 1EW, United Kingdom
- Department
of Genetics, University of Cambridge, Cambridge CB2 3EH, United Kingdom
| | - Robert B. Best
- Laboratory
of Chemical Physics, National Institute of Diabetes and Digestive
and Kidney Diseases, National Institutes
of Health, Bethesda, Maryland 20892, United States
| | - Tuomas P. J. Knowles
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Cambridge CB2 1EW, United Kingdom
- Cavendish
Laboratory, Department of Physics, University
of Cambridge, Cambridge CB3 0HE, United Kingdom
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5
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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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6
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Matsen MW, Beardsley TM, Willis JD. Fluctuation-Corrected Phase Diagrams for Diblock Copolymer Melts. PHYSICAL REVIEW LETTERS 2023; 130:248101. [PMID: 37390438 DOI: 10.1103/physrevlett.130.248101] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Revised: 04/04/2023] [Accepted: 05/22/2023] [Indexed: 07/02/2023]
Abstract
New developments in field-theoretic simulations (FTSs) are used to evaluate fluctuation corrections to the self-consistent field theory of diblock copolymer melts. Conventional simulations have been limited to the order-disorder transition (ODT), whereas FTSs allow us to evaluate complete phase diagrams for a series of invariant polymerization indices. The fluctuations stabilize the disordered phase, which shifts the ODT to higher segregation. Furthermore, they stabilize the network phases at the expense of the lamellar phase, which accounts for the presence of the Fddd phase in experiments. We hypothesize that this is due to an undulation entropy that favors curved interfaces.
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Affiliation(s)
- Mark W Matsen
- Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Tom M Beardsley
- Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - James D Willis
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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7
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Khandagale P, Breitzman T, Majidi C, Dayal K. Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions. Phys Rev E 2023; 107:064501. [PMID: 37464704 DOI: 10.1103/physreve.107.064501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 04/17/2023] [Indexed: 07/20/2023]
Abstract
Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.
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Affiliation(s)
- Pratik Khandagale
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Timothy Breitzman
- Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, USA
| | - Carmel Majidi
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
- Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
- Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Kaushik Dayal
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
- Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
- Center for Nonlinear Analysis, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
- Pittsburgh Quantum Institute, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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8
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Shen K, Nguyen M, Sherck N, Yoo B, Köhler S, Speros J, Delaney KT, Shell MS, Fredrickson GH. Predicting surfactant phase behavior with a molecularly informed field theory. J Colloid Interface Sci 2023; 638:84-98. [PMID: 36736121 DOI: 10.1016/j.jcis.2023.01.015] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2022] [Revised: 12/24/2022] [Accepted: 01/03/2023] [Indexed: 01/09/2023]
Abstract
HYPOTHESIS The computational study of surfactants and self-assembly is challenging because 1) models need to reflect chemistry-specific interactions, and 2) self-assembled structures are difficult to equilibrate with conventional molecular dynamics. We propose to overcome these challenges with a multiscale simulation approach where relative entropy minimization transfers chemically-detailed information from all-atom (AA) simulations to coarse-grained (CG) models that can be simulated using field-theoretic methods. Field-theoretic simulations are not limited by intrinsic physical time scales like diffusion and allow for rigorous equilibration via free energy minimization. This approach should enable the study of properties that are difficult to obtain by particle-based simulations. SIMULATION WORK We apply this workflow to sodium dodecylsulfate. To ensure chemical fidelity we present an AA force field calibrated against interfacial tension experiments. We generate CG models from AA simulation trajectories and show that particle-based and field-theoretic simulations of the CG model reproduce AA simulations and experimental measurements. FINDINGS The workflow captures the complex balance of interactions in a multicomponent system ultimately described by an atomistic model. The resulting CG models can study complex 3D phases like double or alternating gyroids, and reproduce salt effects on properties like aggregation number and shape transitions.
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Affiliation(s)
- Kevin Shen
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara 93106, CA, United States; Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara 93106, CA, United States.
| | - My Nguyen
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara 93106, CA, United States
| | - Nicholas Sherck
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara 93106, CA, United States
| | - Brian Yoo
- BASF Corporation, Tarrytown 10591, NY, United States
| | | | - Joshua Speros
- California Research Alliance (CARA) by BASF, Berkeley 94720, CA, United States
| | - Kris T Delaney
- Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara 93106, CA, United States
| | - M Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara 93106, CA, United States.
| | - Glenn H Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara 93106, CA, United States; Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara 93106, CA, United States; Department of Materials Engineering, University of California, Santa Barbara, Santa Barbara 93106, CA, United States.
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9
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Matsen MW, Beardsley TM, Willis JD. Accounting for the ultraviolet divergence in field-theoretic simulations of block copolymer melts. J Chem Phys 2023; 158:044904. [PMID: 36725530 DOI: 10.1063/5.0134890] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
This study examines the ultraviolet (UV) divergence in field-theoretic simulations (FTSs) of block copolymer melts, which causes an unphysical dependence on the grid resolution, Δ, used to represent the fields. Our FTSs use the discrete Gaussian-chain model and a partial saddle-point approximation to enforce incompressibility. Previous work has demonstrated that the UV divergence can be accounted for by defining an effective interaction parameter, χ=z∞χb+c2χb 2+c3χb 3+⋯, in terms of the bare interaction parameter, χb, used in the FTSs, where the coefficients of the expansion are determined by a Morse calibration. However, the need to use different grid resolutions for different ordered phases generally restricts the calibration to the linear approximation, χ ≈ z∞χb, and prevents the calculation of order-order transitions. Here, we resolve these two issues by showing how the nonlinear calibration can be translated between different grids and how the UV divergence can be removed from free energy calculations. By doing so, we confirm previous observations from particle-based simulations. In particular, we show that the free energy closely matches self-consistent field theory (SCFT) predictions, even in the region where fluctuations disorder the periodic morphologies, and similarly, the periods of the ordered phases match SCFT predictions, provided the SCFT is evaluated with the nonlinear χ.
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Affiliation(s)
- M W Matsen
- Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - T M Beardsley
- Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - J D Willis
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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10
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Najafi S, McCarty J, Delaney KT, Fredrickson GH, Shea JE. Field-Theoretic Simulation Method to Study the Liquid-Liquid Phase Separation of Polymers. Methods Mol Biol 2023; 2563:37-49. [PMID: 36227467 DOI: 10.1007/978-1-0716-2663-4_2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Liquid-liquid phase separation (LLPS) is a process that results in the formation of a polymer-rich liquid phase coexisting with a polymer-depleted liquid phase. LLPS plays a critical role in the cell through the formation of membrane-less organelles, but it also has a number of biotechnical and biomedical applications such as drug confinement and its targeted delivery. In this chapter, we present a computational efficient methodology that uses field-theoretic simulations (FTS) with complex Langevin (CL) sampling to characterize polymer phase behavior and delineate the LLPS phase boundaries. This approach is a powerful complement to analytical and explicit-particle simulations, and it can serve to inform experimental LLPS studies. The strength of the method lies in its ability to properly sample a large ensemble of polymers in a saturated solution while including the effect of composition fluctuations on LLPS. We describe the approaches that can be used to accurately construct phase diagrams of a variety of molecularly designed polymers and illustrate the method by generating an approximation-free phase diagram for a classical symmetric diblock polyampholyte.
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Affiliation(s)
- Saeed Najafi
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA, USA
- Materials Research Laboratory, University of California, Santa Barbara, CA, USA
| | - James McCarty
- Department of Chemistry, Western Washington University, Bellingham, WA, USA
| | - Kris T Delaney
- Materials Research Laboratory, University of California, Santa Barbara, CA, USA
| | - Glenn H Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, CA, USA
- Department of Chemical Engineering, University of California, Santa Barbara, CA, USA
| | - Joan-Emma Shea
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA, USA.
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA, USA.
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11
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Weyman A, Mavrantzas VG. Excluded-Volume Interactions in Field-Theoretic Simulations: Multiconvolutions and Model Equivalence. J Phys Chem B 2022; 126:10948-10954. [PMID: 36516441 PMCID: PMC9806830 DOI: 10.1021/acs.jpcb.2c06734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
To deal with divergences of functional integrals in field-theoretic simulations (FTS) of complex fluids, the microscopic density is often smeared by being replaced by a convoluted one, typically using a Gaussian masking function. The smearing changes radically the nature of nonbonded interactions of the original microscopic density and results in a regularized model that is free of ultraviolet (UV) divergences. In this work, we first resolve a few fundamental issues related with the use of masking functions for δ-interactions in FTS and then we detail a new methodology that builds on the concept of multiconvoluted inverse potentials and a principle of model equivalence for statistical weights to accommodate more physically relevant interactions in FTS. The capabilities of the new approach are highlighted by examining the Gaussian-regularized Edwards model (GREM) and the Yukawa potential. A successful test calculation of the excess chemical potential of a polymer chain in a good solvent with the GREM illustrates the power of the new theoretical framework.
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Affiliation(s)
- Alexander Weyman
- Polymer
Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland,
| | - Vlasis G. Mavrantzas
- Particle
Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland,Department
of Chemical Engineering, University of Patras
& FORTH-ICE/HT, GR 26504 Patras, Greece,
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12
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Schmid F. Understanding and Modeling Polymers: The Challenge of Multiple Scales. ACS POLYMERS AU 2022. [DOI: 10.1021/acspolymersau.2c00049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128Mainz, Germany
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13
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Zaldivar G, Perez Sirkin YA, Debais G, Fiora M, Missoni LL, Gonzalez Solveyra E, Tagliazucchi M. Molecular Theory: A Tool for Predicting the Outcome of Self-Assembly of Polymers, Nanoparticles, Amphiphiles, and Other Soft Materials. ACS OMEGA 2022; 7:38109-38121. [PMID: 36340074 PMCID: PMC9631762 DOI: 10.1021/acsomega.2c04785] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Accepted: 10/05/2022] [Indexed: 06/16/2023]
Abstract
The supramolecular organization of soft materials, such as colloids, polymers, and amphiphiles, results from a subtle balance of weak intermolecular interactions and entropic forces. This competition can drive the self-organization of soft materials at the nano-/mesoscale. Modeling soft-matter self-assembly requires, therefore, considering a complex interplay of forces at the relevant length scales without sacrificing the molecular details that define the chemical identity of the system. This mini-review focuses on the application of a tool known as molecular theory to study self-assembly in different types of soft materials. This tool is based on extremizing an approximate free energy functional of the system, and, therefore, it provides a direct, computationally affordable estimation of the stability of different self-assembled morphologies. Moreover, the molecular theory explicitly incorporates structural details of the chemical species in the system, accounts for their conformational degrees of freedom, and explicitly includes their chemical equilibria. This mini-review introduces the general ideas behind the theoretical formalism and discusses its advantages and limitations compared with other theoretical tools commonly used to study self-assembled soft materials. Recent application examples are discussed: the self-patterning of polyelectrolyte brushes on planar and curved surfaces, the formation of nanoparticle (NP) superlattices, and the self-organization of amphiphiles into micelles of different shapes. Finally, prospective methodological improvements and extensions (also relevant for related theoretical tools) are analyzed.
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Affiliation(s)
- Gervasio Zaldivar
- Departamento
de Química Inorgánica Analítica y Química
Física, Ciudad Universitaria, Facultad de Ciencias Exactas
y Naturales, Universidad de Buenos Aires, Pabellón 2 C1428EGA, Buenos Aires, Argentina
- Instituto
de Química de los Materiales, Ambiente y Energía (INQUIMAE).
Ciudad Universitaria, CONICET, Universidad
de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Pabellón 2 C1428EGA, Buenos Aires, Argentina
| | - Yamila A. Perez Sirkin
- Departamento
de Química Inorgánica Analítica y Química
Física, Ciudad Universitaria, Facultad de Ciencias Exactas
y Naturales, Universidad de Buenos Aires, Pabellón 2 C1428EGA, Buenos Aires, Argentina
- Instituto
de Química de los Materiales, Ambiente y Energía (INQUIMAE).
Ciudad Universitaria, CONICET, Universidad
de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Pabellón 2 C1428EGA, Buenos Aires, Argentina
| | - Gabriel Debais
- Instituto
de Química de los Materiales, Ambiente y Energía (INQUIMAE).
Ciudad Universitaria, CONICET, Universidad
de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Pabellón 2 C1428EGA, Buenos Aires, Argentina
| | - Maria Fiora
- INTI-Micro
y Nanotecnologías, Instituto Nacional
de Tecnología Industrial (INTI), San Martín, Buenos Aires B1650WAB, Argentina
| | - Leandro L. Missoni
- Departamento
de Química Inorgánica Analítica y Química
Física, Ciudad Universitaria, Facultad de Ciencias Exactas
y Naturales, Universidad de Buenos Aires, Pabellón 2 C1428EGA, Buenos Aires, Argentina
- Instituto
de Química de los Materiales, Ambiente y Energía (INQUIMAE).
Ciudad Universitaria, CONICET, Universidad
de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Pabellón 2 C1428EGA, Buenos Aires, Argentina
| | - Estefania Gonzalez Solveyra
- Universidad
Nacional de San Martin, Instituto de Nanosistemas, UNSAM-CONICET, Av. 25 de Mayo 1021, 1650 San Martín, Buenos Aires, Argentina
| | - Mario Tagliazucchi
- Departamento
de Química Inorgánica Analítica y Química
Física, Ciudad Universitaria, Facultad de Ciencias Exactas
y Naturales, Universidad de Buenos Aires, Pabellón 2 C1428EGA, Buenos Aires, Argentina
- Instituto
de Química de los Materiales, Ambiente y Energía (INQUIMAE).
Ciudad Universitaria, CONICET, Universidad
de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Pabellón 2 C1428EGA, Buenos Aires, Argentina
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14
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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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15
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Beardsley TM, Matsen MW. Well-tempered metadynamics applied to field-theoretic simulations of diblock copolymer melts. J Chem Phys 2022; 157:114902. [PMID: 36137783 DOI: 10.1063/5.0112703] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Well-tempered metadynamics (WTMD) is applied to field-theoretic simulations (FTS) to locate the order-disorder transition (ODT) in incompressible melts of diblock copolymer with an invariant polymerization index of N̄=104. The polymers are modeled as discrete Gaussian chains with N = 90 monomers, and the incompressibility is treated by a partial saddle-point approximation. Our implementation of WTMD proves effective at locating the ODT of the lamellar and cylindrical regions, but it has difficulty with that of the spherical and gyroid regions. In the latter two cases, our choice of order parameter cannot sufficiently distinguish the ordered and disordered states because of the similarity in microstructures. The gyroid phase has the added complication that it competes with a number of other morphologies, and thus, it might be beneficial to extend the WTMD to multiple order parameters. Nevertheless, when the method works, the ODT can be located with impressive accuracy (e.g., ΔχN ∼ 0.01).
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Affiliation(s)
- Thomas M Beardsley
- Department of Chemical Engineering, Department of Physics and Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo Ontario N2L 3G1, Canada
| | - Mark 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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16
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Le ML, Grzetic DJ, Delaney KT, Yang KC, Xie S, Fredrickson GH, Chabinyc ML, Segalman RA. Electrostatic Interactions Control the Nanostructure of Conjugated Polyelectrolyte–Polymeric Ionic Liquid Blends. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01142] [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)
- My Linh Le
- Materials Department, University of California, Santa Barbara, California 93106, United States
| | - Douglas J. Grzetic
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Kris T. Delaney
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Kai-Chieh Yang
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Shuyi Xie
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Materials Department, University of California, Santa Barbara, California 93106, United States
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
| | - Michael L. Chabinyc
- Materials Department, University of California, Santa Barbara, California 93106, United States
| | - Rachel A. Segalman
- Materials Department, University of California, Santa Barbara, California 93106, United States
- Chemical Engineering Department, University of California, Santa Barbara, California 93106, United States
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17
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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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18
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Weyman A, Mavrantzas VG, Öttinger HC. Direct calculation of the functional inverse of realistic interatomic potentials in field-theoretic simulations. J Chem Phys 2022; 156:224115. [PMID: 35705412 DOI: 10.1063/5.0090333] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We discuss the functional inverse problem in field-theoretic simulations for realistic pairwise potentials such as the Morse potential (widely used in particle simulations as an alternative to the 12-6 Lennard-Jones one), and we propose the following two solutions: (a) a numerical one based on direct inversion on a regular grid or deconvolution and (b) an analytical one by expressing attractive and repulsive contributions to the Morse potential as higher-order derivatives of the Dirac delta function; the resulting system of ordinary differential equations in the saddle-point approximation is solved numerically with appropriate model-consistent boundary conditions using a Newton-Raphson method. For the first time, exponential-like, physically realistic pair interactions are analytically treated and incorporated into a field-theoretic framework. The advantages and disadvantages of the two approaches are discussed in detail in connection with numerical findings from test simulations for the radial distribution function of a monatomic fluid at realistic densities providing direct evidence for the capability of the analytical method to resolve structural features down to the Angstrom scale.
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Affiliation(s)
- Alexander Weyman
- Polymer Physics, Department of Materials, ETH Zürich, CH-8093 Zurich, Switzerland
| | - Vlasis G Mavrantzas
- Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, CH-8092 Zurich, Switzerland
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19
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Vigil DL, Quah T, Sun D, Delaney KT, Fredrickson GH. Self-Consistent Field Theory Predicts Universal Phase Behavior for Linear, Comb, and Bottlebrush Diblock Copolymers. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00192] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel L. Vigil
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Timothy Quah
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Dan Sun
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
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20
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Direct free energy evaluation of classical and quantum many-body systems via field-theoretic simulation. Proc Natl Acad Sci U S A 2022; 119:e2201804119. [PMID: 35471906 PMCID: PMC9170146 DOI: 10.1073/pnas.2201804119] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The accurate evaluation of free energies within molecular simulations is important to many scientific fields, including fluid and solid phase equilibria, biomolecular condensates, and quantum phase transitions, among others. Unfortunately, free energy estimation is tedious and computationally expensive for molecular models whose degrees of freedom are expressed in particle coordinates. We show that alternative representations of a model as a classical or quantum field theory provide access to a chemical potential operator that can be averaged to yield a direct and low-cost estimate of the Gibbs free energy. The averaging is performed using a “field-theoretic” computer simulation that employs fluctuating fields rather than particles. Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator. We show that this feature leads a “direct” method of free energy evaluation, in which a particle model is converted to a field theory and appropriate field operators are averaged using a field-theoretic simulation conducted with complex Langevin sampling. These averages provide an immediate estimate of the Helmholtz free energy in the canonical ensemble and the entropy in the microcanonical ensemble. The method is illustrated for a classical polymer solution, a block copolymer melt exhibiting liquid crystalline and solid mesophases, and a quantum fluid of interacting bosons.
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21
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Petrov A, Gavrilov AA, Chertovich A. An exotic microstructured globular state formed by a single multiblock copolymer chain. J Chem Phys 2022; 156:034903. [DOI: 10.1063/5.0072568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Artem Petrov
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Alexey A. Gavrilov
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Alexander Chertovich
- Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
- Semenov Federal Research Center for Chemical Physics, 119991 Moscow, Russia
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22
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Nilsson D, Bozorg B, Mohanty S, Söderberg B, Irbäck A. Limitations of field-theory simulation for exploring phase separation: The role of repulsion in a lattice protein model. J Chem Phys 2022; 156:015101. [PMID: 34998327 DOI: 10.1063/5.0070412] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Field-theory simulation by the complex Langevin method offers an alternative to conventional sampling techniques for exploring the forces driving biomolecular liquid-liquid phase separation. Such simulations have recently been used to study several polyampholyte systems. Here, we formulate a field theory corresponding to the hydrophobic/polar (HP) lattice protein model, with finite same-site repulsion and nearest-neighbor attraction between HH bead pairs. By direct comparison with particle-based Monte Carlo simulations, we show that complex Langevin sampling of the field theory reproduces the thermodynamic properties of the HP model only if the same-site repulsion is not too strong. Unfortunately, the repulsion has to be taken weaker than what is needed to prevent condensed droplets from assuming an artificially compact shape. Analysis of a minimal and analytically solvable toy model hints that the sampling problems caused by repulsive interaction may stem from loss of ergodicity.
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Affiliation(s)
- Daniel Nilsson
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Behruz Bozorg
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Sandipan Mohanty
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Bo Söderberg
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Anders Irbäck
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
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23
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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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24
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Arora A, Lin TS, Rebello NJ, Av-Ron SHM, Mochigase H, Olsen BD. Random Forest Predictor for Diblock Copolymer Phase Behavior. ACS Macro Lett 2021; 10:1339-1345. [PMID: 35549019 DOI: 10.1021/acsmacrolett.1c00521] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Physics-based models are the primary approach for modeling the phase behavior of block copolymers. However, the successful use of self-consistent field theory (SCFT) for designing new materials relies on the correct chemistry- and temperature-dependent Flory-Huggins interaction parameter χAB that quantifies the incompatibility between the two blocks A and B as well as accurate estimation of the ratio of Kuhn lengths (bA/bB) and block densities. This work uses machine learning to model the phase behavior of AB diblock copolymers by using the chemical identities of blocks directly, obviating the need for measurement of χAB and bA/bB. The random forest approach employed predicts the phase behavior with almost 90% accuracy after training on a data set of 4768 data points, almost twice the accuracy obtained using SCFT employing χAB from group contribution theory. The machine-learning model is notably sensitive toward the uncertainty in measuring molecular parameters; however, its accuracy still remains at least 60% even for highly uncertain experimental measurements. Accuracy is substantially reduced when extrapolating to chemistries outside the training set. This work demonstrates that a random forest phase predictor performs remarkably well in many scenarios, providing an opportunity to predict self-assembly without measurement of molecular parameters.
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Affiliation(s)
- Akash Arora
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Tzyy-Shyang Lin
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Nathan J. Rebello
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Sarah H. M. Av-Ron
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Hidenobu Mochigase
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Bradley D. Olsen
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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25
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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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26
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Vigil DL, Delaney KT, Fredrickson GH. Quantitative Comparison of Field-Update Algorithms for Polymer SCFT and FTS. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01804] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel L. Vigil
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
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27
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Li W, Delaney KT, Fredrickson GH. Self-consistent field theory study of polymer-mediated colloidal interactions in solution: Depletion effects and induced forces. J Chem Phys 2021; 155:154903. [PMID: 34686054 DOI: 10.1063/5.0065742] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Polymer-mediated colloidal interactions control the stability and phase properties of colloid-polymer mixtures that are critical for a wide range of important applications. In this work, we develop a versatile self-consistent field theory (SCFT) approach to study this type of interaction based on a continuum confined polymer solution model with explicit solvent and confining walls. The model is formulated in the grand canonical ensemble, and the potential of mean force for the polymer-mediated interaction is computed from grand potentials. We focus on the case of non-adsorbing linear polymers and present a systematic investigation on depletion effects using SCFT. The properties of confined polymer solutions are probed, and mean-field profiles of induced interactions are shown across different physical regimes. We expose a detailed parametric dependence of the interaction, concerning both attractive and repulsive parts, on polymer concentration, chain length, and solvent quality and explore the effect of wall surface roughness, demonstrating the versatility of the proposed approach. Our findings show good agreement with previous numerical studies and experiments, yet extend prior work to new regimes. Moreover, the mechanisms of depletion attraction and repulsion, along with the influence of individual control factors, are further discussed. We anticipate that this study will provide useful insights into depletion forces and can be readily extended to examine more complex colloid-polymer mixtures.
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Affiliation(s)
- Wei Li
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Kris T Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Glenn H Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
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28
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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
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29
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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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30
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Dinic J, Marciel AB, Tirrell MV. Polyampholyte physics: Liquid–liquid phase separation and biological condensates. Curr Opin Colloid Interface Sci 2021. [DOI: 10.1016/j.cocis.2021.101457] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
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31
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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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32
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Weyman A, Mavrantzas VG, Öttinger HC. Field-theoretic simulations beyond δ-interactions: Overcoming the inverse potential problem in auxiliary field models. J Chem Phys 2021; 155:024106. [PMID: 34266260 DOI: 10.1063/5.0055255] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Modern field-theoretic simulations of complex fluids and polymers are constructed around a particle-to-field transformation that brings an inverse potential u-1 in the model equations. This has restricted the application of the framework to systems characterized by relatively simple pairwise interatomic interactions; for example, excluded volume effects are treated through the use of δ-function interactions. In this study, we first review available nonbonded pair interactions in field-theoretic models and propose a classification. Then, we outline the inverse potential problem and present an alternative approach on the basis of a saddle-point approximation, enabling the use of a richer set of pair interaction functions. We test our approach by using as an example the Morse potential, which finds extensive applications in particle-based simulations, and we calibrate u-1 with results from a molecular dynamics simulation. The u-1 thus obtained is consistent with the field-theoretic model equations, and when used in stand-alone self-consistent field simulations, it produces the correct fluid structure starting from a random initial state of the density field.
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Affiliation(s)
- Alexander Weyman
- Polymer Physics, Department of Materials, ETH Zurich, CH 8093 Zurich, Switzerland
| | - Vlasis G Mavrantzas
- Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zurich, CH 8092 Zurich, Switzerland
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33
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Najafi S, Lin Y, Longhini AP, Zhang X, Delaney KT, Kosik KS, Fredrickson GH, Shea J, Han S. Liquid-liquid phase separation of Tau by self and complex coacervation. Protein Sci 2021; 30:1393-1407. [PMID: 33955104 PMCID: PMC8197434 DOI: 10.1002/pro.4101] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Revised: 05/01/2021] [Accepted: 05/04/2021] [Indexed: 12/11/2022]
Abstract
The liquid-liquid phase separation (LLPS) of Tau has been postulated to play a role in modulating the aggregation property of Tau, a process known to be critically associated with the pathology of a broad range of neurodegenerative diseases including Alzheimer's Disease. Tau can undergo LLPS by homotypic interaction through self-coacervation (SC) or by heterotypic association through complex-coacervation (CC) between Tau and binding partners such as RNA. What is unclear is in what way the formation mechanisms for self and complex coacervation of Tau are similar or different, and the addition of a binding partner to Tau alters the properties of LLPS and Tau. A combination of in vitro experimental and computational study reveals that the primary driving force for both Tau CC and SC is electrostatic interactions between Tau-RNA or Tau-Tau macromolecules. The liquid condensates formed by the complex coacervation of Tau and RNA have distinctly higher micro-viscosity and greater thermal stability than that formed by the SC of Tau. Our study shows that subtle changes in solution conditions, including molecular crowding and the presence of binding partners, can lead to the formation of different types of Tau condensates with distinct micro-viscosity that can coexist as persistent and immiscible entities in solution. We speculate that the formation, rheological properties and stability of Tau droplets can be readily tuned by cellular factors, and that liquid condensation of Tau can alter the conformational equilibrium of Tau.
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Affiliation(s)
- Saeed Najafi
- Department of Chemistry and BiochemistryUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
- Materials Research LaboratoryUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
| | - Yanxian Lin
- Department of Biomolecular Science and EngineeringUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
| | - Andrew P. Longhini
- Molecular, Cell and Developmental BiologyUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
| | - Xuemei Zhang
- Neuroscience Research Institute, University of California Santa BarbaraSanta BarbaraCaliforniaUSA
| | - Kris T. Delaney
- Materials Research LaboratoryUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
| | - Kenneth S. Kosik
- Molecular, Cell and Developmental BiologyUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
- Neuroscience Research Institute, University of California Santa BarbaraSanta BarbaraCaliforniaUSA
| | - Glenn H. Fredrickson
- Materials Research LaboratoryUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
- Department of Chemical EngineeringUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
| | - Joan‐Emma Shea
- Department of Chemistry and BiochemistryUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
- Department of PhysicsUniversity of California at Santa BarbaraSanta BarbaraCaliforniaUSA
| | - Songi Han
- Department of Chemistry and BiochemistryUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
- Neuroscience Research Institute, University of California Santa BarbaraSanta BarbaraCaliforniaUSA
- Department of Chemical EngineeringUniversity of California Santa BarbaraSanta BarbaraCaliforniaUSA
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34
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Friedowitz S, Lou J, Barker KP, Will K, Xia Y, Qin J. Looping-in complexation and ion partitioning in nonstoichiometric polyelectrolyte mixtures. SCIENCE ADVANCES 2021; 7:eabg8654. [PMID: 34330707 PMCID: PMC8324053 DOI: 10.1126/sciadv.abg8654] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 06/15/2021] [Indexed: 06/13/2023]
Abstract
A wide variety of intracellular membraneless compartments are formed via liquid-liquid phase separation of charged proteins and nucleic acids. Understanding the stability of these compartments, while accounting for the compositional heterogeneity intrinsic to cellular environments, poses a daunting challenge. We combined experimental and theoretical efforts to study the effects of nonstoichiometric mixing on coacervation behavior and accurately measured the concentrations of polyelectrolytes and small ions in the coacervate and supernatant phases. For synthetic polyacrylamides and polypeptides/DNA, with unequal mixing stoichiometry, we report a general "looping-in" phenomenon found around physiological salt concentrations, where the polymer concentrations in the coacervate initially increase with salt addition before subsequently decreasing. This looping-in behavior is captured by a molecular model that considers reversible ion binding and electrostatic interactions. Further analysis in the low-salt regime shows that the looping-in phenomenon originates from the translational entropy of counterions that are needed to neutralize nonstoichiometric coacervates.
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Affiliation(s)
- Sean Friedowitz
- Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Junzhe Lou
- Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA
| | | | - Karis Will
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA
| | - Yan Xia
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA.
| | - Jian Qin
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
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35
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Yu B, Li R, Segalman RA. Tuning the Double Gyroid Phase Window in Block Copolymers via Polymer Chain Conformation Near the Interface. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00048] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Beihang Yu
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Ruipeng Li
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Rachel A. Segalman
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United States
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36
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Sherck N, Shen K, Nguyen M, Yoo B, Köhler S, Speros JC, Delaney KT, Shell MS, Fredrickson GH. Molecularly Informed Field Theories from Bottom-up Coarse-Graining. ACS Macro Lett 2021; 10:576-583. [PMID: 35570772 DOI: 10.1021/acsmacrolett.1c00013] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Polymer formulations possessing mesostructures or phase coexistence are challenging to simulate using atomistic particle-explicit approaches due to the disparate time and length scales, while the predictive capability of field-based simulations is hampered by the need to specify interactions at a coarser scale (e.g., χ-parameters). To overcome the weaknesses of both, we introduce a bottom-up coarse-graining methodology that leverages all-atom molecular dynamics to molecularly inform coarser field-theoretic models. Specifically, we use relative-entropy coarse-graining to parametrize particle models that are directly and analytically transformable into statistical field theories. We demonstrate the predictive capability of this approach by reproducing experimental aqueous poly(ethylene oxide) (PEO) cloud-point curves with no parameters fit to experimental data. This synergistic approach to multiscale polymer simulations opens the door to de novo exploration of phase behavior across a wide variety of polymer solutions and melt formulations.
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Affiliation(s)
- Nicholas Sherck
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Kevin Shen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - My Nguyen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Brian Yoo
- BASF Corporation, Tarrytown, New York 10591, United States
| | | | - Joshua C. Speros
- California Research Alliance (CARA) by BASF, Berkeley, California 94720, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - M. Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
- Department of Materials, University of California, Santa Barbara, California 93106, United States
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37
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Danielsen SPO, Beech HK, Wang S, El-Zaatari BM, Wang X, Sapir L, Ouchi T, Wang Z, Johnson PN, Hu Y, Lundberg DJ, Stoychev G, Craig SL, Johnson JA, Kalow JA, Olsen BD, Rubinstein M. Molecular Characterization of Polymer Networks. Chem Rev 2021; 121:5042-5092. [PMID: 33792299 DOI: 10.1021/acs.chemrev.0c01304] [Citation(s) in RCA: 60] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.
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Affiliation(s)
- Scott P O Danielsen
- Marsico Lung Institute, University of North Carolina, Chapel Hill, North Carolina 27599, United States
| | - Haley K Beech
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Shu Wang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Bassil M El-Zaatari
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Xiaodi Wang
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | | | | | - Zi Wang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Patricia N Johnson
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Yixin Hu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - David J Lundberg
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Georgi Stoychev
- Marsico Lung Institute, University of North Carolina, Chapel Hill, North Carolina 27599, United States
| | - Stephen L Craig
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Jeremiah A Johnson
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Julia A Kalow
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Bradley D Olsen
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Michael Rubinstein
- Marsico Lung Institute, University of North Carolina, Chapel Hill, North Carolina 27599, United States.,Department of Chemistry, Duke University, Durham, North Carolina 27708, United States.,Departments of Biomedical Engineering and Physics, Duke University, Durham, North Carolina 27708, United States.,World Primer Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Kita 21 Nishi 10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
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38
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Shea JE, Best RB, Mittal J. Physics-based computational and theoretical approaches to intrinsically disordered proteins. Curr Opin Struct Biol 2021; 67:219-225. [PMID: 33545530 PMCID: PMC8150118 DOI: 10.1016/j.sbi.2020.12.012] [Citation(s) in RCA: 72] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Revised: 12/24/2020] [Accepted: 12/28/2020] [Indexed: 02/06/2023]
Abstract
Intrinsically disordered proteins (IDPs) are an important class of proteins that do not fold to a well-defined three-dimensional shape but rather adopt an ensemble of inter-converting conformations. This feature makes their experimental characterization challenging and invites a theoretical and computational approach to complement experimental studies. In this review, we highlight the recent progress in developing new computational and theoretical approaches to study the structure and dynamics of monomeric and order higher assemblies of IDPs, with a particular emphasis on their phase separation into protein-rich condensates.
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Affiliation(s)
- Joan-Emma Shea
- Department of Chemistry & Biochemistry, University of California, Santa Barbara, CA 93106, United States; Department of Physics, University of California, Santa Barbara, CA 93106, United States.
| | - Robert B Best
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892, United States
| | - Jeetain Mittal
- Department of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Drive, Bethlehem, PA 18015, United States.
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39
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Beardsley TM, Matsen MW. Fluctuation correction for the order-disorder transition of diblock copolymer melts. J Chem Phys 2021; 154:124902. [PMID: 33810684 DOI: 10.1063/5.0046167] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
The order-disorder transition (ODT) of diblock copolymer melts is evaluated for an invariant polymerization index of N¯=104, using field-theoretic simulations (FTS) supplemented by a partial saddle-point approximation for incompressibility. For computational efficiency, the FTS are performed using the discrete Gaussian-chain model, and results are then mapped onto the continuous model using a linear approximation for the Flory-Huggins χ parameter. Particular attention is paid to the complex phase window. Results are found to be consistent with the well-established understanding that the gyroid phase extends down to the ODT. Furthermore, our simulations are the first to predict that the Fddd phase survives fluctuation effects, consistent with experiments.
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Affiliation(s)
- T M Beardsley
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - M 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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40
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Grzetic DJ, Delaney KT, Fredrickson GH. Electrostatic Manipulation of Phase Behavior in Immiscible Charged Polymer Blends. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00095] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Douglas J. Grzetic
- Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Glenn H. Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, Santa Barbara, California 93106, United States
- Departments of Chemical Engineering and Materials, University of California, Santa Barbara, Santa Barbara, California 93106, United States
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41
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Nguyen PH, Ramamoorthy A, Sahoo BR, Zheng J, Faller P, Straub JE, Dominguez L, Shea JE, Dokholyan NV, De Simone A, Ma B, Nussinov R, Najafi S, Ngo ST, Loquet A, Chiricotto M, Ganguly P, McCarty J, Li MS, Hall C, Wang Y, Miller Y, Melchionna S, Habenstein B, Timr S, Chen J, Hnath B, Strodel B, Kayed R, Lesné S, Wei G, Sterpone F, Doig AJ, Derreumaux P. Amyloid Oligomers: A Joint Experimental/Computational Perspective on Alzheimer's Disease, Parkinson's Disease, Type II Diabetes, and Amyotrophic Lateral Sclerosis. Chem Rev 2021; 121:2545-2647. [PMID: 33543942 PMCID: PMC8836097 DOI: 10.1021/acs.chemrev.0c01122] [Citation(s) in RCA: 378] [Impact Index Per Article: 126.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Protein misfolding and aggregation is observed in many amyloidogenic diseases affecting either the central nervous system or a variety of peripheral tissues. Structural and dynamic characterization of all species along the pathways from monomers to fibrils is challenging by experimental and computational means because they involve intrinsically disordered proteins in most diseases. Yet understanding how amyloid species become toxic is the challenge in developing a treatment for these diseases. Here we review what computer, in vitro, in vivo, and pharmacological experiments tell us about the accumulation and deposition of the oligomers of the (Aβ, tau), α-synuclein, IAPP, and superoxide dismutase 1 proteins, which have been the mainstream concept underlying Alzheimer's disease (AD), Parkinson's disease (PD), type II diabetes (T2D), and amyotrophic lateral sclerosis (ALS) research, respectively, for many years.
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Affiliation(s)
- Phuong H Nguyen
- CNRS, UPR9080, Université de Paris, Laboratory of Theoretical Biochemistry, IBPC, Fondation Edmond de Rothschild, PSL Research University, Paris 75005, France
| | - Ayyalusamy Ramamoorthy
- Biophysics and Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| | - Bikash R Sahoo
- Biophysics and Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| | - Jie Zheng
- Department of Chemical & Biomolecular Engineering, The University of Akron, Akron, Ohio 44325, United States
| | - Peter Faller
- Institut de Chimie, UMR 7177, CNRS-Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France
| | - John E Straub
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, United States
| | - Laura Dominguez
- Facultad de Química, Departamento de Fisicoquímica, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
| | - Joan-Emma Shea
- Department of Chemistry and Biochemistry, and Department of Physics, University of California, Santa Barbara, California 93106, United States
| | - Nikolay V Dokholyan
- Department of Pharmacology and Biochemistry & Molecular Biology, Penn State University College of Medicine, Hershey, Pennsylvania 17033, United States
- Department of Chemistry, and Biomedical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Alfonso De Simone
- Department of Life Sciences, Imperial College London, London SW7 2AZ, U.K
- Molecular Biology, University of Naples Federico II, Naples 80138, Italy
| | - Buyong Ma
- Basic Science Program, Leidos Biomedical Research, Inc., Cancer and Inflammation Program, National Cancer Institute, Frederick, Maryland 21702, United States
- School of Pharmacy, Shanghai Jiao Tong University, Shanghai, China
| | - Ruth Nussinov
- Basic Science Program, Leidos Biomedical Research, Inc., Cancer and Inflammation Program, National Cancer Institute, Frederick, Maryland 21702, United States
- Sackler Institute of Molecular Medicine, Department of Human Genetics and Molecular Medicine Sackler School of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Saeed Najafi
- Department of Chemistry and Biochemistry, and Department of Physics, University of California, Santa Barbara, California 93106, United States
| | - Son Tung Ngo
- Laboratory of Theoretical and Computational Biophysics & Faculty of Applied Sciences, Ton Duc Thang University, 33000 Ho Chi Minh City, Vietnam
| | - Antoine Loquet
- Institute of Chemistry & Biology of Membranes & Nanoobjects, (UMR5248 CBMN), CNRS, Université Bordeaux, Institut Européen de Chimie et Biologie, 33600 Pessac, France
| | - Mara Chiricotto
- Department of Chemical Engineering and Analytical Science, University of Manchester, Manchester M13 9PL, U.K
| | - Pritam Ganguly
- Department of Chemistry and Biochemistry, and Department of Physics, University of California, Santa Barbara, California 93106, United States
| | - James McCarty
- Chemistry Department, Western Washington University, Bellingham, Washington 98225, United States
| | - Mai Suan Li
- Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City 700000, Vietnam
- Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland
| | - Carol Hall
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905, United States
| | - Yiming Wang
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905, United States
| | - Yifat Miller
- Department of Chemistry and The Ilse Katz Institute for Nanoscale Science & Technology, Ben-Gurion University of the Negev, Be'er Sheva 84105, Israel
| | | | - Birgit Habenstein
- Institute of Chemistry & Biology of Membranes & Nanoobjects, (UMR5248 CBMN), CNRS, Université Bordeaux, Institut Européen de Chimie et Biologie, 33600 Pessac, France
| | - Stepan Timr
- CNRS, UPR9080, Université de Paris, Laboratory of Theoretical Biochemistry, IBPC, Fondation Edmond de Rothschild, PSL Research University, Paris 75005, France
| | - Jiaxing Chen
- Department of Pharmacology and Biochemistry & Molecular Biology, Penn State University College of Medicine, Hershey, Pennsylvania 17033, United States
| | - Brianna Hnath
- Department of Pharmacology and Biochemistry & Molecular Biology, Penn State University College of Medicine, Hershey, Pennsylvania 17033, United States
| | - Birgit Strodel
- Institute of Complex Systems: Structural Biochemistry (ICS-6), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Rakez Kayed
- Mitchell Center for Neurodegenerative Diseases, and Departments of Neurology, Neuroscience and Cell Biology, University of Texas Medical Branch, Galveston, Texas 77555, United States
| | - Sylvain Lesné
- Department of Neuroscience, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Guanghong Wei
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory for Computational Physical Science, Multiscale Research Institute of Complex Systems, Fudan University, Shanghai 200438, China
| | - Fabio Sterpone
- CNRS, UPR9080, Université de Paris, Laboratory of Theoretical Biochemistry, IBPC, Fondation Edmond de Rothschild, PSL Research University, Paris 75005, France
| | - Andrew J Doig
- Division of Neuroscience and Experimental Psychology, School of Biological Sciences, Faculty of Biology, Medicine and Health, University of Manchester, Manchester M13 9PT, U.K
| | - Philippe Derreumaux
- CNRS, UPR9080, Université de Paris, Laboratory of Theoretical Biochemistry, IBPC, Fondation Edmond de Rothschild, PSL Research University, Paris 75005, France
- Laboratory of Theoretical Chemistry, Ton Duc Thang University, 33000 Ho Chi Minh City, Vietnam
- Faculty of Pharmacy, Ton Duc Thang University, 33000 Ho Chi Minh City, Vietnam
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42
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Shen K, Sherck N, Nguyen M, Yoo B, Köhler S, Speros J, Delaney KT, Fredrickson GH, Shell MS. Learning composition-transferable coarse-grained models: Designing external potential ensembles to maximize thermodynamic information. J Chem Phys 2020; 153:154116. [DOI: 10.1063/5.0022808] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Kevin Shen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Nicholas Sherck
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - My Nguyen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Brian Yoo
- BASF Corporation, Tarrytown, New York 10591, USA
| | | | - Joshua Speros
- California Research Alliance (CARA) by BASF, Berkeley, California 94720, USA
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
- Department of Materials Engineering, University of California, Santa Barbara, California 93106, USA
| | - M. Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
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43
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Vorselaars B, Spencer RKW, Matsen MW. Instability of the Microemulsion Channel in Block Copolymer-Homopolymer Blends. PHYSICAL REVIEW LETTERS 2020; 125:117801. [PMID: 32976007 DOI: 10.1103/physrevlett.125.117801] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2020] [Accepted: 08/19/2020] [Indexed: 06/11/2023]
Abstract
Field theoretic simulations are used to predict the equilibrium phase diagram of symmetric blends of AB diblock copolymer with A- and B-type homopolymers. Experiments generally observe a channel of bicontinuous microemulsion (BμE) separating the ordered lamellar (LAM) phase from coexisting homopolymer-rich (A+B) phases. However, our simulations find that the channel is unstable with respect to macrophase separation, in particular, A+B+BμE coexistence at high T and A+B+LAM coexistence at low T. The preference for three-phase coexistence is attributed to a weak attractive interaction between diblock monolayers.
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Affiliation(s)
- Bart Vorselaars
- School of Mathematics and Physics, University of Lincoln, Brayford Pool, Lincoln LN6 7TS, United Kingdom
| | - 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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44
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Park S, Barnes R, Lin Y, Jeon BJ, Najafi S, Delaney KT, Fredrickson GH, Shea JE, Hwang DS, Han S. Dehydration entropy drives liquid-liquid phase separation by molecular crowding. Commun Chem 2020; 3:83. [PMID: 36703474 PMCID: PMC9814391 DOI: 10.1038/s42004-020-0328-8] [Citation(s) in RCA: 89] [Impact Index Per Article: 22.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Accepted: 05/15/2020] [Indexed: 01/29/2023] Open
Abstract
Complex coacervation driven liquid-liquid phase separation (LLPS) of biopolymers has been attracting attention as a novel phase in living cells. Studies of LLPS in this context are typically of proteins harboring chemical and structural complexity, leaving unclear which properties are fundamental to complex coacervation versus protein-specific. This study focuses on the role of polyethylene glycol (PEG)-a widely used molecular crowder-in LLPS. Significantly, entropy-driven LLPS is recapitulated with charged polymers lacking hydrophobicity and sequence complexity, and its propensity dramatically enhanced by PEG. Experimental and field-theoretic simulation results are consistent with PEG driving LLPS by dehydration of polymers, and show that PEG exerts its effect without partitioning into the dense coacervate phase. It is then up to biology to impose additional variations of functional significance to the LLPS of biological systems.
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Affiliation(s)
- Sohee Park
- grid.49100.3c0000 0001 0742 4007Division of Environmental Science and Engineering, Pohang University of Science and Technology (POSTECH), 77 Chengam-ro, Nam-gu, Pohang 37673 Republic of Korea
| | - Ryan Barnes
- grid.133342.40000 0004 1936 9676Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 93106 USA
| | - Yanxian Lin
- grid.133342.40000 0004 1936 9676Department of Biomolecular Science and Engineering, University of California, Santa Barbara, CA 93106 USA
| | - Byoung-jin Jeon
- grid.133342.40000 0004 1936 9676Materials Department, University of California, Santa Barbara, CA 93106 USA
| | - Saeed Najafi
- grid.133342.40000 0004 1936 9676Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 93106 USA ,grid.133342.40000 0004 1936 9676Materials Research Laboratory, University of California, Santa Barbara, CA 93106 USA
| | - Kris T. Delaney
- grid.133342.40000 0004 1936 9676Materials Research Laboratory, University of California, Santa Barbara, CA 93106 USA
| | - Glenn H. Fredrickson
- grid.133342.40000 0004 1936 9676Materials Department, University of California, Santa Barbara, CA 93106 USA ,grid.133342.40000 0004 1936 9676Materials Research Laboratory, University of California, Santa Barbara, CA 93106 USA ,grid.133342.40000 0004 1936 9676Department of Chemical Engineering, University of California, Santa Barbara, CA 93106 USA
| | - Joan-Emma Shea
- grid.133342.40000 0004 1936 9676Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 93106 USA ,grid.133342.40000 0004 1936 9676Department of Physics, University of California, Santa Barbara, CA 93106 USA
| | - Dong Soo Hwang
- grid.49100.3c0000 0001 0742 4007Division of Environmental Science and Engineering, Pohang University of Science and Technology (POSTECH), 77 Chengam-ro, Nam-gu, Pohang 37673 Republic of Korea ,grid.49100.3c0000 0001 0742 4007Division of Integrative Biosciences and Biotechnology, Pohang University of Science and Technology (POSTECH), 77 Chengam-ro, Nam-gu, Pohang 37673 Republic of Korea
| | - Songi Han
- grid.133342.40000 0004 1936 9676Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 93106 USA ,grid.133342.40000 0004 1936 9676Department of Chemical Engineering, University of California, Santa Barbara, CA 93106 USA
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45
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Park SJ, Kim JU. Single chain in mean field simulation of flexible and semiflexible polymers: comparison with discrete chain self-consistent field theory. SOFT MATTER 2020; 16:5233-5249. [PMID: 32458920 DOI: 10.1039/d0sm00620c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Single chain in mean field (SCMF) simulation is a theoretical framework performing Monte Carlo moves of explicit polymer chains under quasi-instantaneously updated external fields which were originally imported from the self-consistent field theory (SCFT). Even though functional-based hybrid simulations are often used to compare the results of SCFT and MC simulation, the adoption of a finite number of coarse-grained segments makes direct comparison rather difficult. In this study, we perform SCMF simulation of block copolymers using various chain models and quantitatively compare it with discrete chain SCFT (DCSCFT) which finds the mean field solution of polymers with a finite number of segments. By comparing free energy and natural period of the symmetric block copolymer lamellar phase, we systematically show that DCSCFT serves as an intermediate step between SCMF simulation and SCFT. In addition, by adopting angle dependent bond potential, we perform SCMF simulation of semiflexible polymers using bead-spring and freely jointed chain models. As the chain stiffness increases, the lamellar phase tends to align perpendicular to the surfaces when confined between two neutral walls. We also investigate the effects of fluctuation and chain stiffness on the distribution of chain ends. The tendency of chain end segregation towards the surfaces turns out to increase as the chain stiffness increases for both homopolymer and block copolymer systems.
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Affiliation(s)
- So Jung Park
- Department of Physics, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea.
| | - Jaeup U Kim
- Department of Physics, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea.
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Schauser NS, Grzetic DJ, Tabassum T, Kliegle GA, Le ML, Susca EM, Antoine S, Keller TJ, Delaney KT, Han S, Seshadri R, Fredrickson GH, Segalman RA. The Role of Backbone Polarity on Aggregation and Conduction of Ions in Polymer Electrolytes. J Am Chem Soc 2020; 142:7055-7065. [DOI: 10.1021/jacs.0c00587] [Citation(s) in RCA: 59] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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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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Müller M. Process-directed self-assembly of copolymers: Results of and challenges for simulation studies. Prog Polym Sci 2020. [DOI: 10.1016/j.progpolymsci.2019.101198] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Lequieu J, Koeper T, Delaney KT, Fredrickson GH. Extreme Deflection of Phase Boundaries and Chain Bridging in A(BA′)n Miktoarm Star Polymers. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02254] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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