1
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Iso N, Norizoe Y, Sakaue T. Phase separation in soft repulsive polymer mixtures: foundation and implication for chromatin organization. SOFT MATTER 2024; 20:6848-6856. [PMID: 39157948 DOI: 10.1039/d4sm00309h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/20/2024]
Abstract
Given the wide range of length scales, the analysis of polymer systems often requires coarse-graining, for which various levels of description may be possible depending on the phenomenon under consideration. Here, we provide a super-coarse grained description, where polymers are represented as a succession of mesosopic soft beads which are allowed to overlap with others. We then investigate the phase separation behaviors in a mixture of such homopolymers based on mean-field theory, and discuss universal aspects of the miscibility phase diagram in comparison with the numerical simulation. We also discuss an extension of our analysis to mixtures involving random copolymers, which might be interesting in the context of chromatin organization in a cell nucleus.
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Affiliation(s)
- Naoki Iso
- Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Japan.
| | - Yuki Norizoe
- Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Japan.
| | - Takahiro Sakaue
- Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Japan.
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2
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Mei B, Grest GS, Liu S, O’Connor TC, Schweizer KS. Unified understanding of the impact of semiflexibility, concentration, and molecular weight on macromolecular-scale ring diffusion. Proc Natl Acad Sci U S A 2024; 121:e2403964121. [PMID: 39042674 PMCID: PMC11295076 DOI: 10.1073/pnas.2403964121] [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: 02/26/2024] [Accepted: 06/24/2024] [Indexed: 07/25/2024] Open
Abstract
Conformationally fluctuating, globally compact macromolecules such as polymeric rings, single-chain nanoparticles, microgels, and many-arm stars display complex dynamic behaviors due to their rich topological structure and intermolecular organization. Synthetic rings are hybrid objects with conformations that display both ideal random walk and compact globular features, which can serve as models of genomic DNA. To date, emphasis has been placed on the effect of ring molecular weight on their unusual behaviors. Here, we combine simulations and a microscopic force-level theory to build a unified understanding for how key aspects of ring dynamics depend on different tunable molecular properties including backbone rigidity, monomer concentration, degree of traditional entanglement, and molecular weight. Our large-scale molecular dynamics simulations of ring melts with very different backbone stiffnesses reveal unanticipated behaviors which agree well with our generalized theory. This includes a universal master curve for center-of-mass diffusion constants as a function of molecular weight scaled by a chemistry and thermodynamic state-dependent critical molecular weight that generalizes the concept of an entanglement cross-over for linear chains. The key physics is how backbone rigidity and monomer concentration induced changes of the entanglement length, interring packing, degree of interpenetration, and liquid compressibility slow down space-time dynamic-force correlations on macromolecular scales. A power law decay of the center-of-mass diffusion constant with inverse molecular weight squared is the first consequence, followed by an ultraslow activated hopping transport regime. Our results set the stage to address slow dynamics and kinetic arrest in different families of compact synthetic and biological polymeric systems.
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Affiliation(s)
- Baicheng Mei
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL61801
- Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL61801
| | | | - Songyue Liu
- Department of Materials Science and Engineering, Carnegie-Mellon University, Pittsburgh, PA15213
| | - Thomas C. O’Connor
- Department of Materials Science and Engineering, Carnegie-Mellon University, Pittsburgh, PA15213
| | - Kenneth S. Schweizer
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL61801
- Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL61801
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL61801
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3
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Mei B, Moreno AJ, Schweizer KS. Unified Understanding of the Structure, Thermodynamics, and Diffusion of Single-Chain Nanoparticle Fluids. ACS NANO 2024; 18:15529-15544. [PMID: 38842208 DOI: 10.1021/acsnano.4c00226] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
Single-chain nanoparticles (SCNPs) are a fascinating class of soft nano-objects with promising properties and relevance to protein condensates, polymer nanocomposites, nanomedicine, bioimaging, catalysis, and drug delivery. We combine molecular dynamics simulations and equilibrium and time-dependent statistical mechanical theory to construct a unified understanding of how the internal conformational structure of SCNPs, of both a simple fractal globule-like form and more complex objects with multiple internal intermediate length scales, determines nm-scale intermolecular packing correlations, thermodynamic properties, and center-of-mass diffusion over a wide range of concentrations up to dense melts. The intermolecular pair correlations generically exhibit a distinctive deep correlation hole form due to SCNP internal connectivity structure and repulsive interparticle interactions associated with a globular-like conformation on the macromolecular scale, with concentration-dependent deviations at small separations. Unanticipated exponential-like dependences of the equation-of-state, osmotic compressibility, and center-of-mass diffusion constant on SCNP macromolecular packing fraction are theoretically predicted and confirmed via simulations. System-specific behaviors are found associated with SCNP internal structure, but overarching regularities are identified and understood based on a generalized effective globule conformation on macromolecular scales. Diffusivity slows down by 2-3 decades with increasing concentration and is understood as a consequence of a nonactivated excluded volume-driven weak-caging process associated with space-time correlated intermolecular forces experienced by the SCNP. Good agreement between the theory and simulations is established, testable predictions are made, and a quantitative comparison with viscosity measurements on a specific SCNP fluid is carried out. The basic theoretical approach can potentially be extended to treat the chemical and physical consequences of varying the structure of other classes of soft nanoparticles with distinctive internal nanoscale organization relevant in nanotechnology and nanomedicine, and the possible emergence of macromolecular kinetically arrested glasses.
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Affiliation(s)
- Baicheng Mei
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Angel J Moreno
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, Donostia-San Sebastián E-20018, Spain
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, Donostia-San Sebastián E-20018, Spain
| | - Kenneth S Schweizer
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
- Department of Chemical & Biomolecular Engineering, University of Illinois, Urbana, Illinois 61801, United States
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4
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Goto S, Kim K, Matubayasi N. Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain. ACS POLYMERS AU 2023; 3:437-446. [PMID: 38107414 PMCID: PMC10722566 DOI: 10.1021/acspolymersau.3c00013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Revised: 08/08/2023] [Accepted: 08/08/2023] [Indexed: 12/19/2023]
Abstract
Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.
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Affiliation(s)
- Shota Goto
- Division of Chemical Engineering, Department
of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kang Kim
- Division of Chemical Engineering, Department
of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Department
of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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5
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Tu M, Davydovich O, Mei B, Singh PK, Grest GS, Schweizer KS, O’Connor TC, Schroeder CM. Unexpected Slow Relaxation Dynamics in Pure Ring Polymers Arise from Intermolecular Interactions. ACS POLYMERS AU 2023; 3:307-317. [PMID: 37576713 PMCID: PMC10416323 DOI: 10.1021/acspolymersau.2c00069] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Revised: 02/28/2023] [Accepted: 03/01/2023] [Indexed: 04/03/2023]
Abstract
Ring polymers have fascinated scientists for decades, but experimental progress has been challenging due to the presence of linear chain contaminants that fundamentally alter dynamics. In this work, we report the unexpected slow stress relaxation behavior of concentrated ring polymers that arises due to ring-ring interactions and ring packing structure. Topologically pure, high molecular weight ring polymers are prepared without linear chain contaminants using cyclic poly(phthalaldehyde) (cPPA), a metastable polymer chemistry that rapidly depolymerizes from free ends at ambient temperatures. Linear viscoelastic measurements of highly concentrated cPPA show slow, non-power-law stress relaxation dynamics despite the lack of linear chain contaminants. Experiments are complemented by molecular dynamics (MD) simulations of unprecedentedly high molecular weight rings, which clearly show non-power-law stress relaxation in good agreement with experiments. MD simulations reveal substantial ring-ring interpenetrations upon increasing ring molecular weight or local backbone stiffness, despite the global collapsed nature of single ring conformation. A recently proposed microscopic theory for unconcatenated rings provides a qualitative physical mechanism associated with the emergence of strong inter-ring caging which slows down center-of-mass diffusion and long wavelength intramolecular relaxation modes originating from ring-ring interpenetrations, governed by the onset variable N/ND, where the crossover degree of polymerization ND is qualitatively predicted by theory. Our work overcomes challenges in achieving ring polymer purity and by characterizing dynamics for high molecular weight ring polymers. Overall, these results provide a new understanding of ring polymer physics.
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Affiliation(s)
- Michael
Q. Tu
- Department of Chemical and Biomolecular Engineering, Beckman Institute for Advanced Science
and Technology, Department of Chemistry, Department of Materials Science and Engineering and Materials Research
Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Oleg Davydovich
- Department of Chemical and Biomolecular Engineering, Beckman Institute for Advanced Science
and Technology, Department of Chemistry, Department of Materials Science and Engineering and Materials Research
Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Baicheng Mei
- Department of Chemical and Biomolecular Engineering, Beckman Institute for Advanced Science
and Technology, Department of Chemistry, Department of Materials Science and Engineering and Materials Research
Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Piyush K. Singh
- Department of Chemical and Biomolecular Engineering, Beckman Institute for Advanced Science
and Technology, Department of Chemistry, Department of Materials Science and Engineering and Materials Research
Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Gary S. Grest
- Sandia
National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Kenneth S. Schweizer
- Department of Chemical and Biomolecular Engineering, Beckman Institute for Advanced Science
and Technology, Department of Chemistry, Department of Materials Science and Engineering and Materials Research
Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Thomas C. O’Connor
- Department
of Materials Science and Engineering, Carnegie
Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Charles M. Schroeder
- Department of Chemical and Biomolecular Engineering, Beckman Institute for Advanced Science
and Technology, Department of Chemistry, Department of Materials Science and Engineering and Materials Research
Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
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6
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Vagias A, Nelson A, Wang P, Reitenbach J, Geiger C, Kreuzer LP, Saerbeck T, Cubitt R, Benetti EM, Müller-Buschbaum P. The Topology of Polymer Brushes Determines Their Nanoscale Hydration. Macromol Rapid Commun 2023; 44:e2300035. [PMID: 36815590 DOI: 10.1002/marc.202300035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Indexed: 02/24/2023]
Abstract
Time-of-flight neutron reflectometry (ToF-NR) performed under different relative humidity conditions demonstrates that polymer brushes constituted by hydrophilic, cyclic macromolecules exhibit a more compact conformation with lower roughness as compared to linear brush analogues, due to the absence of dangling chain ends extending at the polymer-vapor interface. In addition, cyclic brushes feature a larger swelling ratio and an increased solvent uptake with respect to their linear counterparts as a consequence of the increased interchain steric repulsions. It is proposed that differences in swelling ratios between linear and cyclic brushes come from differences in osmotic pressure experienced by each brush topology. These differences stem from entropic constraints. The findings suggest that to correlate the equilibrium swelling ratios at different relative humidity for different topologies a new form of the Flory-like expression for equilibrium thicknesses of grafted brushes is needed.
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Affiliation(s)
- Apostolos Vagias
- Heinz Maier-Leibnitz Zentrum (MLZ), Technical University of Munich, Lichtenbergstr. 1, 85748, Garching, Germany
| | - Andrew Nelson
- ANSTO, New Illawarra Road, Lucas Heights, NSW, 2234, Australia
| | - Peixi Wang
- Technical University of Munich, TUM School of Natural Sciences, Department of Physics, Chair for Functional Materials, James-Franck-Str. 1, 85748, Garching, Germany
| | - Julija Reitenbach
- Technical University of Munich, TUM School of Natural Sciences, Department of Physics, Chair for Functional Materials, James-Franck-Str. 1, 85748, Garching, Germany
| | - Christina Geiger
- Technical University of Munich, TUM School of Natural Sciences, Department of Physics, Chair for Functional Materials, James-Franck-Str. 1, 85748, Garching, Germany
| | - Lucas Philipp Kreuzer
- Heinz Maier-Leibnitz Zentrum (MLZ), Technical University of Munich, Lichtenbergstr. 1, 85748, Garching, Germany.,Technical University of Munich, TUM School of Natural Sciences, Department of Physics, Chair for Functional Materials, James-Franck-Str. 1, 85748, Garching, Germany
| | - Thomas Saerbeck
- Institut Laue Langevin (ILL), 71 Avenue des Martyrs, Grenoble, 38000, France
| | - Robert Cubitt
- Institut Laue Langevin (ILL), 71 Avenue des Martyrs, Grenoble, 38000, France
| | - Edmondo Maria Benetti
- Polymer Surfaces Group, Department of Chemical Sciences, University of Padova, Via Marzolo 1, Padova, 35122, Italy.,Laboratory for Surface Science and Technology, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 5, Zürich, 8093, Switzerland
| | - Peter Müller-Buschbaum
- Heinz Maier-Leibnitz Zentrum (MLZ), Technical University of Munich, Lichtenbergstr. 1, 85748, Garching, Germany.,Technical University of Munich, TUM School of Natural Sciences, Department of Physics, Chair for Functional Materials, James-Franck-Str. 1, 85748, Garching, Germany
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7
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Yesbolatova AK, Arai R, Sakaue T, Kimura A. Formulation of Chromatin Mobility as a Function of Nuclear Size during C. elegans Embryogenesis Using Polymer Physics Theories. PHYSICAL REVIEW LETTERS 2022; 128:178101. [PMID: 35570447 DOI: 10.1103/physrevlett.128.178101] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 03/21/2022] [Indexed: 06/15/2023]
Abstract
During early embryogenesis of the nematode, Caenorhabditis elegans, the chromatin motion markedly decreases. Despite its biological implications, the underlying mechanism for this transition was unclear. By combining theory and experiment, we analyze the mean-square displacement (MSD) of the chromatin loci, and demonstrate that MSD-vs-time relationships in various nuclei collapse into a single master curve by normalizing them with the mesh size and the corresponding time scale. This enables us to identify the onset of the entangled dynamics with the size of tube diameter of chromatin polymer in the C. elegans embryo. Our dynamical scaling analysis predicts the transition between unentangled and entangled dynamics of chromatin polymers, the quantitative formula for MSD as a function of nuclear size and timescale, and provides testable hypotheses on chromatin mobility in other cell types and species.
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Affiliation(s)
- Aiya K Yesbolatova
- Department of Genetics, School of Life Science, The Graduate University for Advanced Studies, SOKENDAI, Mishima 411-8540, Japan
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima 411-8540, Japan
| | - Ritsuko Arai
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima 411-8540, Japan
| | - Takahiro Sakaue
- Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan
| | - Akatsuki Kimura
- Department of Genetics, School of Life Science, The Graduate University for Advanced Studies, SOKENDAI, Mishima 411-8540, Japan
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima 411-8540, Japan
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8
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Chubak I, Pachong SM, Kremer K, Likos CN, Smrek J. Active Topological Glass Confined within a Spherical Cavity. Macromolecules 2022; 55:956-964. [PMID: 35153336 PMCID: PMC8830202 DOI: 10.1021/acs.macromol.1c02471] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Revised: 01/13/2022] [Indexed: 11/30/2022]
Abstract
We study active topological glass under spherical confinement, allowing us to exceed the chain lengths simulated previously and determine the critical exponents of the arrested conformations. We find a previously unresolved "tank-treading" dynamic mode of active segments along the ring contour. This mode can enhance active-passive phase separation in the state of active topological glass when both diffusional and conformational relaxation of the rings are significantly suppressed. Within the observational time, we see no systematic trends in the positioning of the separated active domains within the confining sphere. The arrested state exhibits coherent stochastic rotations. We discuss possible connections of the conformational and dynamic features of the system to chromosomes enclosed in the nucleus of a living cell.
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Affiliation(s)
- Iurii Chubak
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
- Physico-Chimie
des Électrolytes et Nanosystèmes Interfaciaux, Sorbonne Université CNRS, F-75005 Paris, France
| | | | - Kurt Kremer
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Christos N. Likos
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Jan Smrek
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
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9
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Sakaue T, Kimura A. Scaling Relationship in Chromatin as a Polymer. Results Probl Cell Differ 2022; 70:263-277. [PMID: 36348110 DOI: 10.1007/978-3-031-06573-6_8] [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
Genomic DNA, which controls genetic information, is stored in the cell nucleus in eukaryotes. Chromatin moves dynamically in the nucleus, and this movement is closely related to the function of chromatin. However, the driving force of chromatin movement, its control mechanism, and the functional significance of movement are unclear. In addition to biochemical and genetic approaches such as identification and analysis of regulators, approaches based on the physical properties of chromatin and cell nuclei are indispensable for this understanding. In particular, the idea of polymer physics is expected to be effective. This paper introduces our efforts to combine biological experiments on chromatin kinetics with theoretical analysis based on polymer physics.
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Affiliation(s)
- Takahiro Sakaue
- Department of Physical Sciences, Aoyama Gakuin University, Sagamihara, Kanagawa, Japan.
| | - Akatsuki Kimura
- Cell Architecture Laboratory, National Institute of Genetics, Mishima, Japan.
- Department of Genetics, The Graduate University for Advanced Studies, Mishima, Japan.
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10
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Mei B, Dell ZE, Schweizer KS. Theory of Transient Localization, Activated Dynamics, and a Macromolecular Glass Transition in Ring Polymer Liquids. ACS Macro Lett 2021; 10:1229-1235. [PMID: 35549053 DOI: 10.1021/acsmacrolett.1c00530] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We construct a segmental scale force level theory for the center-of-mass diffusion constant and corresponding relaxation time for globally compact unconcatenated ring polymer solutions and melts (degree of polymerization N). The approach is based on slowly decaying macromolecular scale intermolecular force dynamic correlations as the origin of their unusual dynamics. Unentangled Rouse, weakly caged, and activated regimes are predicted. The barrier of the activated regime scales linearly with N and as a power law of concentration, which drives a kinetic glass transition on the radius-of-gyration scale. The values of N at the two dynamic crossovers (Rouse to weakly caged, weakly caged to activated) are proportional, with nonuniversality entering mainly via macromolecular volume fraction and dimensionless compressibility. Quantitative comparisons with simulation data reveal good agreement. Aspects of intermediate time dynamics are analyzed, and predictions are made for the conditions required to observe a macromolecular glass transition in the laboratory and on the computer.
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11
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Goto S, Kim K, Matubayasi N. Effects of chain length on Rouse modes and non-Gaussianity in linear and ring polymer melts. J Chem Phys 2021; 155:124901. [PMID: 34598563 DOI: 10.1063/5.0061281] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamics of ring polymer melts are studied via molecular dynamics simulations of the Kremer-Grest bead-spring model. Rouse mode analysis is performed in comparison with linear polymers by changing the chain length. Rouse-like behavior is observed in ring polymers by quantifying the chain length dependence of the Rouse relaxation time, whereas a crossover from Rouse to reptation behavior is observed in linear polymers. Furthermore, the non-Gaussian parameters of the monomer bead displacement and chain center-of-mass displacement are analyzed. It is found that the non-Gaussianity of ring polymers is remarkably suppressed with slight growth for the center-of-mass dynamics at long chain length, which is in contrast to the growth in linear polymers for both the monomer bead and center-of-mass dynamics.
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Affiliation(s)
- Shota Goto
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kang Kim
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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12
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Michieletto D, Sakaue T. Dynamical Entanglement and Cooperative Dynamics in Entangled Solutions of Ring and Linear Polymers. ACS Macro Lett 2021; 10:129-134. [PMID: 35548984 DOI: 10.1021/acsmacrolett.0c00551] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Understanding how entanglements affect the behavior of polymeric complex fluids is an open challenge in many fields. To elucidate the nature and consequence of entanglements in dense polymer solutions, we propose a novel method: a "dynamical entanglement analysis" (DEA) to extract spatiotemporal entanglement structures from the pairwise displacement correlation of entangled chains. By applying this method to large-scale molecular dynamics simulations of linear and unknotted, nonconcatenated ring polymers, we find a strong and unexpected cooperative dynamics: the footprint of mutual entrainment between entangled chains. We show that DEA is a powerful and sensitive probe that reveals previously unnoticed and architecture-dependent spatiotemporal structures of dynamical entanglement in polymeric solutions. We also propose a mean-field approximation of our analysis that provides previously under-appreciated physical insights into the dynamics of generic entangled polymers. We envisage DEA will be useful to analyze the dynamical evolution of entanglements in generic polymeric systems such as blends and composites.
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Affiliation(s)
- Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
- MRC Human Genetics Unit, Institute of Genetics and Molecular Medicine, University of Edinburgh, North Crewe Road, Edinburgh, EH4 2XU, United Kingdom
| | - Takahiro Sakaue
- Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Tokyo 150-8366, Japan
- PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan
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13
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Mei B, Dell ZE, Schweizer KS. Microscopic Theory of Long-Time Center-of-Mass Self-Diffusion and Anomalous Transport in Ring Polymer Liquids. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01737] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Baicheng Mei
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Zachary E. Dell
- Department of Physics, University of Illinois, Urbana, Illinois 61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Kenneth S. Schweizer
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, United States
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
- Department of Chemical & Biomolecular Engineering, University of Illinois, Urbana, Illinois 61801, United States
- Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
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14
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Rosa A, Smrek J, Turner MS, Michieletto D. Threading-Induced Dynamical Transition in Tadpole-Shaped Polymers. ACS Macro Lett 2020; 9:743-748. [PMID: 33828901 PMCID: PMC8016395 DOI: 10.1021/acsmacrolett.0c00197] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2020] [Accepted: 04/30/2020] [Indexed: 01/06/2023]
Abstract
The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring-linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in "chimeric" architectures. The simplest example of this family is a "tadpole"-shaped polymer, a single ring fused to the end of a single linear chain. We show that polymers with this architecture display a threading-induced dynamical transition that substantially slows chain relaxation. Our findings shed light on how threadings control dynamics and may inform design principles for chimeric polymers with topologically tunable bulk rheological properties.
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Affiliation(s)
- Angelo Rosa
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136 Trieste, Italy
| | - Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Matthew S Turner
- Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
- Department of Chemical Engineering, Kyoto University, Kyoto 606-8501, Japan
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
- MRC Human Genetics Unit, Institute of Genetics and Molecular Medicine, University of Edinburgh, Edinburgh EH4 2XU, United Kingdom
- Department of Mathematical Sciences, University of Bath, North Rd, Bath BA2 7AY, United Kingdom
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15
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Ito Y, Kimura A. Session 1SEA-physics of chromatin dynamics at the 57th Biophysical Society of Japan meeting. Biophys Rev 2020; 12:265-266. [PMID: 32056110 DOI: 10.1007/s12551-020-00642-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2020] [Accepted: 02/06/2020] [Indexed: 01/07/2023] Open
Affiliation(s)
- Yuma Ito
- School of Life Science and Technology, Tokyo Institute of Technology, Nagatsuta-cho, Midori, Yokohama, 226-8501, Japan
| | - Akatsuki Kimura
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima, 411-8540, Japan. .,Department of Genetics, School of Life Science, The Graduate University for Advanced Studies, SOKENDAI, Mishima, 411-8540, Japan.
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16
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Tsalikis DG, Mavrantzas VG. Size and Diffusivity of Polymer Rings in Linear Polymer Matrices: The Key Role of Threading Events. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02099] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Dimitrios G. Tsalikis
- Department of Chemical Engineering, University of Patras and FORTH-ICE/HT, GR 26504 Patras, Greece
| | - Vlasis G. Mavrantzas
- Department of Chemical Engineering, University of Patras and FORTH-ICE/HT, GR 26504 Patras, Greece
- Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, CH-8092 Zürich, Switzerland
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17
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Lee E, Jung Y. Slow Dynamics of Ring Polymer Melts by Asymmetric Interaction of Threading Configuration: Monte Carlo Study of a Dynamically Constrained Lattice Model. Polymers (Basel) 2019; 11:E516. [PMID: 30960500 PMCID: PMC6473489 DOI: 10.3390/polym11030516] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Revised: 03/11/2019] [Accepted: 03/14/2019] [Indexed: 12/03/2022] Open
Abstract
Abnormally slower diffusional processes than its internal structure relaxation have been observed in ring polymeric melt systems recently. A key structural feature in ring polymer melts is topological constraints which allow rings to assume a threading configuration in the melt phase. In this work, we constructed a lattice model under the assumption of asymmetric diffusivity between two threading rings, and investigated a link between the structural correlation and its dynamic behavior via Monte Carlo simulations. We discovered that the hierarchical threading configurations render the whole system to exhibit abnormally slow dynamics. By analyzing statistical distributions of timescales of threading configurations, we found that the decoupling between internal structure relaxation and diffusion is crucial to understand the threading effects on the dynamics of a ring melt. In particular, in the limit of small but threaded rings, scaling exponents of the diffusion coefficient D and timescale τ diff with respect to the degree of polymerization N agree well with that of the annealed tree model as well as our mean-field analysis. As N increases, however, the ring diffusion abruptly slows down to the glassy behavior, which is supported by a breakdown of the Stokes⁻Einstein relation.
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Affiliation(s)
- Eunsang Lee
- Department of Chemistry, Seoul National University, Seoul 08826, Korea.
| | - YounJoon Jung
- Department of Chemistry, Seoul National University, Seoul 08826, Korea.
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18
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