1
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Schneck C, Smrek J, Likos CN, Zöttl A. Supercoiled ring polymers under shear flow. NANOSCALE 2024. [PMID: 38639709 DOI: 10.1039/d3nr04258h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/20/2024]
Abstract
We apply monomer-resolved computer simulations of supercoiled ring polymers under shear, taking full account of the hydrodynamic interactions, accompanied, in parallel, by simulations in which these are switched off. The combination of bending and torsional rigidities inherent in these polymers, in conjunction with hydrodynamics, has a profound impact on their flow properties. In contrast to their flexible counterparts, which dramatically deform and inflate under shear [Liebetreu et al., Commun. Mater. 2020, 1, 4], supercoiled rings undergo only weak changes in their overall shape and they display both a reduced propensity to tumbling (at fixed Weissenberg number) and a much stronger orientational resistance with respect to their flexible counterparts. In the presence of hydrodynamic interactions, the coupling of the polymer to solvent flow is capable of bringing about a topological transformation of writhe to twist at strong shear upon conservation of the overall linking number.
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Affiliation(s)
- Christoph Schneck
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain
| | - Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
| | - Christos N Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
| | - Andreas Zöttl
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
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2
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Caraglio M, Micheletti C, Orlandini E. Unraveling the Influence of Topology and Spatial Confinement on Equilibrium and Relaxation Properties of Interlocked Ring Polymers. Macromolecules 2024; 57:3223-3233. [PMID: 38616813 PMCID: PMC11008367 DOI: 10.1021/acs.macromol.3c02203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Revised: 02/27/2024] [Accepted: 03/01/2024] [Indexed: 04/16/2024]
Abstract
We use Langevin dynamics simulations to study linked ring polymers in channel confinement. We address the in- and out-of-equilibrium behavior of the systems for varying degrees of confinement and increasing topological and geometrical complexity of the interlocking. The main findings are three. First, metric observables of different link topologies collapse onto the same master curve when plotted against the crossing number, revealing a universal response to confinement. Second, the relaxation process from initially stretched states is faster for more complex links. We ascribe these properties to the interplay of several effects, including the dependence of topological friction on the link complexity. Finally, we show that transient forms of geometrical entanglement purposely added to the initial stressed state can leave distinctive signatures in force-spectroscopy curves. The insight provided by the findings could be leveraged in single-molecule nanochannel experiments to identify geometric entanglement within topologically linked rings.
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Affiliation(s)
- Michele Caraglio
- Institut
für Theoretische Physik, Universität
Innsbruck, Technikerstraße 21A, Innsbruck A-6020, Austria
| | - Cristian Micheletti
- Scuola
Internazionale Superiore di Studi Avanzati—SISSA, Via Bonomea 265, Trieste 34136, Italy
| | - Enzo Orlandini
- Department
of Physics and Astronomy, University of
Padova, Via Marzolo 8, Padova I-35100, Italy
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3
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Farimani RA, Ahmadian Dehaghani Z, Likos CN, Ejtehadi MR. Effects of Linking Topology on the Shear Response of Connected Ring Polymers: Catenanes and Bonded Rings Flow Differently. PHYSICAL REVIEW LETTERS 2024; 132:148101. [PMID: 38640389 DOI: 10.1103/physrevlett.132.148101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Revised: 10/09/2023] [Accepted: 02/15/2024] [Indexed: 04/21/2024]
Abstract
We perform computer simulations of mechanically linked (poly[2]catenanes, PC) and chemically bonded (bonded rings, BR) pairs of self-avoiding ring polymers in steady shear. We find that BRs develop a novel motif, termed gradient tumbling, rotating around the gradient axis. For the PCs the rings are stretched and display another new pattern, termed slip tumbling. The dynamics of BRs is continuous and oscillatory, whereas that of PCs is intermittent between slip-tumbling attempts. Our findings demonstrate the interplay between topology and hydrodynamics in dilute solutions of connected polymers.
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Affiliation(s)
- Reyhaneh A Farimani
- Department of Physics, Sharif University of Technology, Tehran, Iran
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | | | - Christos N Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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4
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Becerra D, Klotz AR, Hall LM. Single-molecule analysis of solvent-responsive mechanically interlocked ring polymers and the effects of nanoconfinement from coarse-grained simulations. J Chem Phys 2024; 160:114906. [PMID: 38511659 DOI: 10.1063/5.0191295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2023] [Accepted: 03/02/2024] [Indexed: 03/22/2024] Open
Abstract
In this study, we simulate mechanically interlocked semiflexible ring polymers inspired by the minicircles of kinetoplast DNA (kDNA) networks. Using coarse-grained molecular dynamics simulations, we investigate the impact of molecular topological linkage and nanoconfinement on the conformational properties of two- and three-ring polymer systems in varying solvent qualities. Under good-quality solvents, for two-ring systems, a higher number of crossing points lead to a more internally constrained structure, reducing their mean radius of gyration. In contrast, three-ring systems, which all had the same crossing number, exhibited more similar sizes. In unfavorable solvents, structures collapse, forming compact configurations with increased contacts. The morphological diversity of structures primarily arises from topological linkage rather than the number of rings. In three-ring systems with different topological conformations, structural uniformity varies based on link types. Extreme confinement induces isotropic and extended conformations for catenated polymers, aligning with experimental results for kDNA networks and influencing the crossing number and overall shape. Finally, the flat-to-collapse transition in extreme confinement occurs earlier (at relatively better solvent conditions) compared to non-confined systems. This study offers valuable insights into the conformational behavior of mechanically interlocked ring polymers, highlighting challenges in extrapolating single-molecule analyses to larger networks such as kDNA.
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Affiliation(s)
- Diego Becerra
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, USA
| | - Alexander R Klotz
- Department of Physics and Astronomy, California State University, Long Beach, California 90840, USA
| | - Lisa M Hall
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, USA
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5
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Neill P, Crist N, McGorty R, Robertson-Anderson R. Enzymatic cleaving of entangled DNA rings drives scale-dependent rheological trajectories. SOFT MATTER 2024; 20:2750-2766. [PMID: 38440846 DOI: 10.1039/d3sm01641b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/06/2024]
Abstract
DNA, which naturally occurs in linear, ring, and supercoiled topologies, frequently undergoes enzyme-driven topological conversion and fragmentation in vivo, enabling it to perform a variety of functions within the cell. In vitro, highly concentrated DNA polymers form entanglements that yield viscoelastic properties dependent on the topologies and lengths of the DNA. Enzyme-driven alterations of DNA size and shape therefore offer a means of designing active materials with programmable viscoelastic properties. Here, we incorporate multi-site restriction endonucleases into dense DNA solutions to linearize and fragment circular DNA molecules. We pair optical tweezers microrheology with differential dynamic microscopy and single-molecule tracking to measure the linear and nonlinear viscoelastic response and transport properties of entangled DNA solutions over a wide range of spatiotemporal scales throughout the course of enzymatic digestion. We show that, at short timescales, relative to the relaxation timescales of the polymers, digestion of these 'topologically-active' fluids initially causes an increase in elasticity and relaxation times followed by a gradual decrease. Conversely, for long timescales, linear viscoelastic moduli exhibit signatures of increasing elasticity. DNA diffusion, likewise, becomes increasingly slowed, in direct opposition to the short-time behavior. We hypothesize that this scale-dependent rheology arises from the population of small DNA fragments, which increases as digestion proceeds, driving self-association of larger fragments via depletion interactions, giving rise to slow relaxation modes of clusters of entangled chains, interspersed among shorter unentangled fragments. While these slow modes likely dominate at long times, they are presumably frozen out in the short-time limit, which instead probes the faster relaxation modes of the unentangled population.
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Affiliation(s)
- Philip Neill
- Department of Physics and Biophysics, University of San Diego, San Diego, CA 92104, USA.
| | - Natalie Crist
- Department of Physics and Biophysics, University of San Diego, San Diego, CA 92104, USA.
| | - Ryan McGorty
- Department of Physics and Biophysics, University of San Diego, San Diego, CA 92104, USA.
| | - Rae Robertson-Anderson
- Department of Physics and Biophysics, University of San Diego, San Diego, CA 92104, USA.
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6
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Micheletti C, Chubak I, Orlandini E, Smrek J. Topology-Based Detection and Tracking of Deadlocks Reveal Aging of Active Ring Melts. ACS Macro Lett 2024:124-129. [PMID: 38198592 PMCID: PMC10883035 DOI: 10.1021/acsmacrolett.3c00567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
Connecting the viscoelastic behavior of stressed ring melts to the various forms of entanglement that can emerge in such systems is still an open challenge. Here, we consider active ring melts, where stress is generated internally, and introduce a topology-based method to detect and track consequential forms of ring entanglements, namely, deadlocks. We demonstrate that, as stress accumulates, more and more rings are co-opted in a growing web of deadlocks that entrap many other rings by threading, bringing the system to a standstill. The method ought to help the study of topological aging in more general polymer contexts.
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Affiliation(s)
- Cristian Micheletti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
| | - Iurii Chubak
- Sorbonne Université CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Enzo Orlandini
- Università degli studi di Padova, Dipartimento di Fisica "G. Galilei", Via Marzolo 8, I-35100 Padova, Italy
| | - Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
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7
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Mohottalalage SS, Saab AP, Maiti A. Bead-Spring Simulation of Ionomer Melts-Studying the Effects of Chain-Length and Associating Group Fraction on Equilibrium Structure and Extensional Flow Behavior. Polymers (Basel) 2023; 15:4560. [PMID: 38232005 PMCID: PMC10708384 DOI: 10.3390/polym15234560] [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: 10/18/2023] [Revised: 11/22/2023] [Accepted: 11/24/2023] [Indexed: 01/19/2024] Open
Abstract
Ionomers are associative polymers with diverse applications ranging from selective membranes and high-performance adhesives to abrasion- and chemical-resistant coatings, insulation layers, vacuum packaging, and foamed sheets. Within equilibrium melt, the ionic or associating groups are known to form thermally reversible, associative clusters whose presence can significantly affect the system's mechanical, viscoelastic, and transport properties. It is, thus, of great interest to understand how to control such clusters' size distribution, shape, and stability through the designed choice of polymer architecture and the ionic groups' fraction, arrangement, and interaction strength. In this work, we represent linear associating polymers using a Kremer-Grest type bead-spring model and perform large-scale MD simulations to explore the effect of polymer chain-length (l) and fraction (fs) of randomly placed associating groups on the size distribution and stability of formed clusters. We consider different chain-lengths (below and above entanglement), varying fractions of associating groups (represented by 'sticky' beads) between 5 and 20%, and a fixed sticky-sticky nonbond interaction strength of four times that between regular non-associating beads. For all melts containing associating groups the equilibrium structure factor S(q) displays a signature ionomer peak at low wave vector q whose intensity increases with increasing fs and l. The average cluster size Nc increases with fs. However, the effect of chain-length on Nc appears to be pronounced only at higher values of fs. Under extensional flows, the computed stress (and viscosity) is higher at higher fs and l regardless of strain rate. Beyond a critical strain rate, we observe fragmentation of the associative clusters, which has interesting effects on the stress/viscous response.
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Affiliation(s)
| | | | - Amitesh Maiti
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA; (S.S.M.)
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8
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López-Ríos de Castro R, Ziolek RM, Lorenz CD. Topology-controlled self-assembly of amphiphilic block copolymers. NANOSCALE 2023; 15:15230-15237. [PMID: 37671739 PMCID: PMC10540979 DOI: 10.1039/d3nr01204b] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 08/16/2023] [Indexed: 09/07/2023]
Abstract
Contemporary synthetic chemistry approaches can be used to yield a range of distinct polymer topologies with precise control. The topology of a polymer strongly influences its self-assembly into complex nanostructures however a clear mechanistic understanding of the relationship between polymer topology and self-assembly has not yet been developed. In this work, we use atomistic molecular dynamics simulations to provide a nanoscale picture of the self-assembly of three poly(ethylene oxide)-poly(methyl acrylate) block copolymers with different topologies into micelles. We find that the topology affects the ability of the micelle to form a compact hydrophobic core, which directly affects its stability. Also, we apply unsupervised machine learning techniques to show that the topology of a polymer affects its ability to take a conformation in response to the local environment within the micelles. This work provides foundations for the rational design of polymer nanostructures based on their underlying topology.
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Affiliation(s)
- Raquel López-Ríos de Castro
- Biological Physics and Soft Matter Group, Department of Physics, King's College London, London, WC2R 2LS, UK.
- Department of Chemistry, King's College London, London, SE1 1DB, UK
| | - Robert M Ziolek
- Biological Physics and Soft Matter Group, Department of Physics, King's College London, London, WC2R 2LS, UK.
| | - Christian D Lorenz
- Biological Physics and Soft Matter Group, Department of Physics, King's College London, London, WC2R 2LS, UK.
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9
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Ohkuma T, Hagita K, Murashima T, Deguchi T. Miscibility and exchange chemical potential of ring polymers in symmetric ring-ring blends. SOFT MATTER 2023; 19:3818-3827. [PMID: 37191220 DOI: 10.1039/d3sm00108c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Generally, differences of polymer topologies may affect polymer miscibility even with the same repeated units. In this study, the topological effect of ring polymers on miscibility was investigated by comparing symmetric ring-ring and linear-linear polymer blends. To elucidate the topological effect of ring polymers on mixing free energy, the exchange chemical potential of binary blends was numerically evaluated as a function of composition ϕ by performing semi-grand canonical Monte Carlo and molecular dynamics simulations of a bead-spring model. For ring-ring blends, an effective miscibility parameter was evaluated by comparing the exchange chemical potential with that of the Flory-Huggins model for linear-linear polymer blends. It was confirmed that in the mixed states satisfying χN > 0, ring-ring blends are more miscible and stable than the linear-linear blends with the same molecular weight. Furthermore, we investigated finite molecular weight dependence on the miscibility parameter, which reflected the statistical probability of interchain interactions in the blends. The simulation results revealed that the molecular weight dependence on the miscibility parameter was smaller in ring-ring blends. The effect of the ring polymers on miscibility was verified to be consistent with the change in the interchain radial distribution function. In ring-ring blends, it was indicated that the topology affected miscibility by reducing the effect of the direct interaction between the components of the blends.
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Affiliation(s)
- Takahiro Ohkuma
- Digital Engineering Division, Bridgestone Corporation, Kodaira, 187-8531, Japan.
| | - Katsumi Hagita
- Department of Applied Physics, National Defense Academy, 1-10-20, Hashirimizu, Yokosuka, 239-8686, Japan
| | - Takahiro Murashima
- Department of Physics, Tohoku University, 6-3, Aramaki-aza-Aoba, Aoba-ku, Sendai, 980-8578, Japan
| | - Tetsuo Deguchi
- Department of Physics, Faculty of Core Research, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan
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10
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Li YC, Wu ZP, Zong ZH, Cao XZ. Rheological Role of Stiff Nanorings on Concurrently Strengthening and Toughening Polymer Nanocomposites. ACS Macro Lett 2023; 12:183-188. [PMID: 36692488 DOI: 10.1021/acsmacrolett.2c00610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Nanorings, which are increasingly uncovered in natural systems and synthesized in man-made materials, exhibit dynamics distinct from those known for linear chains. We show in this study that, when immersed in a polymer melt matrix, segments of a stiff nanoring (SNR) have more facilitated subdiffusion, i.e., with a larger scaling exponent in the mean squared displacement, than those belonging to one flexible counterpart, while the whole SNR is more suppressed by its surroundings. It is revealed that adding SNRs contributes to achieving the long-anticipated rheological objective of sol- and gel-like characteristics at high and low shearing frequencies, respectively. This study suggests the promising prospect of exploiting SNRs to concurrently strengthen and toughen target polymer nanocomposites.
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Affiliation(s)
- Yu-Chao Li
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, College of Physical Science and Technology, Xiamen University, Xiamen 361005, P.R. China
| | - Zong-Pei Wu
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, College of Physical Science and Technology, Xiamen University, Xiamen 361005, P.R. China
| | - Ze-Hao Zong
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, College of Physical Science and Technology, Xiamen University, Xiamen 361005, P.R. China
| | - Xue-Zheng Cao
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, College of Physical Science and Technology, Xiamen University, Xiamen 361005, P.R. China
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11
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Zheng Y, Tsige M, Wang SQ. Molecular Dynamics Simulation of Entangled Melts at High Rates: Identifying Entanglement Lockup Mechanism Leading to True Strain Hardening. Macromol Rapid Commun 2023; 44:e2200159. [PMID: 35881534 DOI: 10.1002/marc.202200159] [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: 02/20/2022] [Revised: 06/20/2022] [Indexed: 01/11/2023]
Abstract
In the present work, molecular dynamics simulations are carried out based on the bead-spring model to indicate how the entanglement lockup manifests in the late stage of fast Rouse-Weissnberg number (WiR >>1) uniaxial melt stretching of entangled polymer melts. At high strains, distinct features show up to reveal the emergence of an increasingly tightened entanglement network. Chain tension can build up, peaking at the middle of the chain, to a level for chain scission, through accumulated interchain interactions, as if there is a tug-of-war ongoing for each load-bearing chain. Thanks to the interchain uncrossability, network junctions form by the pairing of two or more hairpins. It is hypothesized that the interchain entanglement at junctions can lockup through prevailing twist-like interchain couplings as long as WiR > 9. In this limit, a significant fraction of chains act like cyclic chains to form a network held by interchain uncrossability, and appreciable chain tension emerges.
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Affiliation(s)
- Yexin Zheng
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
| | - Mesfin Tsige
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
| | - Shi-Qing Wang
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
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12
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Staňo R, Likos CN, Smrek J. To thread or not to thread? Effective potentials and threading interactions between asymmetric ring polymers. SOFT MATTER 2022; 19:17-30. [PMID: 36477247 PMCID: PMC9768673 DOI: 10.1039/d2sm01177h] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Accepted: 11/22/2022] [Indexed: 06/17/2023]
Abstract
We use computer simulations to study a system of two unlinked ring polymers, whose length and bending stiffness are systematically varied. We derive the effective potentials between the rings, calculate the areas of minimal surfaces of the same, and characterize the threading between them. When the two rings are of the same kind, threading of a one ring through the surface of the other is immanent for small ring-ring separations. Flexible rings pierce the surface of the other ring several times but only shallowly, as compared to the stiff rings which pierce less frequently but deeply. Typically, the ring that is being threaded swells and flattens up into an oblate-like conformation, while the ring that is threading the other takes a shape of an elongated prolate. The roles of the threader and the threaded ring are being dynamically exchanged. If, on the other hand, the rings are of different kinds, the symmetry is broken and the rings tend to take up roles of the threader and the threaded ring with unequal probabilities. We propose a method how to predict these probabilities based on the parameters of the individual rings. Ultimately, our work captures the interactions between ring polymers in a coarse-grained fashion, opening the way to large-scale modelling of materials such as kinetoplasts, catenanes or topological brushes.
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Affiliation(s)
- Roman Staňo
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
- Vienna Doctoral School in Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christos N Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
| | - Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
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13
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Ubertini MA, Smrek J, Rosa A. Entanglement Length Scale Separates Threading from Branching of Unknotted and Non-concatenated Ring Polymers in Melts. Macromolecules 2022; 55:10723-10736. [PMID: 36530522 PMCID: PMC9753756 DOI: 10.1021/acs.macromol.2c01264] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 11/14/2022] [Indexed: 11/30/2022]
Abstract
Current theories on the conformation and dynamics of unknotted and non-concatenated ring polymers in melt conditions describe each ring as a tree-like double-folded object. While evidence from simulations supports this picture on a single ring level, other works show pairs of rings also thread each other, a feature overlooked in the tree theories. Here we reconcile this dichotomy using Monte Carlo simulations of the ring melts with different bending rigidities. We find that rings are double-folded (more strongly for stiffer rings) on and above the entanglement length scale, while the threadings are localized on smaller scales. The different theories disagree on the details of the tree structure, i.e., the fractal dimension of the backbone of the tree. In the stiffer melts we find an indication of a self-avoiding scaling of the backbone, while more flexible chains do not exhibit such a regime. Moreover, the theories commonly neglect threadings and assign different importance to the impact of the progressive constraint release (tube dilation) on single ring relaxation due to the motion of other rings. Despite that each threading creates only a small opening in the double-folded structure, the threading loops can be numerous and their length can exceed substantially the entanglement scale. We link the threading constraints to the divergence of the relaxation time of a ring, if the tube dilation is hindered by pinning a fraction of other rings in space. Current theories do not predict such divergence and predict faster than measured diffusion of rings, pointing at the relevance of the threading constraints in unpinned systems as well. Revision of the theories with explicit threading constraints might elucidate the validity of the conjectured existence of topological glass.
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Affiliation(s)
- Mattia Alberto Ubertini
- Scuola
Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136Trieste, Italy
| | - Jan Smrek
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090Vienna, Austria
| | - Angelo Rosa
- Scuola
Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136Trieste, Italy
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14
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Murashima T, Hagita K, Kawakatsu T. Topological Transition in Multicyclic Chains with Structural Symmetry Inducing Stress-Overshoot Phenomena in Multicyclic/Linear Blends under Biaxial Elongational Flow. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01579] [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)
- Takahiro Murashima
- Department of Physics, Tohoku University, 6-3 Aramaki-aza-Aoba, Aoba-ku, Sendai980-8578, Japan
| | - Katsumi Hagita
- Department of Applied Physics, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka239-8686, Japan
| | - Toshihiro Kawakatsu
- Department of Physics, Tohoku University, 6-3 Aramaki-aza-Aoba, Aoba-ku, Sendai980-8578, Japan
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15
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Rauscher PM, de Pablo JJ. Random Knotting in Fractal Ring Polymers. Macromolecules 2022; 55:8409-8417. [PMID: 36186575 PMCID: PMC9520986 DOI: 10.1021/acs.macromol.2c01676] [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] [Received: 08/10/2022] [Revised: 08/23/2022] [Indexed: 11/28/2022]
Abstract
![]()
Many ring polymer
systems of physical and biological
interest exhibit
both pronounced topological effects and nontrivial self-similarity,
but the relationship between these two phenomena has not yet been
clearly established. Here, we use theory and simulation to formulate
such a connection by studying a fundamental topological property—the
random knotting probability—for ring polymers with varying
fractal dimension, df. Using straightforward scaling arguments, we generalize a classic
mathematical result, showing that the probability of a trivial knot
decays exponentially with chain size, N, for all
fractal dimensions: P0(N) ∝ exp(−N/N0). However, no such simple considerations can account for
the dependence of the knotting length, N0, on df, necessitating
a more involved analytical calculation. This analysis reveals a complicated
double-exponential dependence, which is well supported by numerical
data. By contrast, functional forms typical of simple scaling theories
fail to adequately describe the observations. These findings are equally
valid for two-dimensional ring polymer systems, where “knotting”
is defined as the intersection of any two segments.
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Affiliation(s)
- Phillip M. Rauscher
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division (MSD) and Center for Molecular Engineering (CME), Argonne National Laboratory, Lemont, Illinois 60439, United States
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16
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Michieletto D, Neill P, Weir S, Evans D, Crist N, Martinez VA, Robertson-Anderson RM. Topological digestion drives time-varying rheology of entangled DNA fluids. Nat Commun 2022; 13:4389. [PMID: 35902575 PMCID: PMC9334285 DOI: 10.1038/s41467-022-31828-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Accepted: 07/04/2022] [Indexed: 11/17/2022] Open
Abstract
Understanding and controlling the rheology of polymeric complex fluids that are pushed out-of-equilibrium is a fundamental problem in both industry and biology. For example, to package, repair, and replicate DNA, cells use enzymes to constantly manipulate DNA topology, length, and structure. Inspired by this feat, here we engineer and study DNA-based complex fluids that undergo enzymatically-driven topological and architectural alterations via restriction endonuclease (RE) reactions. We show that these systems display time-dependent rheological properties that depend on the concentrations and properties of the comprising DNA and REs. Through time-resolved microrheology experiments and Brownian Dynamics simulations, we show that conversion of supercoiled to linear DNA topology leads to a monotonic increase in viscosity. On the other hand, the viscosity of entangled linear DNA undergoing fragmentation displays a universal decrease that we rationalise using living polymer theory. Finally, to showcase the tunability of these behaviours, we design a DNA fluid that exhibits a time-dependent increase, followed by a temporally-gated decrease, of its viscosity. Our results present a class of polymeric fluids that leverage naturally occurring enzymes to drive diverse time-varying rheology by performing architectural alterations to the constituents.
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Affiliation(s)
- D Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Road, Edinburgh, EH9 3FD, UK.
- MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh, EH4 2XU, UK.
| | - P Neill
- Department of Physics and Biophysics, University of San Diego, 5998 Alcala Park, San Diego, CA, 92110, USA
| | - S Weir
- Department of Physics and Biophysics, University of San Diego, 5998 Alcala Park, San Diego, CA, 92110, USA
| | - D Evans
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Road, Edinburgh, EH9 3FD, UK
| | - N Crist
- Department of Physics and Biophysics, University of San Diego, 5998 Alcala Park, San Diego, CA, 92110, USA
| | - V A Martinez
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Road, Edinburgh, EH9 3FD, UK
| | - R M Robertson-Anderson
- Department of Physics and Biophysics, University of San Diego, 5998 Alcala Park, San Diego, CA, 92110, USA.
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17
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Wang J, O'Connor TC, Grest GS, Ge T. Superstretchable Elastomer from Cross-linked Ring Polymers. PHYSICAL REVIEW LETTERS 2022; 128:237801. [PMID: 35749195 DOI: 10.1103/physrevlett.128.237801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 05/20/2022] [Indexed: 06/15/2023]
Abstract
The stretchability of polymeric materials is critical to many applications such as flexible electronics and soft robotics, yet the stretchability of conventional cross-linked linear polymers is limited by the entanglements between polymer chains. We show using molecular dynamics simulations that cross-linked ring polymers are significantly more stretchable than cross-linked linear polymers. Compared to linear polymers, the entanglements between ring polymers do not act as effective cross-links. As a result, the stretchability of cross-linked ring polymers is determined by the maximum extension of polymer strands between cross-links, rather than between trapped entanglements as in cross-linked linear polymers. The more compact conformation of ring polymers before deformation also contributes to the increase in stretchability.
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Affiliation(s)
- Jiuling Wang
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - Thomas C O'Connor
- Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Gary S Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Ting Ge
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
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18
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Conformation and structure of ring polymers in semidilute solutions: A molecular dynamics simulation study. POLYMER 2022. [DOI: 10.1016/j.polymer.2022.124953] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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19
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Roy PK, Chaudhuri P, Vemparala S. Effect of ring stiffness and ambient pressure on the dynamical slowdown in ring polymers. SOFT MATTER 2022; 18:2959-2967. [PMID: 35348146 DOI: 10.1039/d1sm01754c] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Using extensive molecular dynamics simulations, we investigate the slowdown of dynamics in a 3D system of ring polymers by varying the ambient pressure and the stiffness of the rings. Our study demonstrates that the stiffness of the rings determines the dynamics of the ring polymers, leading to glassiness at lower pressures for stiffer rings. The threading of the ring polymers, a unique feature that emerges only due to the topological nature of such polymers in three dimensions, is shown to be the determinant feature of dynamical slowdown, albeit only in a certain stiffness range. Our results suggest a possible framework for exploring the phase space spanned by ring stiffness and pressure to obtain spontaneously emerging topologically constrained polymer glasses.
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Affiliation(s)
- Projesh Kumar Roy
- The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India.
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India.
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Satyavani Vemparala
- The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India.
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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20
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Affiliation(s)
- Qian Huang
- State Key Laboratory of Polymer Materials Engineering, Polymer Research Institute, Sichuan University, 610065 Chengdu, China
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21
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Amici G, Caraglio M, Orlandini E, Micheletti C. Topological Friction and Relaxation Dynamics of Spatially Confined Catenated Polymers. ACS Macro Lett 2022; 11:1-6. [PMID: 35574798 PMCID: PMC8772382 DOI: 10.1021/acsmacrolett.1c00594] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 12/03/2021] [Indexed: 11/30/2022]
Abstract
We study catenated ring polymers confined inside channels and slits with Langevin dynamics simulations and address how the contour position and size of the interlocked or physically linked region evolve with time. We show that the catenation constraints generate a drag, or topological friction, that couples the contour motion of the interlocked regions. Notably, the coupling strength decreases as the interlocking is made tighter, but also shorter, by confinement. Though the coupling strength differs for channel and slit confinement, the data outline a single universal curve when plotted against the size of the linked region. Finally, we study how the relaxation kinetics changes after one of the rings is cut open and conclude that considering interlocked circular polymers is key for isolating the manifestations of topological friction. The results ought to be relevant for linked biomolecules in experimental or biological confining conditions.
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Affiliation(s)
- Giulia Amici
- Scuola
Internazionale Superiore di Studi Avanzati - SISSA, via Bonomea 265, 34136 Trieste, Italy
| | - Michele Caraglio
- Institut
für Theoretische Physik, Universität
Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Enzo Orlandini
- Department
of Physics and Astronomy, University of
Padova, Via Marzolo 8, I-35100 Padova, Italy
| | - Cristian Micheletti
- Scuola
Internazionale Superiore di Studi Avanzati - SISSA, via Bonomea 265, 34136 Trieste, Italy
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22
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Dietz JD, Hoy RS. Facile equilibration of well-entangled semiflexible bead-spring polymer melts. J Chem Phys 2022; 156:014103. [PMID: 34998323 DOI: 10.1063/5.0072386] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [Auhl et al., J. Chem. Phys. 119, 12718-12728 (2003)] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with N ≃ 40Ne and chain stiffnesses all the way up to the isotropic-nematic transition using simulations of no more than 100 × 106 time steps. For semiflexible chains, our method is several times faster than the standard DBH; we exploit this speedup to develop improved expressions for Kremer-Grest melts' chain-stiffness-dependent Kuhn length ℓK and entanglement length Ne.
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Affiliation(s)
- Joseph D Dietz
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Robert S Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
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23
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Clemmer JT, Srivastava I, Grest GS, Lechman JB. Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology. PHYSICAL REVIEW LETTERS 2021; 127:268003. [PMID: 35029501 DOI: 10.1103/physrevlett.127.268003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Revised: 10/08/2021] [Accepted: 11/17/2021] [Indexed: 06/14/2023]
Abstract
Despite there being an infinite variety of types of flow, most rheological studies focus on a single type such as simple shear. Using discrete element simulations, we explore bulk granular systems in a wide range of flow types at large strains and characterize invariants of the stress tensor for different inertial numbers and interparticle friction coefficients. We identify a strong dependence on the type of flow, which grows with increasing inertial number or friction. Standard models of yielding, repurposed to describe the dependence of the stress on flow type in steady-state flow and at finite rates, are compared with data.
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Affiliation(s)
- Joel T Clemmer
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Ishan Srivastava
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Gary S Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Jeremy B Lechman
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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24
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Kim J, Kim JM, Baig C. Intrinsic structure and dynamics of monolayer ring polymer melts. SOFT MATTER 2021; 17:10703-10715. [PMID: 34783328 DOI: 10.1039/d1sm01192h] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We present the general structural and dynamical characteristics of flexible ring polymers in narrowly confined two-dimensional (2D) melt systems using atomistic molecular dynamics simulations. The results are further analyzed via direct comparison with the 2D linear analogue as well as the three-dimensional (3D) ring and linear melt systems. It is observed that dimensional restriction in 2D confined systems results in an increase in the intrinsic chain stiffness of the ring polymer. Fundamentally, this arises from an entropic penalty on polymer chains along with a reduction in the available chain configuration states in phase space and spatial choices for individual segmental walks. This feature in combination with the intermolecular interactions between neighboring ring chains leads to an overall extended interpenetrated chain configuration for the 2D ring melt. In contrast to the generally large differences in structural and dynamical properties between ring and linear polymers in 3D melt systems, relatively similar local-to-global chain structures and dynamics are observed for the 2D ring and linear melts. This is attributed to the general structural similarity (i.e., extended double-stranded chain conformations), the less effective role of the chain ends, and the absence of complex topological constraints between chains (i.e., interchain entanglement and mutual ring threading) in the 2D confined systems compared with the corresponding 3D bulk systems.
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Affiliation(s)
- Jinseong Kim
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan 44919, South Korea.
| | - Jun Mo Kim
- Department of Chemical Engineering, Kyonggi University, 154-42 Gwanggyosan-ro, Yeongtong-gu, Suwon, Kyonggi-do 16227, South Korea
| | - Chunggi Baig
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan 44919, South Korea.
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25
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Jeong SH, Ha TY, Cho S, Roh EJ, Kim JM, Baig C. Melt Rheology of Short-Chain Branched Ring Polymers in Shear Flow. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01727] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Seung Heum Jeong
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
| | - Tae Yong Ha
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
| | - Soowon Cho
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
| | - Eun Jung Roh
- KOLON Advanced Research Cluster, KOLON One & Only Tower, 110, Magokdong-ro, Gangseo-gu, Seoul 07793, South Korea
| | - Jun Mo Kim
- Department of Chemical Engineering, Kyonggi University, 154-42 Gwanggyosan-ro, Yeongtong-gu, Suwon 16227, Kyeonggi-do, South Korea
| | - Chunggi Baig
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
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26
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Orlandini E, Micheletti C. Topological and physical links in soft matter systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:013002. [PMID: 34547745 DOI: 10.1088/1361-648x/ac28bf] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 09/21/2021] [Indexed: 06/13/2023]
Abstract
Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.
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Affiliation(s)
- Enzo Orlandini
- Department of Physics and Astronomy, University of Padova and Sezione INFN, Via Marzolo 8, Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, Trieste, Italy
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27
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Chubak I, Likos CN, Smrek J. Topological and threading effects in polydisperse ring polymer solutions. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1883140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Iurii Chubak
- Faculty of Physics, University of Vienna, Vienna, Austria
| | | | - Jan Smrek
- Faculty of Physics, University of Vienna, Vienna, Austria
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28
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Hagita K, Murashima T. Molecular Dynamics Simulations of Ring Shapes on a Ring Fraction in Ring–Linear Polymer Blends. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00656] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Katsumi Hagita
- Department of Applied Physics, National Defense Academy, 1-10-20, Hashirimizu, Yokosuka 239-8686, Japan
| | - Takahiro Murashima
- Department of Physics, Tohoku University, 6-3, Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8578, Japan
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29
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Affiliation(s)
- Jiuling Wang
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Ting Ge
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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30
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Murashima T, Hagita K, Kawakatsu T. Viscosity Overshoot in Biaxial Elongational Flow: Coarse-Grained Molecular Dynamics Simulation of Ring–Linear Polymer Mixtures. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00267] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Takahiro Murashima
- Department of Physics, Tohoku University, 6-3, Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8578, Japan
| | - Katsumi Hagita
- Department of Applied Physics, National Defense Academy, 1-10-20, Hashirimizu, Yokosuka 239-8686, Japan
| | - Toshihiro Kawakatsu
- Department of Physics, Tohoku University, 6-3, Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8578, Japan
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31
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Parisi D, Kaliva M, Costanzo S, Huang Q, Lutz PJ, Ahn J, Chang T, Rubinstein M, Vlassopoulos D. Nonlinear rheometry of entangled polymeric rings and ring-linear blends. JOURNAL OF RHEOLOGY 2021; 65:695-711. [PMID: 35250122 PMCID: PMC8896906 DOI: 10.1122/8.0000186] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Accepted: 05/06/2021] [Indexed: 06/14/2023]
Abstract
We present a comprehensive experimental rheological dataset for purified entangled ring polystyrenes and their blends with linear chains in nonlinear shear and elongation. In particular, data for shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of shear rate as well as molecular parameters (molar mass, blend composition and decreasing molar mass of linear component in blend). Over the extended parameter range investigated, rings do not exhibit clear transient undershoot in shear, in contrast to their linear counterparts and ring-linear blends. For the latter, the size of the undershoot and respective strain appear to increase with shear rate. Universal scaling of strain at overshoot and fractional overshoot (ratio of maximum to steady-state shear stress growth coefficient) indicates subtle differences in the shear-rate dependence between rings and linear polymers or their blends. The shear thinning behaviour of pure rings yields a slope nearly identical to predictions (-4/7) of a recent shear slit model and molecular dynamics simulations. Data for the second normal stress difference are reported for rings and ring-linear blends. While N 2 is negative and its absolute value stays below that of N 1 , as for linear polymers, the ratio -N 2 /N 1 is unambiguously larger for rings compared to linear polymer solutions with the same number of entanglements (almost by factor of two), in agreement with recent non-equilibrium molecular dynamics simulations. Further, -N 2 exhibits slightly weaker shear rate dependence compared to N 1 at high rates, and the respective power-law exponents can be rationalized in view of the slit model (3/7) and simulations (0.6), although further work is needed to unravel the molecular original of the observed behaviour. The comparison of shear and elongational stress growth coefficients for blends reflects the effect of ring-linear threading which leads to significant viscosity enhancement in elongation. Along the same lines, the elongational stress is much larger than the first normal stress in shear, and their ratio is much larger for rings and ring-linear blends compared to linear polymers. This conforms the interlocking scenario of rings and their important role in mechanically reinforcing linear matrices.
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Affiliation(s)
- Daniele Parisi
- Institute of Electronic Structure & Laser, Foundation for Research and Technology Hellas (FORTH), Heraklion, Crete 70013, Greece
- Department of Materials Science & Technology, University of Crete, Heraklion, Crete 71003, Greece
| | - Maria Kaliva
- Institute of Electronic Structure & Laser, Foundation for Research and Technology Hellas (FORTH), Heraklion, Crete 70013, Greece
- Department of Materials Science & Technology, University of Crete, Heraklion, Crete 71003, Greece
| | - Salvatore Costanzo
- Department of Chemical, Materials, and Production Engineering, Federico II University, 80125 Naples, Italy
| | - Qian Huang
- Department of Chemical and Biochemical Engineering, Technical University of Denmark 2800 Kgs. Lyngby, Denmark
| | - Pierre J Lutz
- Institut Charles Sadron, CNRS UPR 22, University of Strasbourg, 67034, Strasbourg, France
| | - Junyoung Ahn
- Division of Advanced Materials Science and Department of Chemistry, Pohang University of Science & Technology, Pohang 37673, Korea
| | - Taihyun Chang
- Division of Advanced Materials Science and Department of Chemistry, Pohang University of Science & Technology, Pohang 37673, Korea
| | - Michael Rubinstein
- Departments of Mechanical Engineering and Materials Science, Biomedical Engineering, Chemistry, and Physics, Duke University, Durham, NC 27708, USA
| | - Dimitris Vlassopoulos
- Institute of Electronic Structure & Laser, Foundation for Research and Technology Hellas (FORTH), Heraklion, Crete 70013, Greece
- Department of Materials Science & Technology, University of Crete, Heraklion, Crete 71003, Greece
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32
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Chubak I, Likos CN, Egorov SA. Multiscale Approaches for Confined Ring Polymer Solutions. J Phys Chem B 2021; 125:4910-4923. [PMID: 33938750 PMCID: PMC8279562 DOI: 10.1021/acs.jpcb.1c01953] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 04/18/2021] [Indexed: 11/29/2022]
Abstract
We apply a hierarchy of multiscale modeling approaches to investigate the structure of ring polymer solutions under planar confinement. In particular, we employ both monomer-resolved (MR-DFT) and a coarse-grained (CG-DFT) density functional theories for fully flexible ring polymers, with the former based on a flexible tangent hard-sphere model and the latter based on an effective soft-colloid representation, to elucidate the ring polymer organization within slits of variable width in different concentration regimes. The predicted monomer and polymer center-of-mass densities in confinement, as well as the surface tension at the solution-wall interface, are compared to explicit molecular dynamics (MD) simulations. The approaches yield quantitative (MR-DFT) or semiquantitative (CG-DFT) agreement with MD. In addition, we provide a systematic comparison between confined linear and ring polymer solutions. When compared to their linear counterparts, the rings are found to feature a higher propensity to structure in confinement that translates into a distinct shape of the depletion potentials between two walls immersed into a polymer solution. The depletion potentials that we extract from CG-DFT and MR-DFT are in semiquantitative agreement with each other. Overall, we find consistency among all approaches as regards the shapes, trends, and qualitative characteristics of density profiles and depletion potentials induced on hard walls by linear and cyclic polymers.
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Affiliation(s)
- Iurii Chubak
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
- Sorbonne
Université CNRS, Physico-Chimie des
Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Christos N. Likos
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Sergei A. Egorov
- Department
of Chemistry, University of Virginia, Charlottesville, Virginia 22901, United States
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33
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Schaefer C, Laity PR, Holland C, McLeish TCB. Stretching of Bombyx mori Silk Protein in Flow. Molecules 2021; 26:molecules26061663. [PMID: 33809814 PMCID: PMC8002474 DOI: 10.3390/molecules26061663] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2021] [Revised: 03/05/2021] [Accepted: 03/11/2021] [Indexed: 12/31/2022] Open
Abstract
The flow-induced self-assembly of entangled Bombyx mori silk proteins is hypothesised to be aided by the ‘registration’ of aligned protein chains using intermolecularly interacting ‘sticky’ patches. This suggests that upon chain alignment, a hierarchical network forms that collectively stretches and induces nucleation in a precisely controlled way. Through the lens of polymer physics, we argue that if all chains would stretch to a similar extent, a clear correlation length of the stickers in the direction of the flow emerges, which may indeed favour such a registration effect. Through simulations in both extensional flow and shear, we show that there is, on the other hand, a very broad distribution of protein–chain stretch, which suggests the registration of proteins is not directly coupled to the applied strain, but may be a slow statistical process. This qualitative prediction seems to be consistent with the large strains (i.e., at long time scales) required to induce gelation in our rheological measurements under constant shear. We discuss our perspective of how the flow-induced self-assembly of silk may be addressed by new experiments and model development.
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Affiliation(s)
- Charley Schaefer
- Department of Physics, University of York, Heslington, York YO10 5DD, UK;
- Correspondence:
| | - Peter R. Laity
- Department of Materials Science and Engineering, The University of Sheffield, Sir Robert Hadfield Building, Mappin Street, Sheffield S1 3JD, UK; (P.R.L.); (C.H.)
| | - Chris Holland
- Department of Materials Science and Engineering, The University of Sheffield, Sir Robert Hadfield Building, Mappin Street, Sheffield S1 3JD, UK; (P.R.L.); (C.H.)
| | - Tom C. B. McLeish
- Department of Physics, University of York, Heslington, York YO10 5DD, UK;
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34
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Parisi D, Costanzo S, Jeong Y, Ahn J, Chang T, Vlassopoulos D, Halverson JD, Kremer K, Ge T, Rubinstein M, Grest GS, Srinin W, Grosberg AY. Nonlinear Shear Rheology of Entangled Polymer Rings. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02839] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Daniele Parisi
- FORTH and University of Crete, Heraklion 71110, Greece
- Penn State University, State College, Pennsylvania 16801, United States
| | - Salvatore Costanzo
- FORTH and University of Crete, Heraklion 71110, Greece
- University of Naples Federico II, Naples 80125, Italy
| | - Youncheol Jeong
- Pohang University of Science and Technology, Pohang 790-784, South Korea
| | - Junyoung Ahn
- Pohang University of Science and Technology, Pohang 790-784, South Korea
| | - Taihyun Chang
- Pohang University of Science and Technology, Pohang 790-784, South Korea
| | | | | | - Kurt Kremer
- Max Planck Institute for Polymer Research, Mainz 55021, Germany
| | - Ting Ge
- University of South Carolina, Columbia, South Carolina 29208-0001, United States
| | - Michael Rubinstein
- Duke University, Durham, North Carolina 27708-9976, United States
- Hokkaido University, Sapporo, Hokkaido 060-0808, Japan
| | - Gary S. Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Watee Srinin
- Naresuan University, Mueang Phitsanulok, Phitsanulok 65000, Thailand
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35
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Jeong SH, Cho S, Roh EJ, Ha TY, Kim JM, Baig C. Intrinsic Surface Characteristics and Dynamic Mechanisms of Ring Polymers in Solution and Melt under Shear Flow. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01866] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Seung Heum Jeong
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
| | - Soowon Cho
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
| | - Eun Jung Roh
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
| | - Tae Yong Ha
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
| | - Jun Mo Kim
- Department of Chemical Engineering, Kyonggi University, 154-42 Gwanggyosan-ro, Yeongtong-gu, Suwon 16227, Kyeonggi-do, South Korea
| | - Chunggi Baig
- School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), UNIST-gil 50, Ulsan 44919, South Korea
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36
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Borger A, Wang W, O'Connor TC, Ge T, Grest GS, Jensen GV, Ahn J, Chang T, Hassager O, Mortensen K, Vlassopoulos D, Huang Q. Threading-Unthreading Transition of Linear-Ring Polymer Blends in Extensional Flow. ACS Macro Lett 2020; 9:1452-1457. [PMID: 35653662 DOI: 10.1021/acsmacrolett.0c00607] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Adding small amounts of ring polymers to a matrix of their linear counterparts is known to increase the zero-shear-rate viscosity because of linear-ring threading. Uniaxial extensional rheology measurements show that, unlike its pure linear and ring constituents, the blend exhibits an overshoot in the stress growth coefficient. By combining these measurements with ex-situ small-angle neutron scattering and nonequilibrium molecular dynamics simulations, this overshoot is shown to be driven by a transient threading-unthreading transition of rings embedded within the linear entanglement network. Prior to unthreading, embedded rings deform affinely with the linear entanglement network and produce a measurably stronger elongation of the linear chains in the blend compared to the pure linear melt. Thus, rings uniquely alter the mechanisms of transient elongation in linear polymers.
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Affiliation(s)
- Anine Borger
- Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Wendi Wang
- Department of Chemical and Biochemical Engineering, Technical University of Denmark, 2800 Lyngby, Denmark
| | - Thomas C O'Connor
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Ting Ge
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Gary S Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Grethe V Jensen
- The NIST Center for Neutron Research, Gaithersburg, Maryland 20899, United States.,Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, United States
| | - Junyoung Ahn
- Division of Advanced Materials Science and Department of Chemistry, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Taihyun Chang
- Division of Advanced Materials Science and Department of Chemistry, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Ole Hassager
- Department of Chemical and Biochemical Engineering, Technical University of Denmark, 2800 Lyngby, Denmark
| | - Kell Mortensen
- Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Dimitris Vlassopoulos
- Institute of Electronic Structure and Laser, Foundation for Research and Technology Hellas (FORTH), Heraklion, Crete 70013, Greece.,Department of Materials Science and Technology, University of Crete, Heraklion, Crete 71003, Greece
| | - Qian Huang
- Department of Chemical and Biochemical Engineering, Technical University of Denmark, 2800 Lyngby, Denmark
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37
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Rauscher PM, Schweizer KS, Rowan SJ, de Pablo JJ. Dynamics of poly[n]catenane melts. J Chem Phys 2020; 152:214901. [PMID: 32505155 DOI: 10.1063/5.0007573] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inspired by advances in the chemical synthesis of interlocking polymer architectures, extensive molecular dynamics simulations have been conducted to study the dynamical properties of poly[n]catenanes-polymers composed entirely of interlocking rings-in the melt state. Both the degree of polymerization (number of links) and the number of beads per ring are systematically varied, and the results are compared to linear and ring polymers. A simple Rouse-like model is presented, and its analytical solution suggests a decomposition of the dynamics into "ring-like" and "linear-like" regimes at short and long times, respectively. In agreement with this picture, multiple sub-diffusive regimes are observed in the monomer mean-squared-displacements even though interchain entanglement is not prevalent in the system. However, the Rouse-type model does not account for the topological effects of the mechanical bonds, which significantly alter the dynamics at intermediate length scales both within the rings and at the chain segment scales. The stress relaxation in the system is extremely rapid and may be conveniently separated into ring-like and linear-like contributions, again in agreement with the Rouse picture. However, the viscosity has a non-monotonic dependence on the ring size for long chains, which disagrees strongly with theoretical predictions. This unexpected observation cannot be explained in terms of chain disentanglement and is inconsistent with other measures of polymer relaxation. Possible mechanisms for this behavior are proposed and implications for materials design are discussed.
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Affiliation(s)
- Phillip M Rauscher
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
| | - Kenneth S Schweizer
- Department of Materials Science, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801-3028, USA
| | - Stuart J Rowan
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
| | - Juan J de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
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38
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Abstract
The glass transition in soft matter systems is generally triggered by an increase in packing fraction or a decrease in temperature. It has been conjectured that the internal topology of the constituent particles, such as polymers, can cause glassiness too. However, the conjecture relies on immobilizing a fraction of the particles and is therefore difficult to fulfill experimentally. Here we show that in dense solutions of circular polymers containing (active) segments of increased mobility, the interplay of the activity and the topology of the polymers generates an unprecedented glassy state of matter. The active isotropic driving enhances mutual ring threading to the extent that the rings can relax only in a cooperative way, which dramatically increases relaxation times. Moreover, the observed phenomena feature similarities with the conformation and dynamics of the DNA fibre in living nuclei of higher eukaryotes.
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Affiliation(s)
- Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria.
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany.
| | - Iurii Chubak
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria
| | - Christos N Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany
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