1
|
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.
Collapse
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
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
Staňo R, Smrek J, Likos CN. Cluster Formation in Solutions of Polyelectrolyte Rings. ACS NANO 2023; 17:21369-21382. [PMID: 37729077 PMCID: PMC10655244 DOI: 10.1021/acsnano.3c06083] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Accepted: 09/13/2023] [Indexed: 09/22/2023]
Abstract
We use molecular dynamics simulations to explore concentrated solutions of semiflexible polyelectrolyte ring polymers, akin to the DNA mini-circles, with counterions of different valences. We find that the assembly of rings into nanoscopic cylindrical stacks is a generic feature of the systems, but the morphology and dynamics of such a cluster can be steered by the counterion conditions. In general, a small addition of trivalent ions can stabilize the emergence of clusters due to the counterion condensation, which mitigates the repulsion between the like-charged rings. Stoichiometric addition of trivalent ions can even lead to phase separation of the polyelectrolyte ring phase due to the ion-bridging effects promoting otherwise entropically driven clustering. On the other hand, monovalent counterions cause the formation of stacks to be re-entrant with density. The clusters are stable within a certain window of concentration, while above the window the polyelectrolytes undergo an osmotic collapse, disfavoring ordering. The cluster phase exhibits characteristic cluster glass dynamics with arrest of collective degrees of freedom but not the self-ones. On the other hand, the collapsed phase shows arrest on both the collective and single level, suggesting an incipient glass-to-glass transition, from a cluster glass of ring clusters to a simple glass of rings.
Collapse
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
| | - 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
| |
Collapse
|
4
|
Staňo R, Likos CN, Egorov SA. Mixing Linear Polymers with Rings and Catenanes: Bulk and Interfacial Behavior. Macromolecules 2023; 56:8168-8182. [PMID: 37900098 PMCID: PMC10601540 DOI: 10.1021/acs.macromol.3c01267] [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: 06/28/2023] [Revised: 09/11/2023] [Indexed: 10/31/2023]
Abstract
We derive and parameterize effective interaction potentials between a multitude of different types of ring polymers and linear chains, varying the bending rigidity and solvent quality for the former species. We further develop and apply a density functional treatment for mixtures of both disconnected (chain-ring) and connected (chain-polycatenane) mixtures of the same, drawing coexistence binodals and exploring the ensuing response functions as well as the interface and wetting behavior of the mixtures. We show that worsening of the solvent quality for the rings brings about a stronger propensity for macroscopic phase separation in the linear-polycatenane mixtures, which is predominantly of the demixing type between phases of similar overall particle density. We formulate a simple criterion based on the effective interactions, allowing us to determine whether any specific linear-ring mixture will undergo a demixing phase separation.
Collapse
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
| | - Sergei A. Egorov
- Department
of Chemistry, University of Virginia, Charlottesville, Virginia 22901, United States
- Erwin
Schrödinger International Institute for Mathematics and Physics, Boltzmanngasse 9, 1090 Vienna, Austria
| |
Collapse
|
5
|
Li Y, Yao P, Guo H. Non-Rouse behavior of short ring polymers in melts by molecular dynamics simulations. SOFT MATTER 2023; 19:7161-7171. [PMID: 37702037 DOI: 10.1039/d3sm00668a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/14/2023]
Abstract
Short ring polymers are expected to behave nearly Rouse-like due to the little effect of topological constraints of non-knot and non-concatenation. However, this notion is questioned because of several simulation and experiment findings in recent times, which requires a further more quantitative study. Therefore, we perform a deep investigation of statics and dynamics of flexible short ring polymers (N < 2Ne) in melts via molecular dynamics simulations by further taking linear analogues as well as all-crossing ring and linear polymers with switched off topological constraints for comparisons and demonstrate the noticeable deviations from the Rouse model in terms of local and global scales. Although the overall size is compact, the subchains are swollen, which is traced back to the deeper "segmental correlation hole" effect. The same scaling relationship of the non-Gaussian deviation of the static structure factor holds, but the deviation magnitude of rings is larger than that of linear analogues. By checking the non-Gaussian parameter and autocorrelation function of center-of-mass velocity, the physical origin of anomalous sub-diffusions of short rings is identified as unscreened viscoelastic hydrodynamic interactions and not correlation hole effects, like linear analogues.
Collapse
Affiliation(s)
- Yedi Li
- Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Pu Yao
- Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Hongxia Guo
- Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| |
Collapse
|
6
|
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.
Collapse
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.
| |
Collapse
|
7
|
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.
Collapse
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
| |
Collapse
|
8
|
Müller T, Sommer JU, Lang M. Elasticity of Tendomer Gels. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Toni Müller
- Technische Universität Dresden, 01069 Dresden, Germany
| | | | - Michael Lang
- Leibniz-Institut für Polymerforschung Dresden e. V., Hohe Straße 6, 01069 Dresden, Germany
| |
Collapse
|
9
|
Mo JY, Wang ZH, Lu YY, An LJ. Size and Dynamics of Ring Polymers under Different Topological Constraints. CHINESE JOURNAL OF POLYMER SCIENCE 2022. [DOI: 10.1007/s10118-022-2743-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
10
|
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.
Collapse
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
| |
Collapse
|
11
|
Demonstration of reinforcement in polymer composite with rings penetrating the diamond-lattice network. POLYMER 2022. [DOI: 10.1016/j.polymer.2022.124637] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
12
|
Hagita K, Murashima T. Molecular dynamics studies of entropic elasticity of condensed lattice networks connected with uniform functionality f = 4. SOFT MATTER 2022; 18:894-904. [PMID: 35013740 DOI: 10.1039/d1sm01641e] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
To study the linear region of entropic elasticity, we considered the simplest physical model possible and extracted the linear entropic regime by using the least squares fit and the minimum of the mean absolute error. With regard to the effect of the fluctuation of the strand length Ns, the strand length with fluctuation was set to a form proportional to (1.0 + C (R - 0.5)), where R is a uniform random number between 0 and 1 and C is the amplitude of fluctuation. This form enabled us to analytically calculate the fluctuation dependence of the elastic modulus G. To reveal the linear regions of entropic elasticity as a function of the strand length between neighboring nodes in lattices, molecular dynamics (MD) simulations of condensed lattice networks with harmonic bonds without the excluded volume interactions were performed. Stress-strain curves were estimated by performing uniaxial stretching MD simulations under periodic boundary conditions with a bead number density of 0.85. First, we used a diamond lattice with functionality f = 4. The linear region of the entropic elasticity was found to become larger with the increasing number of beads in a strand Ns. For Ns = 100, the linear region had a strain of up to 8 for a regular diamond lattice. We investigated the effect of strand length fluctuation on the diamond lattice, and we confirmed that the equilibrium shear modulus G increases as the obtained analytical prediction and the linear entropic region in the stress-strain curves becomes narrower with increasing fluctuation of Ns. To investigate the difference in network topology with the same functionality f and uniform strand length Ns, we performed MD simulations on regular networks of the BC-8 structure with f = 4 prepared from the ab initio DFT calculations of carbon at high pressure. We found that the elastic behavior depends on the network connectivity (i.e., topology). This indicates that the network topology plays an important role in the emergence of nonlinearity owing to the crossover from entropic to energetic elasticity.
Collapse
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
| |
Collapse
|
13
|
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.
Collapse
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.
| |
Collapse
|
14
|
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
| |
Collapse
|
15
|
Ghobadpour E, Kolb M, Ejtehadi MR, Everaers R. Monte Carlo simulation of a lattice model for the dynamics of randomly branching double-folded ring polymers. Phys Rev E 2021; 104:014501. [PMID: 34412203 DOI: 10.1103/physreve.104.014501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2020] [Accepted: 06/07/2021] [Indexed: 11/07/2022]
Abstract
Supercoiled DNA, crumpled interphase chromosomes, and topologically constrained ring polymers often adopt treelike, double-folded, randomly branching configurations. Here we study an elastic lattice model for tightly double-folded ring polymers, which allows for the spontaneous creation and deletion of side branches coupled to a diffusive mass transport, which is local both in space and on the connectivity graph of the tree. We use Monte Carlo simulations to study systems falling into three different universality classes: ideal double-folded rings without excluded volume interactions, self-avoiding double-folded rings, and double-folded rings in the melt state. The observed static properties are in good agreement with exact results, simulations, and predictions of Flory theory for randomly branching polymers. For example, in the melt state rings adopt compact configurations and exhibit territorial behavior. In particular, we show that the emergent dynamics is in excellent agreement with a recent scaling theory and illustrate the qualitative differences with the familiar reptation dynamics of linear chains.
Collapse
Affiliation(s)
- Elham Ghobadpour
- Université Grenoble Alpes, Centre National de la Recherche Scientifique (CNRS), TIMC, F-38000 Grenoble, France.,School of Nano Science, Institute for Research in Fundamental Sciences (IPM), 19395-5531, Tehran, Iran
| | - Max Kolb
- Université de Lyon, École Normale Supérieure (ENS) de Lyon, CNRS, Laboratoire de Physique and Centre Blaise Pascal de l'ENS de Lyon, F-69342 Lyon, France
| | | | - Ralf Everaers
- Université de Lyon, École Normale Supérieure (ENS) de Lyon, CNRS, Laboratoire de Physique and Centre Blaise Pascal de l'ENS de Lyon, F-69342 Lyon, France
| |
Collapse
|
16
|
Lang M, Kumar KS. Reversible Stepwise Condensation Polymerization with Cyclization: Strictly Alternating Co-polymerization and Homopolymerization Based upon Two Orthogonal Reactions. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00720] [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)
- Michael Lang
- Institut Theorie der Polymere, Leibniz Institut für Polymerforschung Dresden, HoheStraße 6, Dresden 01069, Germany
| | - Kiran Suresh Kumar
- Institut Theorie der Polymere, Leibniz Institut für Polymerforschung Dresden, HoheStraße 6, Dresden 01069, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, Zellescher Weg 17, Dresden 01069, Germany
| |
Collapse
|
17
|
Lang M, Kumar KS. Simple and General Approach for Reversible Condensation Polymerization with Cyclization. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00718] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michael Lang
- Institut Theorie der Polymere, Leibniz Institut für Polymerforschung Dresden, Hohe Straße 6, 01069 Dresden, Germany
| | - Kiran Suresh Kumar
- Institut Theorie der Polymere, Leibniz Institut für Polymerforschung Dresden, Hohe Straße 6, 01069 Dresden, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, Zellescher Weg 17, 01069 Dresden, Germany
| |
Collapse
|
18
|
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.
Collapse
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
| |
Collapse
|
19
|
Smrek J, Garamella J, Robertson-Anderson R, Michieletto D. Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids. SCIENCE ADVANCES 2021; 7:eabf9260. [PMID: 33980492 PMCID: PMC8115916 DOI: 10.1126/sciadv.abf9260] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2020] [Accepted: 03/26/2021] [Indexed: 05/04/2023]
Abstract
Ring polymers in dense solutions are among the most intriguing problems in polymer physics. Because of its natural occurrence in circular form, DNA has been extensively used as a proxy to study the fundamental physics of ring polymers in different topological states. Yet, torsionally constrained-such as supercoiled-topologies have been largely neglected so far. The applicability of existing theoretical models to dense supercoiled DNA is thus unknown. Here, we address this gap by coupling large-scale molecular dynamics simulations with differential dynamic microscopy of entangled supercoiled DNA plasmids. We find that, unexpectedly, larger supercoiling increases the size of entangled plasmids and concomitantly induces an enhancement in DNA mobility. These findings are reconciled as due to supercoiling-driven asymmetric and double-folded plasmid conformations that reduce interplasmid entanglements and threadings. Our results suggest a way to topologically tune DNA mobility via supercoiling, thus enabling topological control over the (micro)rheology of DNA-based complex fluids.
Collapse
Affiliation(s)
- Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Jonathan Garamella
- Department of Physics and Biophysics, University of San Diego, San Diego, CA 92110, USA
| | | | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
- MRC Human Genetics Unit, Institute of Genetics and Molecular Medicine University of Edinburgh, Edinburgh EH4 2XU, UK
| |
Collapse
|
20
|
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
| |
Collapse
|
21
|
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
| |
Collapse
|
22
|
Combined Molecular Dynamics Simulation and Rouse Model Analysis of Static and Dynamic Properties of Unentangled Polymer Melts with Different Chain Architectures. CHINESE JOURNAL OF POLYMER SCIENCE 2020. [DOI: 10.1007/s10118-020-2489-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
23
|
Pachong SM, Chubak I, Kremer K, Smrek J. Melts of nonconcatenated rings in spherical confinement. J Chem Phys 2020; 153:064903. [DOI: 10.1063/5.0013929] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
| | - Iurii Chubak
- 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
| | - Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| |
Collapse
|
24
|
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.
Collapse
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
| |
Collapse
|
25
|
Abstract
Unraveling the packing structure of dense assemblies of semiflexible rings is not only fundamental for the dynamical description of polymer rings, but also key to understand biopackaging, such as observed in circular DNA of viruses or genome folding. Here we use X-ray tomography to study the geometrical and topological features of disordered packings of rubber bands in a cylindrical container. Assemblies of short bands assume a liquid-like disordered structure, with short-range orientational order, and reveal only minor influence of the container. In the case of longer bands, the confinement causes folded configurations and the bands interpenetrate and entangle. Most of the systems are found to display a threading network which percolates the system. Surprisingly, for long bands whose diameter is more than twice the diameter of the container, we found that all bands interpenetrate each other, in a complex fully entangled structure.
Collapse
Affiliation(s)
- Leopoldo R Gómez
- Department of Physics, Universidad Nacional del Sur-IFISUR-CONICET, 8000 Bahía Blanca, Argentina;
| | | | - Thorsten Pöschel
- Institut für Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052 Erlangen, Germany
| |
Collapse
|
26
|
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
| |
Collapse
|
27
|
Zhou X, Guo F, Li K, He L, Zhang L. Entropy-induced Separation of Binary Semiflexible Ring Polymer Mixtures in Spherical Confinement. Polymers (Basel) 2019; 11:E1992. [PMID: 31810347 PMCID: PMC6960585 DOI: 10.3390/polym11121992] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 11/24/2019] [Accepted: 11/27/2019] [Indexed: 11/25/2022] Open
Abstract
Coarse-grained molecular dynamics simulations are used to investigate the conformations of binary semiflexible ring polymers (SRPs) of two different lengths confined in a hard sphere. Segregated structures of SRPs in binary mixtures are strongly dependent upon the number density of system (ρ), the bending energy of long SRPs (Kb, long), and the chain length ratio of long to short SRPs (α). With a low ρ or a weak Kb, long at a small ratio α, long SRPs are immersed randomly in the matrix of short SRPs. As ρ and bending energy of long SRPs (Kb, long) are increased up to a certain value for a large ratio α, a nearly complete segregation between long and short SRPs is observed, which can be further characterized by the ratio of tangential and radial components of long SRPs velocity. These explicit segregated structures of the two components in spherical confinement are induced by a delicate competition between the entropic excluded volume (depletion) effects and bending contributions.
Collapse
Affiliation(s)
- Xiaolin Zhou
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Fuchen Guo
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Ke Li
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Linli He
- Department of Physics, Wenzhou University, Wenzhou 325035, Zhejiang, China
| | - Linxi Zhang
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| |
Collapse
|
28
|
Dabrowski-Tumanski P, Gren B, Sulkowska JI. Statistical Properties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function. Polymers (Basel) 2019; 11:E707. [PMID: 30999683 PMCID: PMC6523798 DOI: 10.3390/polym11040707] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 04/11/2019] [Accepted: 04/12/2019] [Indexed: 12/19/2022] Open
Abstract
The shape and properties of closed loops depend on various topological factors. One of them is loop-threading, which is present in complex lasso proteins. In this work, we analyze the probability of loop-threading by the tail and its influence on the shape of the loop measured by the radius of gyration, distention, asphericity, and prolateness. In particular, we show that the probability of a trivial lasso for phantom polymer is non-zero even for an infinite structure, as well as that the threading flattens the loop by restricting its motion in one dimension. These results are further used to show that there are fewer non-trivial protein lassos than expected and select potentially functional complex lasso proteins.
Collapse
Affiliation(s)
- Pawel Dabrowski-Tumanski
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Poland.
| | - Bartosz Gren
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland.
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Poland.
| |
Collapse
|
29
|
Schram RD, Rosa A, Everaers R. Local loop opening in untangled ring polymer melts: a detailed "Feynman test" of models for the large scale structure. SOFT MATTER 2019; 15:2418-2429. [PMID: 30778466 DOI: 10.1039/c8sm02587h] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for untangled (i.e. non-concatenated and unknotted) rings, which are known to crumple and segregate. Here we study these systems using a computationally efficient multi-scale approach, where we combine massive simulations on the fiber level with the explicit construction of untangled ring melt configurations based on theoretical ideas for their large scale structure. We find (i) that topological constraints may be neglected on scales below the standard entanglement length, Le, (ii) that rings with a size 1 ≤ Lr/Le ≤ 30 exhibit nearly ideal lattice tree behavior characterized by primitive paths which are randomly branched on the entanglement scale, and (iii) that larger rings are compact with gyration radii Rg2(Lr) ∝ Lr2/3. The detailed comparison between equilibrated and constructed ensembles allows us to perform a "Feynman test" of our understanding of untangled rings: can we convert ideas for the large scale ring structure into algorithms for constructing (nearly) equilibrated ring melt samples? We show that most structural observables are quantitatively reproduced by two different construction schemes: hierarchical crumpling and ring melts derived from the analogy to interacting branched polymers. However, the latter fail the "Feynman test" with respect to the magnetic radius, Rm, which we have defined based on an analogy to magnetostatics. While Rm is expected to vanish for double-folded structures, the observed values of Rm2(Lr) ∝ Rg2(Lr) provide a simple and computationally convenient measure of the presence of a non-negligible amount of local loop opening in crumpled rings.
Collapse
Affiliation(s)
- Raoul D Schram
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique and Centre Blaise Pascal, F-69342 Lyon, France.
| | | | | |
Collapse
|
30
|
Smrek J, Kremer K, Rosa A. Threading of Unconcatenated Ring Polymers at High Concentrations: Double-Folded vs Time-Equilibrated Structures. ACS Macro Lett 2019; 8:155-160. [PMID: 30800531 PMCID: PMC6383510 DOI: 10.1021/acsmacrolett.8b00828] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2018] [Accepted: 12/12/2018] [Indexed: 11/28/2022]
Abstract
Unconcatenated ring polymers in concentrated solutions and melt are remarkably well described as double-folded conformations on randomly branched primitive trees. This picture though contrasts recent evidence for extensive intermingling between close-by rings in the form of long-lived topological constraints or threadings. Here, we employ the concept of ring minimal surface to quantify the extent of threadings in polymer solutions of the double-folded rings vs rings in equilibrated molecular dynamics computer simulations. Our results show that the double-folded ring polymers are significantly less threaded compared to their counterparts at equilibrium. Second, threadings form through a slow process whose characteristic time-scale is of the same order of magnitude as that of the diffusion of the rings in solution. These findings are robust, being based on universal (model-independent) observables as the average fraction of threaded length or the total penetrations between close-by rings and the corresponding distribution functions.
Collapse
Affiliation(s)
- Jan Smrek
- Max
Planck Institut for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Kurt Kremer
- Max
Planck Institut for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany
| | - Angelo Rosa
- SISSA
(Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136 Trieste, Italy
| |
Collapse
|
31
|
Rosa A, Everaers R. Conformational statistics of randomly branching double-folded ring polymers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:7. [PMID: 30659391 DOI: 10.1140/epje/i2019-11765-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2018] [Accepted: 12/13/2018] [Indexed: 06/09/2023]
Abstract
The conformations of topologically constrained double-folded ring polymers can be described as wrappings of randomly branched primitive trees. We extend previous work on the tree statistics under different (solvent) conditions to explore the conformational statistics of double-folded rings in the limit of tight wrapping. In particular, we relate the exponents characterizing the ring statistics to those describing the primitive trees and discuss the distribution functions [Formula: see text] and [Formula: see text] for the spatial distance, [Formula: see text], and tree contour distance, L, between monomers as a function of their ring contour distance, [Formula: see text].
Collapse
Affiliation(s)
- Angelo Rosa
- Sissa (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136, Trieste, Italy.
| | - Ralf Everaers
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique and Centre Blaise Pascal, F-69342, Lyon, France
| |
Collapse
|
32
|
Michieletto D, Marenduzzo D, Orlandini E, Turner MS. Ring Polymers: Threadings, Knot Electrophoresis and Topological Glasses. Polymers (Basel) 2017; 9:E349. [PMID: 30971026 PMCID: PMC6418951 DOI: 10.3390/polym9080349] [Citation(s) in RCA: 18] [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: 07/05/2017] [Revised: 08/04/2017] [Accepted: 08/05/2017] [Indexed: 01/12/2023] Open
Abstract
Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physical consequences of such threadings are far-reaching: for instance, they lead to a topologically-driven glassy behaviour of ring polymer melts under pinning perturbations, while they can also account for the shape of experimentally observed patterns in two-dimensional gel electrophoresis of DNA knots.
Collapse
Affiliation(s)
- Davide Michieletto
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy.
| | - Matthew S Turner
- Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, UK.
| |
Collapse
|
33
|
Michieletto D. On the tree-like structure of rings in dense solutions. SOFT MATTER 2016; 12:9485-9500. [PMID: 27781227 DOI: 10.1039/c6sm02168a] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
One of the most challenging problems in polymer physics is providing a theoretical description for the behaviour of rings in dense solutions and melts. Although it is nowadays well established that the overall size of a ring in these conditions scales like that of a collapsed globule, there is compelling evidence that rings may exhibit ramified and tree-like conformations. In this work I show how to characterise these local tree-like structures by measuring the local writhing of the rings' segments and by identifying the patterns of intra-chain contacts. These quantities reveal two major topological structures: loops and terminal branches which strongly suggest that the strictly double-folded "lattice animal" picture for rings in the melt may be replaced by a more relaxed tree-like structure accommodating loops. In particular, I show that one can identify hierarchically looped structures whose degree increases linearly with the size of a ring, and that terminal branches are found to store about 30% of the whole ring mass, irrespectively of its length. Finally, I draw an analogy between rings in the melt and slip-linked chains, where contact points are enforced by mobile slip-links and for which a field-theoretic treatment can be employed to get some insight into their typical conformations. These findings are ultimately discussed in the light of recent works on the static structure of rings and on the existence of inter-ring threadings.
Collapse
Affiliation(s)
- D Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland, UK.
| |
Collapse
|
34
|
Rosa A, Everaers R. Computer simulations of melts of randomly branching polymers. J Chem Phys 2016; 145:164906. [PMID: 27802612 DOI: 10.1063/1.4965827] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Randomly branching polymers with annealed connectivity are model systems for ring polymers and chromosomes. In this context, the branched structure represents transient folding induced by topological constraints. Here we present computer simulations of melts of annealed randomly branching polymers of 3 ≤ N ≤ 1800 segments in d = 2 and d = 3 dimensions. In all cases, we perform a detailed analysis of the observed tree connectivities and spatial conformations. Our results are in excellent agreement with an asymptotic scaling of the average tree size of R ∼ N1/d, suggesting that the trees behave as compact, territorial fractals. The observed swelling relative to the size of ideal trees, R ∼ N1/4, demonstrates that excluded volume interactions are only partially screened in melts of annealed trees. Overall, our results are in good qualitative agreement with the predictions of Flory theory. In particular, we find that the trees swell by the combination of modified branching and path stretching. However, the former effect is subdominant and difficult to detect in d = 3 dimensions.
Collapse
Affiliation(s)
- Angelo Rosa
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136 Trieste, Italy
| | - Ralf Everaers
- Univ Lyon, Ens de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique and Centre Blaise Pascal, F-69342 Lyon, France
| |
Collapse
|
35
|
Abstract
Different methods for creating Olympic gels are analyzed using computer simulations. First ideal reference samples are obtained from freely interpenetrating semi-dilute solutions and melts of cyclic polymers. The distribution of pairwise concatenations per cyclic molecule is given by a Poisson-distribution and can be used to describe the elastic structure of the gels. Several batches of linear chains decorated with different selectively binding groups at their ends are mixed in the "DNA Origami" technique and network formation is realized. While the formation of cyclic molecules follows mean field predictions below overlap of the precursor molecules, an enhanced ring formation above overlap is found that is not explained by mean field arguments. The "progressive construction" method allows to create Olympic gels with a single reaction step from a concentrated mixture of large compressed rings with a low weight fraction of short chains that are below overlap concentration. This method, however, is limited by the difficulty to obtain a sufficiently high degree of polymerization of the large rings.
Collapse
Affiliation(s)
- J Fischer
- Leibniz Institut für Polymerforschung Dresden, Hohe Straße 6, 01069 Dresden, Germany
| | - M Lang
- Leibniz Institut für Polymerforschung Dresden, Hohe Straße 6, 01069 Dresden, Germany
| | - J-U Sommer
- Leibniz Institut für Polymerforschung Dresden, Hohe Straße 6, 01069 Dresden, Germany
| |
Collapse
|
36
|
Abstract
In order to quantify the effect of mutual threading on conformations and dynamics of unconcatenated and unknotted rings in the melt we computationally examine their minimal surfaces. We found a linear scaling of the surface area with the ring length. Minimal surfaces allow for an unambiguous algorithmic definition of mutual threading between rings. Based on it, we found that, although ring threading is frequent, majority of cases correspond to short loops. These findings explain why approximate theories that neglect threading are so unexpectedly successful despite having no small parameter justification. We also examine threading dynamics and identify the threading order parameter that reflects the ring diffusivity.
Collapse
Affiliation(s)
- Jan Smrek
- Center
for Soft Matter Research
and Department of Physics, New York University, New York, New York 10003, United States
| | - Alexander Y. Grosberg
- Center
for Soft Matter Research
and Department of Physics, New York University, New York, New York 10003, United States
| |
Collapse
|
37
|
Tsalikis DG, Mavrantzas VG, Vlassopoulos D. Analysis of Slow Modes in Ring Polymers: Threading of Rings Controls Long-Time Relaxation. ACS Macro Lett 2016; 5:755-760. [PMID: 35614653 DOI: 10.1021/acsmacrolett.6b00259] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Atomistic configurations of pure, precisely monodisperse ring poly(ethylene oxide) (PEO) melts accumulated in the course of very long molecular dynamics (MD) simulations at T = 413 K and P = 1 atm have been subjected to a detailed geometric analysis involving three steps (reduction to ensembles of coarse-grained paths, triangulation of the resulting three-dimensional polygons, and analysis of interpenetrations using vector calculus) in order to locate ring-ring threading events and quantify their strength and survival times. A variety of threading situations have been identified corresponding to single and multiple penetrations. The percentage of inter-ring threadings that correspond to full penetrations has also been quantified. By repeating the analysis for several PEO melts, the dependence of the degree of inter-ring threading on molecular weight (MW) has been obtained. Simulations with MWs up to 10 times the reported entanglement molecular weight (Me) of linear PEO have revealed several multiple threading events in all systems, with their relative number increasing with increasing MW. Our analysis indicates the existence of strong ring-ring topological interactions, which can last up to several times the corresponding average orientational ring polymer relaxation time. We show that these ring-ring interactions, together with the additional ring-linear threadings due to the remaining linear impurities, can explain the appearance of slow relaxation modes observed experimentally in entangled rings.
Collapse
Affiliation(s)
- Dimitrios G. Tsalikis
- Department of Chemical Engineering, University of Patras & FORTH/ICE-HT, Patras GR 26504, Greece
| | - Vlasis G. Mavrantzas
- Department of Chemical Engineering, University of Patras & FORTH/ICE-HT, Patras GR 26504, Greece
- Particle
Technology Laboratory, Department of Mechanical and Process Engineering, ETH-Z, CH-8092 Zurich, Switzerland
| | - Dimitris Vlassopoulos
- FORTH, Institute for Electronic Structure and Laser, Heraklion GR 71110, Greece
- Department of Materials Science & Technology, University of Crete, Heraklion GR 71003, Greece
| |
Collapse
|
38
|
Lang M, John A, Sommer JU. Model simulations on network formation and swelling as obtained from cross-linking co-polymerization reactions. POLYMER 2016. [DOI: 10.1016/j.polymer.2015.10.061] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
39
|
Yamamoto T, Tezuka Y. Cyclic polymers revealing topology effects upon self-assemblies, dynamics and responses. SOFT MATTER 2015; 11:7458-7468. [PMID: 26264187 DOI: 10.1039/c5sm01557j] [Citation(s) in RCA: 99] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
A variety of single- and multicyclic polymers having programmed chemical structures with guaranteed purity have now become obtainable owing to a number of synthetic breakthroughs achieved in recent years. Accordingly, a broadening range of studies has been undertaken to gain updated insights on fundamental polymer properties of cyclic polymers in either solution or bulk, in either static or dynamic states, and in self-assemblies, leading to unusual properties and functions of polymer materials based on their cyclic topologies. In this article, we review recent studies aiming to achieve distinctive properties and functions by cyclic polymers unattainable by their linear or branched counterparts. We focus, in particular, on selected examples of unprecedented topology effects of cyclic polymers upon self-assemblies, dynamics and responses, to highlight current progress in Topological Polymer Chemistry.
Collapse
Affiliation(s)
- Takuya Yamamoto
- Department of Organic and Polymeric Materials, Graduate School of Science and Engineering, Tokyo Institute of Technology, Tokyo, 152-8552, Japan.
| | | |
Collapse
|
40
|
Lang M, Rubinstein M, Sommer JU. Conformations of a Long Polymer in a Melt of Shorter Chains: Generalizations of the Flory Theorem. ACS Macro Lett 2015; 4:177-181. [PMID: 26543675 PMCID: PMC4621164 DOI: 10.1021/mz500777r] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Accepted: 01/05/2015] [Indexed: 11/28/2022]
Abstract
Large-scale simulations of the swelling of a long N-mer in a melt of chemically identical P-mers are used to investigate a discrepancy between theory and experiments. Classical theory predicts an increase of probe chain size R ∼ P-0.18 with decreasing degree of polymerization P of melt chains in the range of 1 < P < N1/2. However, both experiment and simulation data are more consistent with an apparently slower swelling R ∼ P-0.1 over a wider range of melt degrees of polymerization. This anomaly is explained by taking into account the recently discovered long-range bond correlations in polymer melts and corrections to excluded volume. We generalize the Flory theorem and demonstrate that it is in excellent agreement with experiments and simulations.
Collapse
Affiliation(s)
- Michael Lang
- Leibniz Institute of Polymer Research Dresden, Hohe Straße 6, 01069 Dresden, Germany
| | - Michael Rubinstein
- Department
of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States
| | - Jens-Uwe Sommer
- Leibniz Institute of Polymer Research Dresden, Hohe Straße 6, 01069 Dresden, Germany
- Institute
of Theoretical Physics, Technische Universität Dresden, Zellescher Weg
17, 01062 Dresden, Germany
| |
Collapse
|
41
|
Lang M, Fischer J, Werner M, Sommer JU. Swelling of Olympic gels. PHYSICAL REVIEW LETTERS 2014; 112:238001. [PMID: 24972227 DOI: 10.1103/physrevlett.112.238001] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2014] [Indexed: 06/03/2023]
Abstract
The swelling equilibrium of Olympic gels, which are composed of entangled cyclic polymers, is studied by Monte Carlo simulations. In contrast to chemically cross-linked polymer networks, we observe that Olympic gels made of chains with a larger degree of polymerization, N, exhibit a smaller equilibrium swelling degree, Q ∝ N(-0.28)ϕ(0)(-0.72), at the same polymer volume fraction ϕ(0) at network preparation. This observation is explained by a desinterspersion (reorganization with release of nontrapped entanglements) process of overlapping nonconcatenated rings upon swelling.
Collapse
Affiliation(s)
- M Lang
- Leibniz Institute for Polymer Research, Hohe Straße 6, 01069 Dresden, Germany
| | - J Fischer
- Leibniz Institute for Polymer Research, Hohe Straße 6, 01069 Dresden, Germany
| | - M Werner
- Leibniz Institute for Polymer Research, Hohe Straße 6, 01069 Dresden, Germany
| | - J-U Sommer
- Leibniz Institute for Polymer Research, Hohe Straße 6, 01069 Dresden, Germany
| |
Collapse
|
42
|
Lang M. Monomer Fluctuations and the Distribution of Residual Bond Orientations in Polymer Networks. Macromolecules 2013. [DOI: 10.1021/ma402013b] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Michael Lang
- Leibniz Institute of Polymer Research, Hohe Straße 6, 01069 Dresden, Germany
| |
Collapse
|