1
|
Initial Crystallization Effects in Coarse-Grained Polyethylene Systems After Uni- and Biaxial Stretching in Blow-Molding Cooling Scenarios. Polymers (Basel) 2022; 14:polym14235144. [PMID: 36501539 PMCID: PMC9740480 DOI: 10.3390/polym14235144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Revised: 11/21/2022] [Accepted: 11/22/2022] [Indexed: 11/30/2022] Open
Abstract
This study investigates the initial stage of the thermo-mechanical crystallization behavior for uni- and biaxially stretched polyethylene. The models are based on a mesoscale molecular dynamics approach. We take constraints that occur in real-life polymer processing into account, especially with respect to the blowing stage of the extrusion blow-molding process. For this purpose, we deform our systems using a wide range of stretching levels before they are quenched. We discuss the effects of the stretching procedures on the micro-mechanical state of the systems, characterized by entanglement behavior and nematic ordering of chain segments. For the cooling stage, we use two different approaches which allow for free or hindered shrinkage, respectively. During cooling, crystallization kinetics are monitored: We precisely evaluate how the interplay of chain length, temperature, local entanglements and orientation of chain segments influence crystallization behavior. Our models reveal that the main stretching direction dominates microscopic states of the different systems. We are able to show that crystallization mainly depends on the (dis-)entanglement behavior. Nematic ordering plays a secondary role.
Collapse
|
2
|
Molecular simulation guided constitutive modeling of filled rubber: Bridging structural parameters to constitutive equations. POLYMER 2022. [DOI: 10.1016/j.polymer.2022.125090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
3
|
Singh H, Virga EG. A Ribbon Model for Nematic Polymer Networks. JOURNAL OF ELASTICITY 2022; 153:613-634. [PMID: 37293564 PMCID: PMC10244295 DOI: 10.1007/s10659-022-09900-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/28/2021] [Accepted: 05/09/2022] [Indexed: 06/10/2023]
Abstract
We present a theory of deformation of ribbons made of nematic polymer networks (NPNs). These materials exhibit properties of rubber and nematic liquid crystals, and can be activated by external stimuli of heat and light. A two-dimensional energy for a sheet of such a material has already been derived from the celebrated neo-classical energy of nematic elastomers in three space dimensions. Here, we use a dimension reduction method to obtain the appropriate energy for a ribbon from the aforementioned sheet energy. We also present an illustrative example of a rectangular NPN ribbon that undergoes in-plane serpentine deformations upon activation under an appropriate set of boundary conditions.
Collapse
Affiliation(s)
- Harmeet Singh
- Laboratory for Computation and Visualization in Mathematics and Mechanics, Institute of Mathematics, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | | |
Collapse
|
4
|
Effect of Nonisoprene Degradation and Naturally Occurring Network during Maturation on the Properties of Natural Rubber. Polymers (Basel) 2022; 14:polym14112180. [PMID: 35683854 PMCID: PMC9183052 DOI: 10.3390/polym14112180] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Revised: 05/12/2022] [Accepted: 05/20/2022] [Indexed: 02/04/2023] Open
Abstract
It well-known that the superior performance of natural rubber (NR) compared to its synthetic counterpart mainly derives from nonisoprene components and naturally occurring network, which varies during the progress of the maturation and thereby results in technically graded rubber with different properties. However, identifying the roles of these two factors in the forming of excellent performance of NR is still a challenge as they change simultaneously during the maturation process. Here, influences of naturally occurring networking and nonisoprene degradation on the components, structures and properties of NR were systematically investigated by tailored treatments of maturation. It was found that the maturation-induced formation of natural network structure contributes to the increase in initial plastic value, Mooney viscosity and gel content for un-crosslinked NR, while the decomposition of nonisoprene components plays a dominant role in improving the mechanical properties of vulcanized NR. Stress-strain curve and Mooney-Rivlin analysis demonstrate that the biodegradation of the nonisoprene components significantly boost the vulcanization process, which significantly increases the number of chemical cross-link networks and effective cross-link density of the material, greatly improving the mechanical properties of NR vulcanizates. This resulted in the tensile strength of TSR 10CV being able to reach 22.6 MPa, which is significantly improved compared to 15.8 MPa of TSR 3CV. Evidenced by tubular model fitting, the increase in chemical cross-linking points effectively reduces the movable radius of the molecular chain under dynamic loading, making the molecular chain more difficult to move, which suppresses the entropy change under dynamic loading and consequently endows NR excellent dynamic mechanical properties. This resulted in a significant decrease in the temperature rising of TSR 10CV to 3.3 °C, while the temperature rising of TSR 3CV was still as high as 14.5 °C. As a minor factor, the naturally occurring network improves the mechanical properties of vulcanizates in the form of sacrificial bonds.
Collapse
|
5
|
Grommes D, Schenk MR, Bruch O, Reith D. Investigation of Crystallization and Relaxation Effects in Coarse-Grained Polyethylene Systems after Uniaxial Stretching. Polymers (Basel) 2021; 13:4466. [PMID: 34961016 PMCID: PMC8703326 DOI: 10.3390/polym13244466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 12/13/2021] [Accepted: 12/16/2021] [Indexed: 11/23/2022] Open
Abstract
In this study, we investigate the thermo-mechanical relaxation and crystallization behavior of polyethylene using mesoscale molecular dynamics simulations. Our models specifically mimic constraints that occur in real-life polymer processing: After strong uniaxial stretching of the melt, we quench and release the polymer chains at different loading conditions. These conditions allow for free or hindered shrinkage, respectively. We present the shrinkage and swelling behavior as well as the crystallization kinetics over up to 600 ns simulation time. We are able to precisely evaluate how the interplay of chain length, temperature, local entanglements and orientation of chain segments influences crystallization and relaxation behavior. From our models, we determine the temperature dependent crystallization rate of polyethylene, including crystallization onset temperature.
Collapse
Affiliation(s)
- Dirk Grommes
- Institute of Technology, Resource and Energy-Efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, 53757 Sankt Augustin, Germany; (D.G.); (M.R.S.); (O.B.)
- Dr. Reinold Hagen Stiftung, Kautexstrasse 53, 53229 Bonn, Germany
| | - Martin R. Schenk
- Institute of Technology, Resource and Energy-Efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, 53757 Sankt Augustin, Germany; (D.G.); (M.R.S.); (O.B.)
| | - Olaf Bruch
- Institute of Technology, Resource and Energy-Efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, 53757 Sankt Augustin, Germany; (D.G.); (M.R.S.); (O.B.)
- Dr. Reinold Hagen Stiftung, Kautexstrasse 53, 53229 Bonn, Germany
| | - Dirk Reith
- Institute of Technology, Resource and Energy-Efficient Engineering (TREE), Bonn-Rhein-Sieg University of Applied Sciences, Grantham-Allee 20, 53757 Sankt Augustin, Germany; (D.G.); (M.R.S.); (O.B.)
- Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, 53754 Sankt Augustin, Germany
| |
Collapse
|
6
|
Negi V, Picu RC. Tensile behavior of non-crosslinked networks of athermal fibers in the presence of entanglements and friction. SOFT MATTER 2021; 17:10186-10197. [PMID: 33030165 PMCID: PMC8026777 DOI: 10.1039/d0sm01297a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Many biological and soft artificial materials contain a random network of non-crosslinked fibers as their main structural component. The excluded volume interactions (contact forces) at fiber contacts control the mechanical behavior of these systems. This physics has been studied extensively in compression, but little is known about the relation between network structure and its mechanical response in tension. In particular, although occasionally used conjecturally, the notion of fiber entanglements in athermal networks is not well defined, nor is it clear what role entanglements play in athermal network mechanics. The primary contribution of this work is the introduction of a measure of the degree of entanglement of a system of random athermal fibers, and the definition of its relationship with the mechanical behavior of the network. Entanglements confine the fibers during tensile loading, reduce the auxetic effect in mat-like networks, and maintain the inter-fiber contact density. In the absence of this contribution, reduction of the contact density during tensile loading due to auxeticity results in stress reduction. Entanglements stabilize the network via a tensegrity mechanism similar to that operating in woven materials and lead to network stiffening. The relation between the proposed measure of entanglements and the fiber volume fraction is defined. The effect of inter-fiber friction on the mechanics of entangled mat-like non-crosslinked fiber networks is also evaluated.
Collapse
Affiliation(s)
- V Negi
- Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
| | - R C Picu
- Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
| |
Collapse
|
7
|
Pedrini A, Virga EG. Ridge energy for thin nematic polymer networks. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:7. [PMID: 33616761 PMCID: PMC7900098 DOI: 10.1140/epje/s10189-021-00012-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 12/23/2020] [Indexed: 06/10/2023]
Abstract
Minimizing the elastic free energy of a thin sheet of nematic polymer network among smooth isometric immersions is the strategy purported by the mainstream theory. In this paper, we broaden the class of admissible spontaneous deformations: we consider ridged isometric immersions, which can cause a sharp ridge in the immersed surfaces. We propose a model to compute the extra energy distributed along such ridges. This energy comes from bending; it is shown under what circumstances it scales quadratically with the sheet's thickness, falling just in between stretching and bending energies. We put our theory to the test by studying the spontaneous deformation of a disk on which a radial hedgehog was imprinted at the time of crosslinking. We predict the number of folds that develop in terms of the degree of order induced in the material by external agents (such as heat and illumination).
Collapse
Affiliation(s)
- Andrea Pedrini
- Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy
| | - Epifanio G. Virga
- Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy
| |
Collapse
|
8
|
Pestryaev EM. Chain Heterogeneity in Simulated Polymer Melts: Segment Orientational Autocorrelation Function. POLYMER SCIENCE SERIES A 2020. [DOI: 10.1134/s0965545x20060085] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
9
|
Ozenda O, Sonnet AM, Virga EG. A blend of stretching and bending in nematic polymer networks. SOFT MATTER 2020; 16:8877-8892. [PMID: 33026035 DOI: 10.1039/d0sm00642d] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Nematic polymer networks are (heat and light) activable materials, which combine the features of rubber and nematic liquid crystals. When only the stretching energy of a thin sheet of nematic polymer network is minimized, the intrinsic (Gaussian) curvature of the shape it takes upon (thermal or optical) actuation is determined. This, unfortunately, produces a multitude of possible shapes, for which we need a selection criterion, which may only be provided by a correcting bending energy depending on the extrinsic curvatures of the deformed shape. The literature has so far offered approximate corrections depending on the mean curvature. In this paper, we derive the appropriate bending energy for a sheet of nematic polymer network from the celebrated neo-classical energy of nematic elastomers in three space dimensions. This task is performed via a dimension reduction based on a modified Kirchhoff-Love hypothesis, which withstands the criticism of more sophisticated analytical tools. The result is a surface elastic free-energy density where stretching and bending are blended together; they may or may not be length-separated, and should be minimized together. The extrinsic curvatures of the deformed shape not only feature in the bending energy through the mean curvature, but also through the relative orientation of the nematic director in the frame of the directions of principal curvatures.
Collapse
Affiliation(s)
- Olivier Ozenda
- Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy.
| | - André M Sonnet
- Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK.
| | - Epifanio G Virga
- Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy.
| |
Collapse
|
10
|
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
|
11
|
Villani V, Lavallata V. Entanglement Locking in the Unique Elasticity of Polydimethylsiloxane Rubbers. MACROMOL CHEM PHYS 2020. [DOI: 10.1002/macp.201900497] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Vincenzo Villani
- Dipartimento di ScienzeCampus Macchia RomanaUniversità degli Studi della Basilicata Potenza 85100 Italy
| | - Vito Lavallata
- Dipartimento di ScienzeCampus Macchia RomanaUniversità degli Studi della Basilicata Potenza 85100 Italy
| |
Collapse
|
12
|
Bobbili SV, Milner ST. Simulation Study of Entanglement in Semiflexible Polymer Melts and Solutions. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02681] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sai Vineeth Bobbili
- Pennsylvania State University, University Park 16801, Pennsylvania, United States
| | - Scott T. Milner
- Pennsylvania State University, University Park 16801, Pennsylvania, United States
| |
Collapse
|
13
|
Milner ST. Unified Entanglement Scaling for Flexible, Semiflexible, and Stiff Polymer Melts and Solutions. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02684] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| |
Collapse
|
14
|
Hou JX. Microscopic topology of entangled polymeric liquids. POLYMER 2020. [DOI: 10.1016/j.polymer.2019.122033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
15
|
Xi L. Molecular simulation for predicting the rheological properties of polymer melts. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1605600] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Li Xi
- Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada
| |
Collapse
|
16
|
Bae S, Galant O, Diesendruck CE, Silberstein MN. The Effect of Intrachain Cross-Linking on the Thermomechanical Behavior of Bulk Polymers Assembled Solely from Single Chain Polymer Nanoparticles. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01027] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Suwon Bae
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14850, United States
| | - Or Galant
- Schulich Faculty of Chemistry and Russell-Berrie Nanotechnology Institute, Technion - Israel Institute of Technology, Haifa, Israel
| | - Charles E. Diesendruck
- Schulich Faculty of Chemistry and Russell-Berrie Nanotechnology Institute, Technion - Israel Institute of Technology, Haifa, Israel
| | - Meredith N. Silberstein
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14850, United States
| |
Collapse
|
17
|
Goundaroulis D, Gügümcü N, Lambropoulou S, Dorier J, Stasiak A, Kauffman L. Topological Models for Open-Knotted Protein Chains Using the Concepts of Knotoids and Bonded Knotoids. Polymers (Basel) 2017; 9:polym9090444. [PMID: 30965745 PMCID: PMC6418563 DOI: 10.3390/polym9090444] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2017] [Revised: 09/08/2017] [Accepted: 09/11/2017] [Indexed: 11/16/2022] Open
Abstract
In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids and bonded knotoids. We show that the planar knotoids technique provides more refined information regarding the knottedness of a protein when compared to established methods in the literature. Moreover, we demonstrate that our topological model for bonded proteins is robust enough to distinguish all types of lassos in proteins.
Collapse
Affiliation(s)
- Dimos Goundaroulis
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Neslihan Gügümcü
- Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece.
| | - Sofia Lambropoulou
- Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece.
| | - Julien Dorier
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- Vital-IT, SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Louis Kauffman
- Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA.
| |
Collapse
|
18
|
Hou JX, Yu XC, Huang ZW. Primitive path analysis of linear polymer embedded in post array. JOURNAL OF POLYMER RESEARCH 2017. [DOI: 10.1007/s10965-017-1258-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
19
|
|
20
|
Papadopoulos GD, Tsalikis DG, Mavrantzas VG. Microscopic Dynamics and Topology of Polymer Rings Immersed in a Host Matrix of Longer Linear Polymers: Results from a Detailed Molecular Dynamics Simulation Study and Comparison with Experimental Data. Polymers (Basel) 2016; 8:E283. [PMID: 30974560 PMCID: PMC6432050 DOI: 10.3390/polym8080283] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2016] [Revised: 07/21/2016] [Accepted: 07/27/2016] [Indexed: 11/20/2022] Open
Abstract
We have performed molecular dynamics (MD) simulations of melt systems consisting of a small number of long ring poly(ethylene oxide) (PEO) probes immersed in a host matrix of linear PEO chains and have studied their microscopic dynamics and topology as a function of the molecular length of the host linear chains. Consistent with a recent neutron spin echo spectroscopy study (Goossen et al., Phys. Rev. Lett. 2015, 115, 148302), we have observed that the segmental dynamics of the probe ring molecules is controlled by the length of the host linear chains. In matrices of short, unentangled linear chains, the ring probes exhibit a Rouse-like dynamics, and the spectra of their dynamic structure factor resemble those in their own melt. In striking contrast, in matrices of long, entangled linear chains, their dynamics is drastically altered. The corresponding dynamic structure factor spectra exhibit a steep initial decay up to times on the order of the entanglement time τe of linear PEO at the same temperature but then they become practically time-independent approaching plateau values. The plateau values are different for different wavevectors; they also depend on the length of the host linear chains. Our results are supported by a geometric analysis of topological interactions, which reveals significant threading of all ring molecules by the linear chains. In most cases, each ring is simultaneously threaded by several linear chains. As a result, its dynamics at times longer than a few τe should be completely dictated by the release of the topological restrictions imposed by these threadings (interpenetrations). Our topological analysis did not indicate any effect of the few ring probes on the statistical properties of the network of primitive paths of the host linear chains.
Collapse
Affiliation(s)
- George D Papadopoulos
- Department of Chemical Engineering, University of Patras and FORTH-ICE/HT, Patras, GR 26504, Greece.
| | - Dimitrios G Tsalikis
- Department of Chemical Engineering, University of Patras and FORTH-ICE/HT, Patras, GR 26504, Greece.
| | - Vlasis G Mavrantzas
- Department of Chemical Engineering, University of Patras and FORTH-ICE/HT, Patras, GR 26504, Greece.
- Department of Mechanical and Process Engineering, Particle Technology Laboratory, ETH-Z, CH-8092 Zürich, Switzerland.
| |
Collapse
|
21
|
Jeong SH, Kim JM, Yoon J, Tzoumanekas C, Kröger M, Baig C. Influence of molecular architecture on the entanglement network: topological analysis of linear, long- and short-chain branched polyethylene melts via Monte Carlo simulations. SOFT MATTER 2016; 12:3770-3786. [PMID: 26997526 DOI: 10.1039/c5sm03016a] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present detailed results on the effect of chain branching on the topological properties of entangled polymer melts via an advanced connectivity-altering Monte Carlo (MC) algorithm. Eleven representative model linear, short-chain branched (SCB), and long-chain branched (LCB) polyethylene (PE) melts were employed, based on the total chain length and/or the longest linear chain dimension. Directly analyzing the entanglement [or the primitive path (PP)] network of the system via the Z-code, we quantified several important topological measures: (a) the PP contour length Lpp, (b) the number of entanglements Zes per chain, (c) the end-to-end length of an entanglement strand des, (d) the number of carbon atoms per entanglement strand Nes, and (e) the probability distribution for each of these quantities. The results show that the SCB polymer melts have significantly more compact overall chain conformations compared to the linear polymers, exhibiting, relative to the corresponding linear analogues, (a) ∼20% smaller values of 〈Lpp〉 (the statistical average of Lpp), (b) ∼30% smaller values of 〈Zes〉, (c) ∼20% larger values of 〈des〉, and (d) ∼50% larger values of 〈Nes〉. In contrast, despite the intrinsically smaller overall chain dimensions than those of the linear analogues, the LCB (H-shaped and A3AA3 multiarm) PE melts exhibit relatively (a) 7-8% larger values of 〈Lpp〉, (b) 6-11% larger values of 〈Zes〉 for the H-shaped melt and ∼2% smaller values of 〈Zes〉 for the A3AA3 multiarm, (c) 2-5% smaller values of 〈des〉, and (d) 7-11% smaller values of 〈Nes〉. Several interesting features were also found in the results of the probability distribution functions P for each topological measure.
Collapse
Affiliation(s)
- Seung Heum Jeong
- Department of Chemical Engineering, School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, South Korea.
| | - Jun Mo Kim
- Department of Chemical Engineering, School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, South Korea.
| | - Jeongha Yoon
- Department of Chemical Engineering, School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, South Korea.
| | - Christos Tzoumanekas
- National Technical University of Athens, School of Chemical Engineering, Zografou Campus, Athens, GR 15780, Greece and Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
| | - Martin Kröger
- Polymer Physics, ETH Zurich, Department of Materials, Leopold-Ruzicka-Weg 4, CH-8093, Zurich, Switzerland
| | - Chunggi Baig
- Department of Chemical Engineering, School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, South Korea.
| |
Collapse
|
22
|
Serna P, Bunin G, Nahum A. Topological Constraints in Directed Polymer Melts. PHYSICAL REVIEW LETTERS 2015; 115:228303. [PMID: 26650320 DOI: 10.1103/physrevlett.115.228303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2015] [Indexed: 06/05/2023]
Abstract
Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be trivial changes the polymer conformations drastically. Polymers of length L wander in the transverse direction only by a distance of order (lnL)^{ζ} with ζ≃1.5. This is strongly suppressed in comparison with the Brownian L^{1/2} scaling which holds in the absence of the topological constraint. It is also much smaller than the predictions of standard heuristic approaches-in particular the L^{1/4} of a mean-field-like "array of obstacles" model-so our results present a sharp challenge to theory. Dynamics are also strongly affected by the constraints, and a tagged monomer in an infinite system performs logarithmically slow subdiffusion in the transverse direction. To cast light on the suppression of the strands' wandering, we analyze the topological complexity of subregions of the melt: the complexity is also logarithmically small, and is related to the wandering by a power law. We comment on insights the results give for 3D melts, directed and nondirected.
Collapse
Affiliation(s)
- Pablo Serna
- Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom
- Departamento de Física-CIOyN, Universidad de Murcia, Murcia 30.071, Spain
| | - Guy Bunin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Adam Nahum
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
23
|
Moreira LA, Zhang G, Müller F, Stuehn T, Kremer K. Direct Equilibration and Characterization of Polymer Melts for Computer Simulations. MACROMOL THEOR SIMUL 2015. [DOI: 10.1002/mats.201500013] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Livia A. Moreira
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Guojie Zhang
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Franziska Müller
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Torsten Stuehn
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Kurt Kremer
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| |
Collapse
|
24
|
Katashima T, Urayama K, Chung UI, Sakai T. Probing the cross-effect of strains in non-linear elasticity of nearly regular polymer networks by pure shear deformation. J Chem Phys 2015; 142:174908. [DOI: 10.1063/1.4919653] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Takuya Katashima
- Department of Bioengineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Kenji Urayama
- Department of Macromolecular Science and Engineering, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585, Japan
| | - Ung-il Chung
- Department of Bioengineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Takamasa Sakai
- Department of Bioengineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| |
Collapse
|
25
|
Nie Y. Thermodynamic Description of Strain-Induced Crystallization of Natural Rubber by a Combination of the Tube Model and a Scaling Argument. J MACROMOL SCI B 2015. [DOI: 10.1080/00222348.2015.1019959] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
26
|
Kondo Y, Urayama K, Kidowaki M, Mayumi K, Takigawa T, Ito K. Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation. J Chem Phys 2014; 141:134906. [DOI: 10.1063/1.4897134] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuuki Kondo
- Department of Material Chemistry, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
| | - Kenji Urayama
- Department of Macromolecular Science and Engineering, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585, Japan
| | - Masatoshi Kidowaki
- Department of Applied Chemistry, Shibaura Institute of Technology, Tokyo 135-8548, Japan
| | - Koichi Mayumi
- Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8561, Japan
| | - Toshikazu Takigawa
- Department of Material Chemistry, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
| | - Kohzo Ito
- Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8561, Japan
| |
Collapse
|
27
|
Brassinne J, Gohy JF, Fustin CA. Controlling the Cross-Linking Density of Supramolecular Hydrogels Formed by Heterotelechelic Associating Copolymers. Macromolecules 2014. [DOI: 10.1021/ma500537t] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Jérémy Brassinne
- Institute of Condensed Matter
and Nanosciences (IMCN), Bio and Soft Matter Division (BSMA), Université catholique de Louvain, Place L. Pasteur 1, bte L4.01.01, B-1348 Louvain-la-Neuve, Belgium
| | - Jean-François Gohy
- Institute of Condensed Matter
and Nanosciences (IMCN), Bio and Soft Matter Division (BSMA), Université catholique de Louvain, Place L. Pasteur 1, bte L4.01.01, B-1348 Louvain-la-Neuve, Belgium
| | - Charles-André Fustin
- Institute of Condensed Matter
and Nanosciences (IMCN), Bio and Soft Matter Division (BSMA), Université catholique de Louvain, Place L. Pasteur 1, bte L4.01.01, B-1348 Louvain-la-Neuve, Belgium
| |
Collapse
|
28
|
Krokhotin A, Nicolis S, Niemi AJ. Long range correlations and folding angle with applications to α-helical proteins. J Chem Phys 2014; 140:095103. [PMID: 24606382 DOI: 10.1063/1.4865933] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The conformational complexity of chain-like macromolecules such as proteins and other linear polymers is much larger than that of point-like atoms and molecules. Unlike particles, chains can bend, twist, and even become knotted. Thus chains might also display a much richer phase structure. Unfortunately, it is not very easy to characterize the phase of a long chain. Essentially, the only known attribute is the radius of gyration. The way how it changes when the degree of polymerization becomes different, and how it evolves when the ambient temperature and solvent properties change, is commonly used to disclose the phase. But in any finite length chain there are corrections to scaling that complicate the detailed analysis of the phase structure. Here we introduce a quantity that we call the folding angle to identify and scrutinize the phase structure, as a complement to the radius of gyration. We argue for a mean-field level relationship between the folding angle and the scaling exponent in the radius of gyration. We then estimate the value of the folding angle in the case of crystallographic α-helical protein structures in the Protein Data Bank. We also show how the experimental value of the folding angle can be obtained computationally, using a semiclassical Born-Oppenheimer description of α-helical chiral chains.
Collapse
Affiliation(s)
- Andrey Krokhotin
- Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala, Sweden
| | - Stam Nicolis
- Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200 Tours, France
| | - Antti J Niemi
- Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala, Sweden
| |
Collapse
|
29
|
Nie Y, Qu L, Huang G, Wang X, Weng G, Wu J. Homogenization of natural rubber network induced by nanoclay. J Appl Polym Sci 2014. [DOI: 10.1002/app.40324] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Yijing Nie
- College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering; Sichuan University; Chengdu 610065 People's Republic of China
- School of Materials Science and Engineering; Jiangsu University; 301 Xuefu Road Zhenjiang 212013 People's Republic of China
| | - Liangliang Qu
- College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering; Sichuan University; Chengdu 610065 People's Republic of China
| | - Guangsu Huang
- College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering; Sichuan University; Chengdu 610065 People's Republic of China
| | - Xiaoan Wang
- College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering; Sichuan University; Chengdu 610065 People's Republic of China
| | - Gengsheng Weng
- College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering; Sichuan University; Chengdu 610065 People's Republic of China
| | - Jinrong Wu
- College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering; Sichuan University; Chengdu 610065 People's Republic of China
| |
Collapse
|
30
|
Halverson JD, Smrek J, Kremer K, Grosberg AY. From a melt of rings to chromosome territories: the role of topological constraints in genome folding. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:022601. [PMID: 24472896 DOI: 10.1088/0034-4885/77/2/022601] [Citation(s) in RCA: 179] [Impact Index Per Article: 17.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.
Collapse
Affiliation(s)
- Jonathan D Halverson
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
| | | | | | | |
Collapse
|
31
|
Abstract
Polypeptide chains form open knots in many proteins. How these knotted proteins fold and finding the evolutionary advantage provided by these knots are among some of the key questions currently being studied in the protein folding field. The detection and identification of protein knots are substantial challenges. Different methods and many variations of them have been employed, but they can give different results for the same protein. In the present article, we review the various knot identification algorithms and compare their relative strengths when applied to the study of knots in proteins. We show that the statistical approach based on the uniform closure method is advantageous in comparison with other methods used to characterize protein knots.
Collapse
|
32
|
White EM, Yatvin J, Grubbs JB, Bilbrey JA, Locklin J. Advances in smart materials: Stimuli-responsive hydrogel thin films. ACTA ACUST UNITED AC 2013. [DOI: 10.1002/polb.23312] [Citation(s) in RCA: 130] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Evan M. White
- Department of Chemistry and College of Engineering; University of Georgia; 220 Riverbend Road, Riverbend Research South Athens Georgia 30602
| | - Jeremy Yatvin
- Department of Chemistry and College of Engineering; University of Georgia; 220 Riverbend Road, Riverbend Research South Athens Georgia 30602
| | - Joe B. Grubbs
- Department of Chemistry and College of Engineering; University of Georgia; 220 Riverbend Road, Riverbend Research South Athens Georgia 30602
| | - Jenna A. Bilbrey
- Department of Chemistry and College of Engineering; University of Georgia; 220 Riverbend Road, Riverbend Research South Athens Georgia 30602
| | - Jason Locklin
- Department of Chemistry and College of Engineering; University of Georgia; 220 Riverbend Road, Riverbend Research South Athens Georgia 30602
| |
Collapse
|
33
|
Wang SQ, Wang Y, Cheng S, Li X, Zhu X, Sun H. New Experiments for Improved Theoretical Description of Nonlinear Rheology of Entangled Polymers. Macromolecules 2013. [DOI: 10.1021/ma300398x] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shi-Qing Wang
- Maurice Morton Institute of Polymer
Science and Engineering, University of Akron, Akron, Ohio 44325, United States
| | - Yangyang Wang
- Maurice Morton Institute of Polymer
Science and Engineering, University of Akron, Akron, Ohio 44325, United States
| | - Shiwang Cheng
- Maurice Morton Institute of Polymer
Science and Engineering, University of Akron, Akron, Ohio 44325, United States
| | - Xin Li
- Maurice Morton Institute of Polymer
Science and Engineering, University of Akron, Akron, Ohio 44325, United States
| | - Xiangyang Zhu
- Maurice Morton Institute of Polymer
Science and Engineering, University of Akron, Akron, Ohio 44325, United States
| | - Hao Sun
- Maurice Morton Institute of Polymer
Science and Engineering, University of Akron, Akron, Ohio 44325, United States
| |
Collapse
|
34
|
|
35
|
Anogiannakis SD, Tzoumanekas C, Theodorou DN. Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes. Macromolecules 2012. [DOI: 10.1021/ma300912z] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Stefanos D. Anogiannakis
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
| | - Christos Tzoumanekas
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven,
The Netherlands
| | - Doros N. Theodorou
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven,
The Netherlands
| |
Collapse
|
36
|
Sliozberg YR, Sirk TW, Brennan JK, Andzelm JW. Bead-spring models of entangled polymer melts: Comparison of hard-core and soft-core potentials. ACTA ACUST UNITED AC 2012. [DOI: 10.1002/polb.23175] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
37
|
Everaers R. Topological versus rheological entanglement length in primitive-path analysis protocols, tube models, and slip-link models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:022801. [PMID: 23005812 DOI: 10.1103/physreve.86.022801] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2011] [Revised: 06/18/2012] [Indexed: 06/01/2023]
Abstract
We show that the front factor appearing in the shear modulus of a phantom network, G(ph) = (1-2/f)(ρk(B)T)/N(s), also controls the ratio of the strand length, N(s), and the number of monomers per Kuhn length of the primitive paths, N(ph)(PPKuhn), characterizing the average network conformation. In particular, N(ph)(PPKuhn) = N(s)/(1-2/f) and G(ph) = (ρk(B)T)/N(ph)(PPKuhn). Neglecting the difference between cross-links and slip-links, these results can be transferred to entangled systems and the interpretation of primitive path analysis data. In agreement with the tube model, the analogy to phantom networks suggest that the rheological entanglement length, N(e)(rheo) = (ρk(B)T)/G(e), should equal N(e)(PPKuhn). Assuming binary entanglements with f = 4 functional junctions, we expect that N(e)(rheo) should be twice as large as the topological entanglement length, N(e)(topo). These results are in good agreement with reported primitive path analysis results for model systems and a wide range of polymeric materials. Implications for tube and slip-link models are discussed.
Collapse
|
38
|
Sliozberg YR, Andzelm JW. Fast protocol for equilibration of entangled and branched polymer chains. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2011.12.040] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
|
39
|
New insights into thermodynamic description of strain-induced crystallization of peroxide cross-linked natural rubber filled with clay by tube model. POLYMER 2011. [DOI: 10.1016/j.polymer.2011.05.004] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
40
|
Eskandari M, Brey E, Cinar A. A gaussian model for substrates of entangled cross-linked poly(ethylene glycol) in biomedical applications. Biotechnol Bioeng 2010; 108:435-45. [PMID: 21170900 DOI: 10.1002/bit.22889] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2010] [Revised: 05/28/2010] [Accepted: 06/23/2010] [Indexed: 11/06/2022]
Abstract
Cells usually spread on a synthetic substrate through bonds between receptors and chemical groups on the substrate (ligands). Therefore, it is valuable to study the effects of the average number density of these chemical groups and the average distance between them to model and predict the cell behavior. Poly(ethylene glycol) [PEG] modified with peptide groups has been used widely in biomedical applications as a substrate material. In this study, a coarse-grained model is proposed for PEG to predict the average number density of ligands and the average distance between them. Molecular information such as initial molecular weight distribution, average molecular weight between cross-links, and average molecular weight between entanglements is used as input parameters. Based on simulation results, it is concluded that both entanglement and cross-link densities are required to create a network structure. The results suggest that an average initial molecular weight 2-3 times the average molecular weight between entanglements and a moderate cross-link density are sufficient to create a closed network structure with a high ligand density and a small average distance between them.
Collapse
Affiliation(s)
- Mahnaz Eskandari
- Chemical and Biological Engineering Department, Illinois Institute of Technology, Chicago, 60616, USA.
| | | | | |
Collapse
|
41
|
Baig C, Mavrantzas VG, Kröger M. Flow Effects on Melt Structure and Entanglement Network of Linear Polymers: Results from a Nonequilibrium Molecular Dynamics Simulation Study of a Polyethylene Melt in Steady Shear. Macromolecules 2010. [DOI: 10.1021/ma100826u] [Citation(s) in RCA: 134] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Chunggi Baig
- 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
| | - Martin Kröger
- Polymer Physics, ETH Zürich, Department of Materials, Wolfgang-Pauli-Strasse 10, CH-8093 Zürich, Switzerland
| |
Collapse
|
42
|
Nie Y, Huang G, Qu L, Zhang P, Weng G, Wu J. Structural evolution during uniaxial deformation of natural rubber reinforced with nano-alumina. POLYM ADVAN TECHNOL 2010. [DOI: 10.1002/pat.1709] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
43
|
Hoy RS, Foteinopoulou K, Kröger M. Topological analysis of polymeric melts: chain-length effects and fast-converging estimators for entanglement length. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:031803. [PMID: 19905139 DOI: 10.1103/physreve.80.031803] [Citation(s) in RCA: 201] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2009] [Revised: 06/22/2009] [Indexed: 05/28/2023]
Abstract
Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N_{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.
Collapse
Affiliation(s)
- Robert S Hoy
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA.
| | | | | |
Collapse
|
44
|
Khaliullin RN, Schieber JD. Analytic expressions for the statistics of the primitive-path length in entangled polymers. PHYSICAL REVIEW LETTERS 2008; 100:188302. [PMID: 18518421 DOI: 10.1103/physrevlett.100.188302] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2007] [Indexed: 05/26/2023]
Abstract
An analytic expression is proposed for the primitive-path length of entangled polymer chains. The expression is derived from statistical mechanics of a chain that is a random walk with randomly scattered entanglements. The only parameters are the number of Kuhn steps in the chain and a dimensionless parameter beta that contains information about the entanglement density and Kuhn step size. The expression is found to compare very favorably with numerical results recently found from examining topological constraints in microscopic simulations. The comparison also predicts well the plateau modulus of polyethylene, suggesting that the slip-link model is a viable intermediate in the search for true ab initio rheology predictions. Since the expression is analytic, it can be used to make predictions where the simulations cannot reach, and hence is applicable for coarse graining.
Collapse
Affiliation(s)
- Renat N Khaliullin
- Department of Chemical and Biological Engineering, and Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 10 W. 33rd Street, Chicago, Illinois, USA
| | | |
Collapse
|
45
|
Uchida N, Grest GS, Everaers R. Viscoelasticity and primitive path analysis of entangled polymer liquids: From F-actin to polyethylene. J Chem Phys 2008; 128:044902. [DOI: 10.1063/1.2825597] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
46
|
López-Manchado M, Valentín J, Carretero J, Barroso F, Arroyo M. Rubber network in elastomer nanocomposites. Eur Polym J 2007. [DOI: 10.1016/j.eurpolymj.2007.07.023] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
47
|
Kilian HG, Höhne GWH, Trögele P, Ambacher H. Stretching calorimetry and thermoelasticity of rubbers at different temperatures. ACTA ACUST UNITED AC 2007. [DOI: 10.1002/polc.5070710120] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
|
48
|
Shanbhag S, Park SJ, Zhou Q, Larson RG. Implications of microscopic simulations of polymer melts for mean-field tube theories. Mol Phys 2007. [DOI: 10.1080/00268970601143333] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
49
|
Urayama K, Ogasawara S, Takigawa T. Pure shear deformation of physical and chemical gels of poly(vinyl alcohol). POLYMER 2006. [DOI: 10.1016/j.polymer.2006.07.021] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
50
|
Tzoumanekas C, Theodorou DN. Topological Analysis of Linear Polymer Melts: A Statistical Approach. Macromolecules 2006. [DOI: 10.1021/ma0607057] [Citation(s) in RCA: 245] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christos Tzoumanekas
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece, and Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
| | - Doros N. Theodorou
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece, and Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
| |
Collapse
|