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Tubiana L, Ferrari F, Orlandini E. Circular Polycatenanes: Supramolecular Structures with Topologically Tunable Properties. PHYSICAL REVIEW LETTERS 2022; 129:227801. [PMID: 36493458 DOI: 10.1103/physrevlett.129.227801] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2021] [Revised: 08/11/2022] [Accepted: 10/04/2022] [Indexed: 06/17/2023]
Abstract
Polycatenanes, macrochains of topologically interlocked rings with unique physical properties have recently gained considerable interest in supramolecular chemistry, biology, and soft matter. Most of the work has been, so far, focused on linear chains and on their variety of conformational properties compared to standard polymers. Here we go beyond the linear case and show that, by circularizing such macrochains, one can exploit the topology of the local interlockings to store twist in the system, significantly altering its metric and local properties. Moreover, by properly defining the twist (Tw) and writhe (Wr) of these macrorings we show the validity of a relation equivalent to the Călugăreanu-White-Fuller theorem Tw+Wr=const, originally proved for ribbonlike structures such as double stranded DNA. Our results suggest that circular polycatenanes with storable and tunable twist can form a new category of highly designable multiscale structures with potential applications in supramolecular chemistry and material science.
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Affiliation(s)
- L Tubiana
- Physics Department, University of Trento, via Sommarive, 14 I-38123 Trento, Italy; INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy and Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - F Ferrari
- CASA* and Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
| | - E Orlandini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy and INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
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2
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Lang M, Müller T. On the Reference Size of Chains in a Network and the Shear Modulus of Unentangled Networks Made of Real Chains. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Michael Lang
- Institut Theorie der Polymere, Leibniz Institut für Polymerforschung Dresden, Hohe Straße 6, 01069 Dresden, Germany
| | - Toni Müller
- 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
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3
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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
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4
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Liu G, Rauscher PM, Rawe BW, Tranquilli MM, Rowan SJ. Polycatenanes: synthesis, characterization, and physical understanding. Chem Soc Rev 2022; 51:4928-4948. [PMID: 35611843 DOI: 10.1039/d2cs00256f] [Citation(s) in RCA: 26] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Chemical composition and architecture are two key factors that control the physical and material properties of polymers. Some of the more unusual and intriguing polymer architectures are the polycatenanes, which are a class of polymers that contain mechanically interlocked rings. Since the development of high yielding synthetic routes to catenanes, there has been an interest in accessing their polymeric counterparts, primarily on account of the unique conformations and degrees of freedom offered by non-bonded interlocked rings. This has lead to the synthesis of a wide variety of polycatenane architectures and to studies aimed at developing structure-property relationships of these interesting materials. In this review, we provide an overview of the field of polycatenanes, exploring synthesis, architecture, properties, simulation, and modelling, with a specific focus on some of the more recent developments.
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Affiliation(s)
- Guancen Liu
- Department of Chemistry, University of Chicago, Chicago, IL, USA.
| | - Phillip M Rauscher
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Benjamin W Rawe
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | | | - Stuart J Rowan
- Department of Chemistry, University of Chicago, Chicago, IL, USA. .,Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA.,Chemical and Engineering Sciences, Argonne National Laboratory, Lemont, IL, USA
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5
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Ubertini MA, Rosa A. Computer simulations of melts of ring polymers with nonconserved topology: A dynamic Monte Carlo lattice model. Phys Rev E 2021; 104:054503. [PMID: 34942724 DOI: 10.1103/physreve.104.054503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Accepted: 10/26/2021] [Indexed: 11/07/2022]
Abstract
We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on a fcc lattice which explicitly takes into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer strands may cross through each other. By applying the method to systems of interacting ring polymers at melt conditions, we characterize their structure and dynamics by measuring, in particular, the amounts of knots and links which are formed during the relaxation process. In comparison with standard melts of unknotted and unconcatenated rings, our simulations demonstrate that the mechanism of strand crossing makes polymer dynamics faster provided the characteristic timescale of the process is smaller than the typical timescale for chain relaxation in the unperturbed state, in agreement with recent experiments employing solutions of DNA rings in the presence of the type II topoisomerase enzyme. In the opposite case of slow rates the melt is shown to become slower, and this prediction may be easily validated experimentally.
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Affiliation(s)
- Mattia Alberto Ubertini
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Angelo Rosa
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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6
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Polson JM, Garcia EJ, Klotz AR. Flatness and intrinsic curvature of linked-ring membranes. SOFT MATTER 2021; 17:10505-10515. [PMID: 34755161 DOI: 10.1039/d1sm01307f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Recent experiments have elucidated the physical properties of kinetoplasts, which are chain-mail-like structures found in the mitochondria of trypanosome parasites formed from catenated DNA rings. Inspired by these studies, we use Monte Carlo simulations to examine the behavior of two-dimensional networks ("membranes") of linked rings. For simplicity, we consider only identical rings that are circular and rigid and that form networks with a regular linking structure. We find that the scaling of the eigenvalues of the shape tensor with membrane size are consistent with the behavior of the flat phase observed in self-avoiding covalent membranes. Increasing ring thickness tends to swell the membrane. Remarkably, unlike covalent membranes, the linked-ring membranes tend to form concave structures with an intrinsic curvature of entropic origin associated with local excluded-volume interactions. The degree of concavity increases with increasing ring thickness and is also affected by the type of linking network. The relevance of the properties of linked-ring model membranes to those observed in kinetoplasts is discussed.
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Affiliation(s)
- James M Polson
- Department of Physics, University of Prince Edward Island, Charlottetown, Prince Edward Island, C1A 4P3, Canada.
| | - Edgar J Garcia
- Department of Physics and Astronomy, California State University, Long Beach, California, 90840, USA
| | - Alexander R Klotz
- Department of Physics and Astronomy, California State University, Long Beach, California, 90840, USA
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7
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Characterization of Monte Carlo Dynamic/Kinetic Properties of Local Structure in Bond Fluctuation Model of Polymer System. MATERIALS 2021; 14:ma14174962. [PMID: 34501051 PMCID: PMC8433752 DOI: 10.3390/ma14174962] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Revised: 08/19/2021] [Accepted: 08/25/2021] [Indexed: 11/19/2022]
Abstract
We report the results of the characterization of local Monte Carlo (MC) dynamics of an equilibrium bond fluctuation model polymer matrix (BFM), in time interval typical for MC simulations of non-linear optical phenomena in host-guest systems. The study contributes to the physical picture of the dynamical aspects of quasi-binary mosaic states characterized previously in the static regime. The polymer dynamics was studied at three temperatures (below, above and close to the glass transition), using time-dependent generalization of the static parameters which characterize local free volume and local mobility of the matrix. Those parameters play the central role in the kinetic MC model of host-guest systems. The analysis was done in terms of the probability distributions of instantaneous and time-averaged local parameters. The main result is the characterization of time scales characteristic of various local structural processes. Slowing down effects close to the glass transition are clearly marked. The approach yields an elegant geometric criterion for the glass transition temperature. A simplified quantitative physical picture of the dynamics of guest molecules dispersed in BFM matrix at low temperatures offers a starting point for stochastic modeling of host-guest systems.
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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
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9
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Affiliation(s)
- Toni Müller
- Technical University Dresden, 01069 Dresden, Germany
- Leibniz Institute of Polymer Research Dresden, Hohe Str. 6, 01069 Dresden, Germany
| | - Jens-Uwe Sommer
- Technical University Dresden, 01069 Dresden, Germany
- Leibniz Institute of Polymer Research Dresden, Hohe Str. 6, 01069 Dresden, Germany
| | - Michael Lang
- Leibniz Institute of Polymer Research Dresden, Hohe Str. 6, 01069 Dresden, Germany
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10
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Danielsen SPO, Beech HK, Wang S, El-Zaatari BM, Wang X, Sapir L, Ouchi T, Wang Z, Johnson PN, Hu Y, Lundberg DJ, Stoychev G, Craig SL, Johnson JA, Kalow JA, Olsen BD, Rubinstein M. Molecular Characterization of Polymer Networks. Chem Rev 2021; 121:5042-5092. [PMID: 33792299 DOI: 10.1021/acs.chemrev.0c01304] [Citation(s) in RCA: 60] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.
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Affiliation(s)
- Scott P O Danielsen
- Marsico Lung Institute, University of North Carolina, Chapel Hill, North Carolina 27599, United States
| | - Haley K Beech
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Shu Wang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Bassil M El-Zaatari
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Xiaodi Wang
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | | | | | - Zi Wang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Patricia N Johnson
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Yixin Hu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - David J Lundberg
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Georgi Stoychev
- Marsico Lung Institute, University of North Carolina, Chapel Hill, North Carolina 27599, United States
| | - Stephen L Craig
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Jeremiah A Johnson
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Julia A Kalow
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Bradley D Olsen
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Michael Rubinstein
- Marsico Lung Institute, University of North Carolina, Chapel Hill, North Carolina 27599, United States.,Department of Chemistry, Duke University, Durham, North Carolina 27708, United States.,Departments of Biomedical Engineering and Physics, Duke University, Durham, North Carolina 27708, United States.,World Primer Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Kita 21 Nishi 10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
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11
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Mitus AC, Saphiannikova M, Radosz W, Toshchevikov V, Pawlik G. Modeling of Nonlinear Optical Phenomena in Host-Guest Systems Using Bond Fluctuation Monte Carlo Model: A Review. MATERIALS (BASEL, SWITZERLAND) 2021; 14:1454. [PMID: 33809785 PMCID: PMC8002275 DOI: 10.3390/ma14061454] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Revised: 03/05/2021] [Accepted: 03/08/2021] [Indexed: 12/14/2022]
Abstract
We review the results of Monte Carlo studies of chosen nonlinear optical effects in host-guest systems, using methods based on the bond-fluctuation model (BFM) for a polymer matrix. In particular, we simulate the inscription of various types of diffraction gratings in degenerate two wave mixing (DTWM) experiments (surface relief gratings (SRG), gratings in polymers doped with azo-dye molecules and gratings in biopolymers), poling effects (electric field poling of dipolar molecules and all-optical poling) and photomechanical effect. All these processes are characterized in terms of parameters measured in experiments, such as diffraction efficiency, nonlinear susceptibilities, density profiles or loading parameters. Local free volume in the BFM matrix, characterized by probabilistic distributions and correlation functions, displays a complex mosaic-like structure of scale-free clusters, which are thought to be responsible for heterogeneous dynamics of nonlinear optical processes. The photoinduced dynamics of single azopolymer chains, studied in two and three dimensions, displays complex sub-diffusive, diffusive and super-diffusive dynamical regimes. A directly related mathematical model of SRG inscription, based on the continuous time random walk (CTRW) formalism, is formulated and studied. Theoretical part of the review is devoted to the justification of the a priori assumptions made in the BFM modeling of photoinduced motion of the azo-polymer chains.
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Affiliation(s)
- Antoni C. Mitus
- Department of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland; (A.C.M.); (W.R.)
| | - Marina Saphiannikova
- Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Strasse 6, 01069 Dresden, Germany;
| | - Wojciech Radosz
- Department of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland; (A.C.M.); (W.R.)
| | - Vladimir Toshchevikov
- Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoi Prospect 31, 199004 Saint Petersburg, Russia;
| | - Grzegorz Pawlik
- Department of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland; (A.C.M.); (W.R.)
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12
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Factors influencing mechanical long-term stability of condensation curing silicone elastomers. JOURNAL OF POLYMER RESEARCH 2020. [DOI: 10.1007/s10965-020-02272-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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13
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Ahmadian Dehaghani Z, Chubak I, Likos CN, Ejtehadi MR. Effects of topological constraints on linked ring polymers in solvents of varying quality. SOFT MATTER 2020; 16:3029-3038. [PMID: 32129365 DOI: 10.1039/c9sm02374g] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their θ-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. Using molecular dynamics simulations, we study the scaling of the poly[n]catenane's radius of gyration in a good solvent, assuming in general that Rg∼mμnν and we find that μ = 0.65 ± 0.02 and ν = 0.60 ± 0.01 for the range of n and m considered. These findings are further rationalized with the help of a mean-field Flory-like theory yielding the values of μ = 16/25 and ν = 3/5, consistent with the numerical results. We show that individual rings within catenanes feature a surplus swelling due to the presence of NL topological links. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its θ-temperature in comparison to isolated linear and ring chains with the following ordering: T > T > T. Finally, we show that the presence of links similarly raises the θ-temperature of a single linked ring in comparison to an unlinked one, bringing its θ-temperature close to the one of a poly[n]catenane.
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14
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Mechanical Properties of Interlocked-ring Polymers: A Molecular Dynamics Simulation Study. CHINESE JOURNAL OF POLYMER SCIENCE 2019. [DOI: 10.1007/s10118-019-2279-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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Müller T, Sommer JU, Lang M. Tendomers - force sensitive bis-rotaxanes with jump-like deformation behavior. SOFT MATTER 2019; 15:3671-3679. [PMID: 30950476 DOI: 10.1039/c9sm00292h] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We consider tendomers, which are formed by pairs of rotaxane molecules where each one consists of a linear chain with N Kuhn segments that are threaded through m + 1 small rings. These rings can slide freely along the chains but cannot pass through each other or detach from the chain. By crosslinking the first slide rings of the two rotaxanes a slip-link between the two polymer backbones is formed. The remaining m slide rings form a one-dimensional real gas confined between the slip-link and the other chain end. When pulling the two ends of the chains which are next to the slip-link, an applied external force causes a compression of the slide rings. We consider the exact partition function of this model taking into account the repulsion between the slide rings and the finite extensibility of the polymer chains which is compared with Monte-Carlo simulation data for the tendomer under external force. To understand the underlying physics of the tendomer, we discuss also a simplified thermodynamic approach by taking into account the interplay between chain deformation and compression of the gas of slide rings. We show that tendomers exhibit a jump like mechanical response at a critical pulling force ∝ (m/N)1/2, where the compression of the gas of slide rings sets is. While the tendomer deforms at low forces similar to a short chain of about 2(N - m)/(m + 2) segments, it displays a jump-like decrease in elasticity beyond the critical force and deforms then like a chain of about 2(N - m) segments, before the finite extensibility of the chains sets in. This results in a strong peak of the mechanical susceptibility of the tendomer as a function of the applied force. Thus, tendomers are molecular-elastic elements with a jump-like strain-softening behavior. Our results are generalized to asymmetric tendomers that differ in the number of slide rings per rotaxane, which allows to design multi-step force extension curves with defined critical forces. Finally, we discuss some aspects of gels formed by tendomers, which are promising candidates for tailor-made stress sensitive elastomers.
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Affiliation(s)
- Toni Müller
- Institut Theorie der Polymere, Leibniz-Institut für Polymerforschung Dresden, Hohe Straße 6, 01069 Dresden, Germany.
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Lang M, Böhme F. Competing Exchange and Irreversible Reactions in a Linear Co‐Polycondensation Lead to a Broad Composition Window Where Tunable High Molecular Weight Polymers can be Prepared. MACROMOL THEOR SIMUL 2019. [DOI: 10.1002/mats.201800069] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Michael Lang
- Leibniz‐Institut für Polymerforschung Dresden Hohe Straße 6 01069 Dresden Germany
| | - Frank Böhme
- Leibniz‐Institut für Polymerforschung Dresden Hohe Straße 6 01069 Dresden Germany
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17
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Xu D, Ni CY, Zhu YL, Lu ZY, Xue YH, Liu H. Kinetic step-growth polymerization: A dissipative particle dynamics simulation study. J Chem Phys 2018; 148:024901. [DOI: 10.1063/1.4999050] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Dan Xu
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China
| | - Chun-Yan Ni
- Department of Anesthesiology, Cancer Hospital of Jilin Province, Huguang Road, No. 1018, Changchun 130012, China
| | - You-Liang Zhu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
| | - Zhong-Yuan Lu
- State Key Laboratory of Supramolecular Structure and Materials, Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
| | - Yao-Hong Xue
- School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China
| | - Hong Liu
- State Key Laboratory of Supramolecular Structure and Materials, Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität, Darmstadt 64287, Germany
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