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Le Roy H, Song J, Lundberg D, Zhukhovitskiy AV, Johnson JA, McKinley GH, Holten-Andersen N, Lenz M. Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels. SCIENCE ADVANCES 2024; 10:eadl5056. [PMID: 38748785 PMCID: PMC11095449 DOI: 10.1126/sciadv.adl5056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 04/10/2024] [Indexed: 05/19/2024]
Abstract
Gels made of telechelic polymers connected by reversible cross-linkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low-valence cross-linkers, while larger supramolecular cross-linkers bring about much slower dynamics involving a wide distribution of timescales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring cross-linkers all disconnect. Larger cross-linkers allow for a greater average number of bonds connecting them but also generate more heterogeneity. We characterize the resulting distribution of relaxation timescales analytically and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of cross-linker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any cross-linker size and could thus be harnessed for the rational design of complex viscoelastic materials.
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Affiliation(s)
- Hugo Le Roy
- Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
| | - Jake Song
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
- Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
| | - David Lundberg
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Aleksandr V. Zhukhovitskiy
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| | - Jeremiah A. Johnson
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Gareth H. McKinley
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Niels Holten-Andersen
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
- Department of Bioengineering and Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, USA
| | - Martin Lenz
- Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France
- PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005 Paris, France
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2
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Song J, Holten-Andersen N, McKinley GH. Non-Maxwellian viscoelastic stress relaxations in soft matter. SOFT MATTER 2023; 19:7885-7906. [PMID: 37846782 DOI: 10.1039/d3sm00736g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2023]
Abstract
Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.
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Affiliation(s)
- Jake Song
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
- Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA.
| | - Niels Holten-Andersen
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Bioengineering, Lehigh University, Bethlehem, PA 18015, USA
- Department of Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, USA
| | - Gareth H McKinley
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
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3
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Shi Z, Rao L, Wang P, Zhang L. Influences of different carbon substrates on the morphologies of carbon/g-C 3N 4 photocatalytic composites and the purification capacities of different composites in the weak UV underwater environment. CHEMOSPHERE 2022; 308:136257. [PMID: 36057358 DOI: 10.1016/j.chemosphere.2022.136257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2022] [Revised: 08/11/2022] [Accepted: 08/26/2022] [Indexed: 06/15/2023]
Abstract
In order to explore the influence of various carbon introduction on the morphology and photodegradation performance of C/g-C3N4 composites, three kinds of different carbon materials: carbon nanotubes (CNT), graphene (GN) and carbon fibers (CF) were introduced to modify g-C3N4, and the morphologies, light absorption capacities and the underwater purifications of the composite photocatalysts were investigated. Results showed that the composites synthesized with different carbon substrates shows great differences in growth morphology. In addition, the introduction of various carbon sources also has a great impact on the physical and chemical properties of the composites. Compared with GN/g-C3N4 and CF/g-C3N4, CNT/g-C3N4 shows strong light absorption ability, especially in long-wavelength region (570-660 nm). To further study the difference of degradation ability of the composites in the underwater environment, the purification performance of modified g-C3N4 at different water depths were carried out. The results show that under 40 cm of water, where the light intensity and ultra violet spectral are seriously attenuated, the purification efficiency of CNT/g-C3N4 at 40 cm is 3.35 times than that of g-C3N4. This work provides insight in the design of highly efficient metal-free photocatalysts for the environmental remediation.
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Affiliation(s)
- Zhenyu Shi
- Key Laboratory of Integrated Regulation and Resource Development on Shallow Lakes, Ministry of Education, College of Environment, Hohai University, Nanjing, 210098, China
| | - Lei Rao
- College of Mechanics and Materials, Hohai University, Nanjing, 210098, China.
| | - Peifang Wang
- Key Laboratory of Integrated Regulation and Resource Development on Shallow Lakes, Ministry of Education, College of Environment, Hohai University, Nanjing, 210098, China.
| | - Lixin Zhang
- Key Laboratory of Integrated Regulation and Resource Development on Shallow Lakes, Ministry of Education, College of Environment, Hohai University, Nanjing, 210098, China
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Hem J, Crauste-Thibierge C, Merlette TC, Clément F, Long DR, Ciliberto S. Microscopic Dynamics in the Strain Hardening Regime of Glassy Polymers. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00802] [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)
- Jérôme Hem
- ENS de Lyon, CNRS, Laboratoire de physique, F-69342 Lyon, France
| | | | - Thomas C. Merlette
- CNRS/Solvay, UMR 5268, Laboratoire Polymères et Matériaux Avancés, 87 avenue des Frères Perret, 69192 Cedex Saint Fons, France
| | - Florence Clément
- CNRS/Solvay, UMR 5268, Laboratoire Polymères et Matériaux Avancés, 87 avenue des Frères Perret, 69192 Cedex Saint Fons, France
| | - Didier R. Long
- CNRS/Solvay, UMR 5268, Laboratoire Polymères et Matériaux Avancés, 87 avenue des Frères Perret, 69192 Cedex Saint Fons, France
- CNRS, INSA Lyon, MATEIS, UMR5510, Univ. Lyon, Université Claude Bernard Lyon 1, 69100 Villeurbanne, France
| | - Sergio Ciliberto
- ENS de Lyon, CNRS, Laboratoire de physique, F-69342 Lyon, France
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5
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Evolution of mechanical properties of aged poly(ether ketone ketone) explained by a microstructural approach. Polym Degrad Stab 2021. [DOI: 10.1016/j.polymdegradstab.2020.109412] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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6
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Chandran S, Reiter G. Segmental Rearrangements Relax Stresses in Nonequilibrated Polymer Films. ACS Macro Lett 2019; 8:646-650. [PMID: 35619518 DOI: 10.1021/acsmacrolett.9b00116] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
We probed the relaxation of preparation-induced residual stresses in nonequilibrated polymer films through dewetting experiments. While we observed fast relaxations at temperatures close to or below the glass transition, at elevated temperatures these relaxation times were orders of magnitude longer than the reptation time. Intriguingly, applying appropriate scaling of preparation conditions allowed us to present all relaxation times, including published data, from various complementary experiments on a single master curve exhibiting an Arrhenius-type behavior. The corresponding activation energy (75 ± 10 kJ/mol) is similar to values obtained for the relaxation of segments in polystyrene. The observed long relaxation times suggest that residual stresses, a consequence of nonequilibrium conformations inherited from preparation, relax via concerted rearrangements of many segments.
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Affiliation(s)
- Sivasurender Chandran
- Institute of Physics, University of Freiburg, Herman Herder Str. 3, Freiburg, 79104, Germany
| | - Günter Reiter
- Institute of Physics, University of Freiburg, Herman Herder Str. 3, Freiburg, 79104, Germany
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7
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Shang B, Rottler J, Guan P, Barrat JL. Local versus Global Stretched Mechanical Response in a Supercooled Liquid near the Glass Transition. PHYSICAL REVIEW LETTERS 2019; 122:105501. [PMID: 30932637 DOI: 10.1103/physrevlett.122.105501] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 06/09/2023]
Abstract
Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the local region that is probed. The local relaxation time displays a broad distribution, as expected based on dynamic heterogeneity concepts, but the stretching is obtained independently of this distribution. We find that the size dependence of the local relaxation time and moduli can be well explained by the elastic shoving model.
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Affiliation(s)
- Baoshuang Shang
- Beijing Computational Science Research Center, Beijing 100193, China
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Jörg Rottler
- Department of Physics and Astronomy and Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Pengfei Guan
- Beijing Computational Science Research Center, Beijing 100193, China
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Masurel RJ, Gelineau P, Lequeux F, Cantournet S, Montes H. Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:116. [PMID: 29274066 DOI: 10.1140/epje/i2017-11606-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Accepted: 12/04/2017] [Indexed: 06/07/2023]
Abstract
In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.
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Affiliation(s)
- R J Masurel
- CNRS UPMC ESPCI ParisTech PSL Res Univ, Lab. SIMM, UMR 7615, F-75231, Paris, France
| | - P Gelineau
- CNRS UPMC ESPCI ParisTech PSL Res Univ, Lab. SIMM, UMR 7615, F-75231, Paris, France
| | - F Lequeux
- CNRS UPMC ESPCI ParisTech PSL Res Univ, Lab. SIMM, UMR 7615, F-75231, Paris, France
| | - S Cantournet
- MINES ParisTech, PSL-Research University, MAT - Centre des Matériaux, CNRS UMR 7633, BP 87, 91003, Evry, France
| | - H Montes
- CNRS UPMC ESPCI ParisTech PSL Res Univ, Lab. SIMM, UMR 7615, F-75231, Paris, France.
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9
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Conca L, Dequidt A, Sotta P, Long DR. Acceleration and Homogenization of the Dynamics during Plastic Deformation. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b01391] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Luca Conca
- Laboratoire
Polymères et Matériaux Avancés, UMR 5268 CNRS/Solvay, 87 avenue des Frères Perret, F-69192 Saint-Fons, France
| | - Alain Dequidt
- Institut
de Chimie, Université de Clermont-Ferrand, F-63000 Clermont-Ferrand, France
| | - Paul Sotta
- Laboratoire
Polymères et Matériaux Avancés, UMR 5268 CNRS/Solvay, 87 avenue des Frères Perret, F-69192 Saint-Fons, France
| | - Didier R. Long
- Laboratoire
Polymères et Matériaux Avancés, UMR 5268 CNRS/Solvay, 87 avenue des Frères Perret, F-69192 Saint-Fons, France
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10
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Masurel RJ, Gelineau P, Cantournet S, Dequidt A, Long DR, Lequeux F, Montes H. Role of Dynamical Heterogeneities on the Mechanical Response of Confined Polymer. PHYSICAL REVIEW LETTERS 2017; 118:047801. [PMID: 28186782 DOI: 10.1103/physrevlett.118.047801] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Indexed: 06/06/2023]
Abstract
Confinement induces various modifications in the dynamics of polymers as compared to bulk. We focus here on the role of dynamical heterogeneities on the mechanics of confined polymers. Using a simple model that allows computation of the mechanical response over 10 decades in frequency, we show that the local mechanical coupling controlling the macroscopic response in the bulk disappears in a confined geometry. The slowest domains significantly contribute to the mechanical response for increasing confinement. As a consequence, the apparent glass transition is broadened and shifted towards lower frequencies as confinement increases. We compare our numerical predictions with experiments performed on poly(ethylacrylate) chains in model filled elastomers. We suggest that the change of elastic coupling between domains induced by confinement should contribute significantly to the polymer mobility shift observed on filled systems.
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Affiliation(s)
- R J Masurel
- Laboratoire Sciences et Ingénierie de la Matière Molle (SIMM), CNRS-UMR 7615, Ecole Supérieure de Physique et Chimie Industrielles de Paris (ESPCI Paris), PSL Research University, Université Pierre et Marie Curie (UPMC), Sorbonne-Universités, 10 rue Vauquelin, F-75005 Paris, France
| | - P Gelineau
- Laboratoire Sciences et Ingénierie de la Matière Molle (SIMM), CNRS-UMR 7615, Ecole Supérieure de Physique et Chimie Industrielles de Paris (ESPCI Paris), PSL Research University, Université Pierre et Marie Curie (UPMC), Sorbonne-Universités, 10 rue Vauquelin, F-75005 Paris, France
| | - S Cantournet
- MINES ParisTech, PSL-Research University, MAT-Centre des Matériaux, CNRS UMR 7633, BP 87 91003 Evry, France
| | - A Dequidt
- Univ. Clermont Ferrand, Inst. Chim. Clermont Ferrand, UMR 6296, F-63171 Aubiere, France
| | - D R Long
- Laboratoire Polymères et Matériaux Avancés, UMR 5268 CNRS/Solvay, 87, rue des frères Perret, F-69192 Saint Fons, France
| | - F Lequeux
- Laboratoire Sciences et Ingénierie de la Matière Molle (SIMM), CNRS-UMR 7615, Ecole Supérieure de Physique et Chimie Industrielles de Paris (ESPCI Paris), PSL Research University, Université Pierre et Marie Curie (UPMC), Sorbonne-Universités, 10 rue Vauquelin, F-75005 Paris, France
| | - H Montes
- Laboratoire Sciences et Ingénierie de la Matière Molle (SIMM), CNRS-UMR 7615, Ecole Supérieure de Physique et Chimie Industrielles de Paris (ESPCI Paris), PSL Research University, Université Pierre et Marie Curie (UPMC), Sorbonne-Universités, 10 rue Vauquelin, F-75005 Paris, France
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Dequidt A, Conca L, Delannoy JY, Sotta P, Lequeux F, Long DR. Heterogeneous Dynamics and Polymer Plasticity. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01375] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alain Dequidt
- Institut de Chimie, Université de Clermont-Ferrand, F-63000 Clermont-Ferrand, France
| | - Luca Conca
- Laboratoire Polymères et Matériaux
Avancés, UMR 5268 CNRS/Solvay, 85 avenue des Frères Perret, F-69192 Saint-Fons, France
| | - Jean-Yves Delannoy
- Laboratoire Polymères et Matériaux
Avancés, UMR 5268 CNRS/Solvay, 85 avenue des Frères Perret, F-69192 Saint-Fons, France
| | - Paul Sotta
- Laboratoire Polymères et Matériaux
Avancés, UMR 5268 CNRS/Solvay, 85 avenue des Frères Perret, F-69192 Saint-Fons, France
| | - François Lequeux
- École Supérieure de Physique et de Chimie
Industrielles de la Ville de Paris (ESPCI) ParisTech, PSL Research
University, CNRS UMR 7615, Sciences et Ingénierie de la matière Molle, 10, Rue Vauquelin, F-75231 Paris, Cedex 05, France
| | - Didier R. Long
- Laboratoire Polymères et Matériaux
Avancés, UMR 5268 CNRS/Solvay, 85 avenue des Frères Perret, F-69192 Saint-Fons, France
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