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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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Sojecka AA, Drozd-Rzoska A. Global population: from Super-Malthus behavior to Doomsday criticality. Sci Rep 2024; 14:9853. [PMID: 38684786 PMCID: PMC11058850 DOI: 10.1038/s41598-024-60589-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2024] [Accepted: 04/24/2024] [Indexed: 05/02/2024] Open
Abstract
The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate r ( t ) or relaxation time τ ( t ) = 1 / r ( t ) : P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( β > 1 ) to the stretched exponential one ( β < 1 ). For SM-2 dependence, linear changes of τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior P t = P 0 e x p b ' t / T C - t , whereT C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.
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Affiliation(s)
- Agata Angelika Sojecka
- Department of Marketing, University of Economics in Katowice, ul. 1 Maja 50, 40-257, Katowice, Poland.
| | - Aleksandra Drozd-Rzoska
- Institute of High Pressure Physics Polish Academy of Sciences, ul. Sokołowska 29/37, 01-142, Warsaw, Poland.
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Lancelotti RF, Zanotto ED, Sen S. Kinetics of physical aging of a silicate glass following temperature up- and down-jumps. J Chem Phys 2024; 160:034504. [PMID: 38235796 DOI: 10.1063/5.0185538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 12/22/2023] [Indexed: 01/19/2024] Open
Abstract
In this article, we investigate the structural relaxation of lithium silicate glass during isothermal physical aging by monitoring the temporal evolution of its refractive index and enthalpy following relatively large (10-40 °C) up- and down-jumps in temperature. The Kohlrausch-Williams-Watts function aptly describes the up- and down-jump data when analyzed separately. For temperature down-jumps, the glass exhibits a typical stretched exponential kinetic behavior with the non-exponentiality parameter β < 1, whereas up-jumps show a compressed exponential behavior (β > 1). We analyzed these datasets using the non-exponential and non-linear Tool-Narayanaswamy-Moynihan (TNM) model, aiming to provide a comprehensive description of the primary or α-relaxation of the glass. This model described both up- and down-jump datasets using a single value of β ≤ 1. However, the standard TNM model exhibited a progressively reduced capacity to describe the data for larger temperature jumps, which is likely a manifestation of the temperature dependence of the non-exponentiality or non-linearity of the relaxation process. We hypothesize that the compressed exponential relaxation kinetics observed for temperature up-jumps stems from a nucleation-growth-percolation-based evolution on the dynamically mobile regions within the structure, leading to a self-acceleration of the dynamics. On the other hand, temperature down-jumps result in self-retardation, as the slow-relaxing denser regions percolate in the structure to give rise to a stretched exponential behavior.
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Affiliation(s)
- Ricardo F Lancelotti
- Federal University of São Carlos, Graduate Program in Materials Science and Engineering, São Carlos, São Paulo 13565-905, Brazil
- Department of Materials Science and Engineering, University of California at Davis, Davis, California 95616, USA
| | - Edgar D Zanotto
- Federal University of São Carlos, Graduate Program in Materials Science and Engineering, São Carlos, São Paulo 13565-905, Brazil
| | - Sabyasachi Sen
- Department of Materials Science and Engineering, University of California at Davis, Davis, California 95616, USA
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Zhang X, Lou H, Ruta B, Chushkin Y, Zontone F, Li S, Xu D, Liang T, Zeng Z, Mao HK, Zeng Q. Pressure-induced nonmonotonic cross-over of steady relaxation dynamics in a metallic glass. Proc Natl Acad Sci U S A 2023; 120:e2302281120. [PMID: 37276419 PMCID: PMC10268294 DOI: 10.1073/pnas.2302281120] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2023] [Accepted: 05/14/2023] [Indexed: 06/07/2023] Open
Abstract
Relaxation dynamics, as a key to understand glass formation and glassy properties, remains an elusive and challenging issue in condensed matter physics. In this work, in situ high-pressure synchrotron high-energy X-ray photon correlation spectroscopy has been developed to probe the atomic-scale relaxation dynamics of a cerium-based metallic glass during compression. Although the sample density continuously increases, the collective atomic motion initially slows down as generally expected and then counterintuitively accelerates with further compression (density increase), showing an unusual nonmonotonic pressure-induced steady relaxation dynamics cross-over at ~3 GPa. Furthermore, by combining in situ high-pressure synchrotron X-ray diffraction, the relaxation dynamics anomaly is evidenced to closely correlate with the dramatic changes in local atomic structures during compression, rather than monotonically scaling with either sample density or overall stress level. These findings could provide insight into relaxation dynamics and their relationship with local atomic structures of glasses.
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Affiliation(s)
- Xin Zhang
- Center for High Pressure Science and Technology Advanced Research, Shanghai201203, China
| | - Hongbo Lou
- Center for High Pressure Science and Technology Advanced Research, Shanghai201203, China
| | - Beatrice Ruta
- Université Lyon, Université Claude Bernard Lyon 1, Centre national de la recherche scientifique, Institut Lumière Matière, Campus LyonTech–La Doua, LyonF-69622, France
| | - Yuriy Chushkin
- European Synchrotron Radiation Facility-The European Synchrotron, GrenobleCS 40220, 38043, France
| | - Federico Zontone
- European Synchrotron Radiation Facility-The European Synchrotron, GrenobleCS 40220, 38043, France
| | - Shubin Li
- Université Lyon, Université Claude Bernard Lyon 1, Centre national de la recherche scientifique, Institut Lumière Matière, Campus LyonTech–La Doua, LyonF-69622, France
| | - Dazhe Xu
- Center for High Pressure Science and Technology Advanced Research, Shanghai201203, China
| | - Tao Liang
- Center for High Pressure Science and Technology Advanced Research, Shanghai201203, China
| | - Zhidan Zeng
- Center for High Pressure Science and Technology Advanced Research, Shanghai201203, China
| | - Ho-kwang Mao
- Center for High Pressure Science and Technology Advanced Research, Shanghai201203, China
- Shanghai Key Laboratory of Material Frontiers Research in Extreme Environments, Shanghai Advanced Research in Physical Sciences, Shanghai201203, China
| | - Qiaoshi Zeng
- Center for High Pressure Science and Technology Advanced Research, Shanghai201203, China
- Shanghai Key Laboratory of Material Frontiers Research in Extreme Environments, Shanghai Advanced Research in Physical Sciences, Shanghai201203, China
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Striker NN, Lokteva I, Dartsch M, Dallari F, Goy C, Westermeier F, Markmann V, Hövelmann SC, Grübel G, Lehmkühler F. Dynamics and Time Scales of Higher-Order Correlations in Supercooled Colloidal Systems. J Phys Chem Lett 2023; 14:4719-4725. [PMID: 37171882 DOI: 10.1021/acs.jpclett.3c00631] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
The dynamics and time scales of higher-order correlations are studied in supercooled colloidal systems. A combination of X-ray photon correlation spectroscopy (XPCS) and X-ray cross-correlation analysis (XCCA) shows the typical slowing of the dynamics of a hard sphere system when approaching the glass transition. The time scales of higher-order correlations are probed using a novel time correlation function gC, tracking the time evolution of cross-correlation function C. With an increasing volume fraction, the ratio of relaxation times of gC to the standard individual particle relaxation time obtained by XPCS increases from ∼0.4 to ∼0.9. While a value of ∼0.5 is expected for free diffusion, the increasing values suggest that the local orders within the sample are becoming more long-lived for larger volume fractions. Furthermore, the dynamics of local order is more heterogeneous than the individual particle dynamics. These results indicate that not only the presence but also the lifetime of locally favored structures increases close to the glass transition.
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Affiliation(s)
- Nele N Striker
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Irina Lokteva
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael Dartsch
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Francesco Dallari
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Claudia Goy
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Fabian Westermeier
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Verena Markmann
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Svenja C Hövelmann
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 19, 24098 Kiel, Germany
| | - Gerhard Grübel
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Felix Lehmkühler
- Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
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Liu W, Zhu Y, Li Y, Han J, Ngai T. Unveiling the structural relaxation of microgel suspensions at hydrophilic and hydrophobic interfaces. J Colloid Interface Sci 2023; 633:948-958. [PMID: 36509038 DOI: 10.1016/j.jcis.2022.11.150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Revised: 11/24/2022] [Accepted: 11/29/2022] [Indexed: 12/12/2022]
Abstract
HYPOTHESIS Poly(N-isopropylacrylamide) (PNIPAM) microgel particles show considerable hydrophilicity below the lower critical solution temperature (LCST) while they become hydrophobic above LCST. We hypothesize that interfacial wettability could tune particle-surface interaction and subsequent structural relaxation of microgel suspensions at interfaces during the volume phase transition. EXPERIMENTS The evanescent-wave scattering images of microgels at hydrophilic and hydrophobic interfaces are analyzed by a density-fluctuation autocorrelation function (δACF) over a wide range of particle volume fraction ϕ. The structural relaxation is characterized by the decay behavior of δACF. The scattering images in bulk are also processed as a comparison. FINDINGS A two-step relaxation decay is observed at both hydrophilic and hydrophobic interfaces. Relative to fast decay, the rate of structural relaxation in slow decay is reduced by a factor of ∼ 500 and ∼ 50 at hydrophilic and hydrophobic interfaces, respectively. The relaxation times obey divergent power-law dependences on intermediate regime of observing length scales at the two interfaces. Besides, the distribution of fluctuation for relaxation time at different local regions reveals that the structural relaxation is much more homogenous at hydrophilic interfaces than that at hydrophobic interfaces, especially at high ϕ.
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Affiliation(s)
- Wei Liu
- The Key Laboratory of Synthetic and Biological Colloids, Ministry of Education & School of Chemical and Material Engineering, Jiangnan University, Wuxi 214122, China
| | - Yuwei Zhu
- Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
| | - Yinan Li
- Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
| | - Jie Han
- School of Science and Technology, Hong Kong Metropolitan University, Homantin, Kowloon, Hong Kong, China.
| | - To Ngai
- The Key Laboratory of Synthetic and Biological Colloids, Ministry of Education & School of Chemical and Material Engineering, Jiangnan University, Wuxi 214122, China; Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China.
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7
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Chushkin Y, Gulotta A, Roosen-Runge F, Pal A, Stradner A, Schurtenberger P. Probing Cage Relaxation in Concentrated Protein Solutions by X-Ray Photon Correlation Spectroscopy. PHYSICAL REVIEW LETTERS 2022; 129:238001. [PMID: 36563210 DOI: 10.1103/physrevlett.129.238001] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 10/21/2022] [Indexed: 06/17/2023]
Abstract
Diffusion of proteins on length scales of their size is crucial for understanding the machinery of living cells. X-ray photon correlation spectroscopy (XPCS) is currently the only way to access long-time collective diffusion on these length scales, but radiation damage so far limits the use in biological systems. We apply a new approach to use XPCS to measure cage relaxation in crowded α-crystallin solutions. This allows us to correct for radiation effects, obtain missing information on long time diffusion, and support the fundamental analogy between protein and colloid dynamical arrest.
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Affiliation(s)
- Yuriy Chushkin
- ESRF, The European Synchrotron, 71 Avenue des Martyrs, CS40220, 38043 Grenoble Cedex 9, France
| | - Alessandro Gulotta
- Division of Physical Chemistry, Lund University, Naturvetarvägen 14, 22100 Lund, Sweden
| | - Felix Roosen-Runge
- Division of Physical Chemistry, Lund University, Naturvetarvägen 14, 22100 Lund, Sweden
- Department of Biomedical Science and Biofilms Research Center for Biointerfaces (BRCB), Faculty of Health and Society, Malmö University, Sweden
| | - Antara Pal
- Division of Physical Chemistry, Lund University, Naturvetarvägen 14, 22100 Lund, Sweden
| | - Anna Stradner
- Division of Physical Chemistry, Lund University, Naturvetarvägen 14, 22100 Lund, Sweden
- Lund Institute of advanced Neutron and X-ray Science LINXS, Lund University, Lund, Sweden
| | - Peter Schurtenberger
- Division of Physical Chemistry, Lund University, Naturvetarvägen 14, 22100 Lund, Sweden
- Lund Institute of advanced Neutron and X-ray Science LINXS, Lund University, Lund, Sweden
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Ginzburg VV. Modeling the Glass Transition of Free-Standing Polymer Thin Films Using the “SL-TS2” Mean-Field Approach. Macromolecules 2022. [DOI: 10.1021/acs.macromol.1c02370] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Valeriy V. Ginzburg
- Department of Chemical Engineering and Materials Science, Michigan State University, 428 S. Shaw Lane, Room 2100, East Lansing, Michigan 48824-1226, United States
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9
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Galashev AY. Study of the structure of a multicomponent salt melt using molecular dynamics modeling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:495103. [PMID: 34525454 DOI: 10.1088/1361-648x/ac26fa] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 09/15/2021] [Indexed: 06/13/2023]
Abstract
The composition of the electrolyte is critical in the electrodeposition of high-purity silicon. In this work, molecular dynamics modeling of the preparation of liquid salt melt KF-KCl-KI and a detailed study of its structure based on the method of statistical geometry have been performed. Partial radial distribution functions reflect the size of the ions under consideration and the averaged structure of the generated ionic subsystems. Halogen subsystems have domed angular distributions of nearest geometric neighbors, a wide range of face types of combined polyhedra, and fifth order rotational symmetry. The shape of the distribution of distances to the nearest neighbors of a given type depends on the amount of these ions in the melt. Small-scale thermal fluctuations in the halogen subsystems are predominantly represented by small triangular faces in combined polyhedra. The electrodeposition of silicon was carried out in a homogeneous salt melt, in which each halogen ion had from one to three close contacts with halogen ions of any other type. The simulations performed provide a fundamental understanding of the structure of the electrolyte molten salts used to produce solar silicon.
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Affiliation(s)
- Alexander Y Galashev
- Institute of High-Temperature Electrochemistry, Ural Branch, Russian Academy of Sciences, Yekaterinburg 620990, Russia
- Ural Federal University named after the first President of Russia B.N. Yeltsin, Yekaterinburg 620002, Russia
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