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Robin C, Robertson CG. Glass-like Signatures in the Dynamic Rheology of Particle-Filled Polymers. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Clément Robin
- Hutchinson Research and Innovation Center, Châlette-sur-Loing 45120, Centre-Val de Loire, France
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2
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Sánchez-Rey B, Prados A. Linear response in the uniformly heated granular gas. Phys Rev E 2021; 104:024903. [PMID: 34525635 DOI: 10.1103/physreve.104.024903] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 07/29/2021] [Indexed: 11/07/2022]
Abstract
We analyze the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the nonequilibrium steady state reached by the system. Here, we investigate two specific situations. First, we look into the "direct" relaxation of the system after a single (small) jump of the driving intensity. This study is carried out by two different methods. Not only do we linearize the evolution equations around the steady state, but we also derive generalized out-of-equilibrium fluctuation-dissipation relations for the relevant response functions. Second, we investigate the behavior of the system in a more complex experiment, specifically a Kovacs-like protocol with two jumps in the driving. The emergence of an anomalous Kovacs response is explained in terms of the properties of the direct relaxation function: it is the second mode changing sign at the critical value of the inelasticity that demarcates anomalous from normal behavior. The analytical results are compared with numerical simulations of the kinetic equation, and a good agreement is found.
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Affiliation(s)
- Bernardo Sánchez-Rey
- Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, E-41011 Sevilla, Spain
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
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Lira-Escobedo J, Mendoza-Méndez P, Medina-Noyola M, McKenna GB, Ramírez-González PE. On a fundamental description of the Kovacs' kinetic signatures in glass-forming systems. J Chem Phys 2021; 155:014503. [PMID: 34241391 DOI: 10.1063/5.0054520] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The time-evolution equation for the time-dependent static structure factor of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory was used to investigate the kinetics of glass-forming systems under isochoric conditions. The kinetics are studied within the framework of the fictive temperature (TF) of the glassy structure. We solve for the kinetics of TF(t) and the time-dependent structure factor and find that they are different but closely related by a function that depends only on temperature. Furthermore, we are able to solve for the evolution of TF(t) in a set of temperature-jump histories referred to as the Kovacs' signatures. We demonstrate that the NE-SCGLE theory reproduces all the Kovacs' signatures, namely, intrinsic isotherm, asymmetry of approach, and memory effect. In addition, we extend the theory into largely unexplored, deep glassy state, regions that are below the notionally "ideal" glass temperature.
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Affiliation(s)
- J Lira-Escobedo
- Instituto de Física "Manuel Sandoval Vallarta", Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - P Mendoza-Méndez
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apdo. Postal 1152, 72570 Puebla, Mexico
| | - M Medina-Noyola
- Instituto de Física "Manuel Sandoval Vallarta", Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - G B McKenna
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, USA
| | - P E Ramírez-González
- CONACYT-Instituto de Física "Manuel Sandoval Vallarta", Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
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Bennin T, Xing E, Ricci J, Ediger MD. Rejuvenation Versus Overaging: The Effect of Cyclic Loading/Unloading on the Segmental Dynamics of Poly(methyl methacrylate) Glasses. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01489] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Trevor Bennin
- Department of Chemistry, University of Wisconsin—Madison, Madison, Wisconsin 53706, United States
| | - Enran Xing
- Department of Chemistry, University of Wisconsin—Madison, Madison, Wisconsin 53706, United States
| | - Josh Ricci
- Department of Chemistry, University of Wisconsin—Madison, Madison, Wisconsin 53706, United States
| | - M. D. Ediger
- Department of Chemistry, University of Wisconsin—Madison, Madison, Wisconsin 53706, United States
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Song L, Xu W, Huo J, Li F, Wang LM, Ediger MD, Wang JQ. Activation Entropy as a Key Factor Controlling the Memory Effect in Glasses. PHYSICAL REVIEW LETTERS 2020; 125:135501. [PMID: 33034495 DOI: 10.1103/physrevlett.125.135501] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 09/02/2020] [Indexed: 06/11/2023]
Abstract
As opposed to the common monotonic relaxation process of glasses, the Kovacs memory effect describes an isothermal annealing experiment, in which the enthalpy and volume of a preannealed glass first increases before finally decreasing toward equilibrium. This interesting behavior has been observed for many materials and is generally explained in terms of heterogeneous dynamics. In this Letter, the memory effect in a model Au-based metallic glass is studied using a high-precision high-rate calorimeter. The activation entropy (S^{*}) during isothermal annealing is determined according to the absolute reaction rate theory. We observe that the memory effect appears only when the second-annealing process has a large S^{*}. These results indicate that a large value of S^{*} is a key requirement for observation of the memory effect and this may provide a useful perspective for understanding the memory effect in both thermal and athermal systems.
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Affiliation(s)
- Lijian Song
- CAS Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Wei Xu
- CAS Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Juntao Huo
- CAS Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Fushan Li
- School of Materials Science and Engineering, Zhengzhou University, Zhengzhou 450001, China
| | - Li-Min Wang
- State Key Lab of Metastable Materials Science and Technology, and College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China
| | - M D Ediger
- Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Jun-Qiang Wang
- CAS Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
- School of Materials Science and Engineering, Zhengzhou University, Zhengzhou 450001, China
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Wang JG, Li Q, Peng X, McKenna GB, Zia RN. "Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics. SOFT MATTER 2020; 16:7370-7389. [PMID: 32696798 DOI: 10.1039/d0sm00999g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.
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Affiliation(s)
- J Galen Wang
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
| | - Qi Li
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Xiaoguang Peng
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Gregory B McKenna
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Roseanna N Zia
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
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Lulli M, Lee CS, Deng HY, Yip CT, Lam CH. Spatial Heterogeneities in Structural Temperature Cause Kovacs' Expansion Gap Paradox in Aging of Glasses. PHYSICAL REVIEW LETTERS 2020; 124:095501. [PMID: 32202859 DOI: 10.1103/physrevlett.124.095501] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Accepted: 02/05/2020] [Indexed: 06/10/2023]
Abstract
Volume and enthalpy relaxation of glasses after a sudden temperature change has been extensively studied since Kovacs' seminal work. One observes an asymmetric approach to equilibrium upon cooling versus heating and, more counterintuitively, the expansion gap paradox, i.e., a dependence on the initial temperature of the effective relaxation time even close to equilibrium when heating. Here, we show that a distinguishable-particle lattice model can capture both the asymmetry and the paradox. We quantitatively characterize the energetic states of the particle configurations using a physical realization of the fictive temperature called the structural temperature, which, in the heating case, displays a strong spatial heterogeneity. The system relaxes by nucleation and expansion of warmer mobile domains having attained the final temperature, against cooler immobile domains maintained at the initial temperature. A small population of these cooler regions persists close to equilibrium, thus explaining the paradox.
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Affiliation(s)
- Matteo Lulli
- Department of Applied Physics, Hong Kong Polytechnic University, Hong Kong, China
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
| | - Chun-Shing Lee
- Department of Applied Physics, Hong Kong Polytechnic University, Hong Kong, China
| | - Hai-Yao Deng
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
- School of Physics and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, United Kingdom
| | - Cho-Tung Yip
- School of Science, Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, Guangdong 518055, China
| | - Chi-Hang Lam
- Department of Applied Physics, Hong Kong Polytechnic University, Hong Kong, China
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Li Q, Peng X, McKenna GB. Physical aging and compressed exponential behaviors in a model soft colloidal system. SOFT MATTER 2019; 15:2336-2347. [PMID: 30758036 DOI: 10.1039/c8sm02042f] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Diffusing wave spectroscopy (DWS)-based micro-rheology has been used in different optical geometries (backscattering and transmission) as well as different sample thicknesses in order to probe system dynamics at different length scales [D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer. J. Phys., 1990, 51(18), 2101-2127]. Previous study from this lab [Q. Li, X. Peng, G. B. McKenna. Soft Matter, 2017, 13(7), 1396-1404] indicates the DWS-based micro-rheology observes the system non-equilibrium behaviors differently from macro-rheology. The object of the present work was to further explore the non-equilibrium dynamics and to address the range of utility of DWS as a micro-rheological method. A thermo-sensitive core-shell colloidal system was investigated both during aging and subsequent to aging into a metastable equilibrium state using temperature-jump induced volume fraction-jump experiments. We find that in the non-equilibrium state, significant differences in the measured dynamics are observed for the different geometries and length scales. Compressed exponential relaxations for the autocorrelation function g2(t) were observed for large length scales. However, upon converting the g2(t) data to the mean square displacement (MSD), such differences with length scale diminished and the long-time MSD behavior was consistent with diffusive behavior. These observations in the non-equilibrium behaviors for different length scales leads to questioning of some interpretations in the current field of light scattering-based micro-rheology and provides a possibility to interrogate the aging mechanisms in colloidal glasses from a broader perspective than normally considered in measurements of g2(t) using DWS-based micro-rheology.
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Affiliation(s)
- Qi Li
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA.
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