1
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Ma XJ, Zhang R. Cooperative activated hopping dynamics in binary glass-forming liquids: effects of the size ratio, composition, and interparticle interactions. SOFT MATTER 2023. [PMID: 37317997 DOI: 10.1039/d3sm00312d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Slow dynamics in supercooled and glassy liquids is an important research topic in soft matter physics. Compared to the traditionally focused one-component systems, glassy dynamics in mixture systems adds in a rich set of new complexities, which are fundamentally interesting and also relevant for many technological applications. In this paper, we apply the recently developed self-consistent cooperative hopping theory (SCCHT) to systematically investigate the effects of the size ratio, composition and interparticle interactions on the cooperative activated hopping dynamics of matrix (in larger size) and penetrant (in smaller size) particles in varied binary sphere mixture model systems, with a specific focus on ultrahigh mixture packing fractions that mimic the deeply supercooled glass transition conditions for molecular/polymeric mixture materials. Analysis shows that in these high activation barrier cases, the long-range elastic distortion associated with a matrix particle hopping over its cage confinement always generates an elastic barrier of a nonnegligible magnitude, although the ratio between the elastic barrier and local barrier contribution is sensitively dependent on all three mixture-specific system factors considered in this work. SCCHT predicts two general scenarios of penetrant-matrix cooperative activated hopping dynamics: matrix/penetrant co-hopping (regime 1) or the penetrant mean barrier hopping time shorter than that of the matrix (regime 2). Increasing the penetrant-to-matrix size ratio or the penetrant-matrix cross-attraction strength is found to universally enlarge the composition window of regime 1. Diverse dynamical properties characterising different aspects of the cooperative activated hopping process, including the penetrant and matrix transient localization lengths, penetrant and matrix hopping jump distances, different types of local and elastic activated barriers, and matrix long-time diffusivity, relaxation time and dynamic fragility are quantitatively studied against a wide range of variations over the three system factors. Of particular interest is the universal "anti-plasticization" phenomenon achievable for sufficiently strong cross-attractive interactions. The prospects this work opens for the exploration of a wide variety of polymer-based mixture materials are briefly discussed at the end.
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Affiliation(s)
- Xiao-Juan Ma
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China.
- Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou 510640, China
| | - Rui Zhang
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China.
- Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou 510640, China
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2
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Singh A, Singh Y. Structure ordering and glass transition in size-asymmetric ternary mixtures of hard spheres: Variation from fragile to strong glasses. Phys Rev E 2023; 107:014119. [PMID: 36797956 DOI: 10.1103/physreve.107.014119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 12/21/2022] [Indexed: 01/15/2023]
Abstract
We investigate the structure and activated dynamics of a binary mixture of colloidal particles dispersed in a solvent of much smaller-sized particles. The solvent degrees of freedom are traced out from the grand partition function of the colloid-solvent mixture which reduces the system from ternary to effective binary mixture of colloidal particles. In the effective binary mixture colloidal particles interact via effective potential that consists of bare potential plus the solvent-induced interaction. Expressions for the effective potentials and pair correlation functions are derived. We used the result of pair correlation functions to determine the number of particles in a cooperatively reorganizing cluster (CRC) in which localized particles form "long-lived" nonchemical bonds with the central particle. For an event of relaxation to take place these bonds have to reorganize irreversibly, the energy involved in the processes is the effective activation energy of relaxation. Results are reported for hard sphere colloidal particles dispersed in a solvent of hard sphere particles. Our results show that the concentration of solvent can be used as a control parameter to fine-tune the microscopic structural ordering and the size of CRC that governs the glassy dynamics. We show that a small variation in the concentration of solvent creates a bigger change in the kinetic fragility which highlights a wide variation in behavior, ranging from fragile to strong glasses. We conclude that the CRC which is determined from the static pair correlation function and the fluctuations embedded in the system is probably the sole player in the physics of glass transition.
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Affiliation(s)
- Ankit Singh
- Department of Physics, Banaras Hindu University, Varanasi 221 005, India
| | - Yashwant Singh
- Department of Physics, Banaras Hindu University, Varanasi 221 005, India
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3
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Luo C, Robinson JF, Pihlajamaa I, Debets VE, Royall CP, Janssen LMC. Many-Body Correlations Are Non-negligible in Both Fragile and Strong Glassformers. PHYSICAL REVIEW LETTERS 2022; 129:145501. [PMID: 36240416 DOI: 10.1103/physrevlett.129.145501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2022] [Revised: 06/29/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
It is widely believed that the emergence of slow glassy dynamics is encoded in a material's microstructure. First-principles theory [mode-coupling theory (MCT)] is able to predict the dramatic slowdown of the dynamics from only static two-point correlations as input, yet it cannot capture all of the observed dynamical behavior. Here we go beyond two-point spatial correlation functions by extending MCT systematically to include higher-order static and dynamic correlations. We demonstrate that only adding the static triplet direct correlations already qualitatively changes the predicted glass-transition diagram of binary hard spheres and silica. Moreover, we find a nontrivial competition between static triplet correlations that work to stabilize the glass state and dynamic higher-order correlations that destabilize it for both materials. We conclude that the conventionally neglected static triplet direct correlations as well as higher-order dynamic correlations are, in fact, non-negligible in both fragile and strong glassformers.
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Affiliation(s)
- Chengjie Luo
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - Joshua F Robinson
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Ilian Pihlajamaa
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - Vincent E Debets
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - C Patrick Royall
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
- School of Chemistry, Cantock's Close, University of Bristol, Bristol BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, University of Bristol, Bristol BS8 1FD, United Kingdom
| | - Liesbeth M C Janssen
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
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4
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Mallamace F, Mensitieri G, Salzano de Luna M, Lanzafame P, Papanikolaou G, Mallamace D. The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems. Int J Mol Sci 2022; 23:5316. [PMID: 35628124 PMCID: PMC9141735 DOI: 10.3390/ijms23105316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Revised: 05/03/2022] [Accepted: 05/04/2022] [Indexed: 12/04/2022] Open
Abstract
In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.
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Affiliation(s)
- Francesco Mallamace
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy
| | - Giuseppe Mensitieri
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, 80125 Naples, Italy; (G.M.); (M.S.d.L.)
| | - Martina Salzano de Luna
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, 80125 Naples, Italy; (G.M.); (M.S.d.L.)
| | - Paola Lanzafame
- Departments of ChiBioFarAm and MIFT—Section of Industrial Chemistry, University of Messina, CASPE-INSTM, V.le F. Stagno d’Alcontres 31, 98166 Messina, Italy; (P.L.); (G.P.)
| | - Georgia Papanikolaou
- Departments of ChiBioFarAm and MIFT—Section of Industrial Chemistry, University of Messina, CASPE-INSTM, V.le F. Stagno d’Alcontres 31, 98166 Messina, Italy; (P.L.); (G.P.)
| | - Domenico Mallamace
- Departments of ChiBioFarAm—Section of Industrial Chemistry, University of Messina, CASPE-INSTM, V.le F. Stagno d’Alcontres 31, 98166 Messina, Italy;
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Ciarella S, Luo C, Debets VE, Janssen LMC. Multi-component generalized mode-coupling theory: predicting dynamics from structure in glassy mixtures. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:91. [PMID: 34231080 PMCID: PMC8260512 DOI: 10.1140/epje/s10189-021-00095-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 06/21/2021] [Indexed: 06/13/2023]
Abstract
The emergence of glassy dynamics and the glass transition in dense disordered systems is still not fully understood theoretically. Mode-coupling theory (MCT) has shown to be effective in describing some of the non-trivial features of glass formation, but it cannot explain the full glassy phenomenology due to the strong approximations on which it is based. Generalized mode-coupling theory (GMCT) is a hierarchical extension of the theory, which is able to outclass MCT by carefully describing the dynamics of higher-order correlations in its generalized framework. Unfortunately, the theory has so far only been developed for single-component systems and as a result works poorly for highly polydisperse materials. In this paper, we solve this problem by developing GMCT for multi-component systems. We use it to predict the glassy dynamics of the binary Kob-Andersen Lennard-Jones mixture, as well as its purely repulsive Weeks-Chandler-Andersen analogue. Our results show that each additional level of the GMCT hierarchy gradually improves the predictive power of GMCT beyond its previous limit. This implies that our theory is able to harvest more information from the static correlations, thus being able to better understand the role of attraction in supercooled liquids from a first-principles perspective.
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Affiliation(s)
- Simone Ciarella
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Chengjie Luo
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Vincent E. Debets
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Liesbeth M. C. Janssen
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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6
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Marín-Aguilar S, Smallenburg F, Sciortino F, Foffi G. Monodisperse patchy particle glass former. J Chem Phys 2021; 154:174501. [PMID: 34241071 DOI: 10.1063/5.0036963] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Glass formers are characterized by their ability to avoid crystallization. As monodisperse systems tend to rapidly crystallize, the most common glass formers in simulations are systems composed of mixtures of particles with different sizes. Here, we make use of the ability of patchy particles to change their local structure to propose them as monodisperse glass formers. We explore monodisperse systems with two patch geometries: a 12-patch geometry that enhances the formation of icosahedral clusters and an 8-patch geometry that does not appear to strongly favor any particular local structure. We show that both geometries avoid crystallization and present glassy features at low temperatures. However, the 8-patch geometry better preserves the structure of a simple liquid at a wide range of temperatures and packing fractions, making it a good candidate for a monodisperse glass former.
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Affiliation(s)
- Susana Marín-Aguilar
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Francesco Sciortino
- Department of Physics, Sapienza University of Rome, P.le Aldo Moro 5, 00185 Rome, Italy
| | - Giuseppe Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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7
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Ruscher C, Ciarella S, Luo C, Janssen LMC, Farago J, Baschnagel J. Glassy dynamics of a binary Voronoi fluid: a mode-coupling analysis. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:064001. [PMID: 33105111 DOI: 10.1088/1361-648x/abc4cc] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The binary Voronoi mixture is a fluid model whose interactions are derived from the Voronoi-Laguerre tessellation of the configurations of the system. The resulting interactions are local and many-body. Here we perform molecular-dynamics (MD) simulations of an equimolar mixture that is weakly polydisperse and additive. For the first time we study the structural relaxation of this mixture in the supercooled-liquid regime. From the simulations we determine the time- and temperature-dependent coherent and incoherent scattering functions for a large range of wave vectors, as well as the mean-square displacements of both particle species. We perform a detailed analysis of the dynamics by comparing the MD results with the first-principles-based idealized mode-coupling theory (MCT). To this end, we employ two approaches: fits to the asymptotic predictions of the theory, and fit-parameter-free binary MCT calculations based on static-structure-factor input from the simulations. We find that many-body interactions of the Voronoi mixture do not lead to strong qualitative differences relative to similar analyses carried out for simple liquids with pair-wise interactions. For instance, the fits give an exponent parameter λ ≈ 0.746 comparable to typical values found for simple liquids, the wavevector dependence of the Kohlrausch relaxation time is in good qualitative agreement with literature results for polydisperse hard spheres, and the MCT calculations based on static input overestimate the critical temperature, albeit only by a factor of about 1.2. This overestimation appears to be weak relative to other well-studied supercooled-liquid models such as the binary Kob-Andersen Lennard-Jones mixture. Overall, the agreement between MCT and simulation suggests that it is possible to predict several microscopic dynamic properties with qualitative, and in some cases near-quantitative, accuracy based solely on static two-point structural correlations, even though the system itself is inherently governed by many-body interactions.
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Affiliation(s)
- C Ruscher
- Université de Strasbourg, Institut Charles Sadron, CNRS-UPR22, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
- Department of Physics and Astronomy and Quantum Matter Institute, University of British Columbia, Vancouver BC V6T 1Z1, Canada
| | - S Ciarella
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600MB Eindhoven, The Netherlands
| | - C Luo
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600MB Eindhoven, The Netherlands
| | - L M C Janssen
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600MB Eindhoven, The Netherlands
| | - J Farago
- Université de Strasbourg, Institut Charles Sadron, CNRS-UPR22, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - J Baschnagel
- Université de Strasbourg, Institut Charles Sadron, CNRS-UPR22, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
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8
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Voigtmann T, Siebenbürger M, Amann CP, Egelhaaf SU, Fritschi S, Krüger M, Laurati M, Mutch KJ, Samwer KH. Rheology of colloidal and metallic glass formers. Colloid Polym Sci 2020. [DOI: 10.1007/s00396-020-04654-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
AbstractColloidal hard-sphere suspensions are convenient experimental models to understand soft matter, and also by analogy the structural-relaxation behavior of atomic or small-molecular fluids. We discuss this analogy for the flow and deformation behavior close to the glass transition. Based on a mapping of temperature to effective hard-sphere packing, the stress–strain curves of typical bulk metallic glass formers can be quantitatively compared with those of hard-sphere suspensions. Experiments on colloids give access to the microscopic structure under deformation on a single-particle level, providing insight into the yielding mechanisms that are likely also relevant for metallic glasses. We discuss the influence of higher-order angular signals in connection with non-affine particle rearrangements close to yielding. The results are qualitatively explained on the basis of the mode-coupling theory. We further illustrate the analogy of pre-strain dependence of the linear-elastic moduli using data on PS-PNiPAM suspensions.
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Zirdehi EM, Voigtmann T, Varnik F. Multiple character of non-monotonic size-dependence for relaxation dynamics in polymer-particle and binary mixtures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:275104. [PMID: 32287041 DOI: 10.1088/1361-648x/ab757c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Adding plasticizers is a well-known procedure to reduce the glass transition temperature in polymers. It has been recently shown that this effect shows a non-monotonic dependence on the size of additive molecules (2019 J. Chem. Phys. 150 024903). In this work, we demonstrate that, as the size of the additive molecules is changed at fixed concentration, multiple extrema emerge in the dependence of the system's relaxation time on the size ratio. The effect occurs on all relevant length scales including single monomer dynamics, decay of Rouse modes and relaxation of the chain's end-to-end vector. A qualitatively similar trend is found within mode-coupling theoretical results for a binary hard-sphere mixture. An interpretation of the effect in terms of local packing efficiency and coupling between the dynamics of minority and majority species is provided.
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Affiliation(s)
- Elias M Zirdehi
- Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany
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10
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Marín-Aguilar S, Wensink HH, Foffi G, Smallenburg F. Tetrahedrality Dictates Dynamics in Hard Sphere Mixtures. PHYSICAL REVIEW LETTERS 2020; 124:208005. [PMID: 32501099 DOI: 10.1103/physrevlett.124.208005] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2019] [Accepted: 05/01/2020] [Indexed: 06/11/2023]
Abstract
The link between local structure and dynamical slowdown in glassy fluids has been the focus of intense debate for the better part of a century. Nonetheless, a simple method to predict the dynamical behavior of a fluid purely from its local structural features is still missing. Here, we demonstrate that the diffusivity of perhaps the most fundamental family of glass formers-hard sphere mixtures-can be accurately predicted based on just the packing fraction and a simple order parameter measuring the tetrahedrality of the local structure. Essentially, we show that the number of tetrahedral clusters in a hard sphere mixture is directly linked to its global diffusivity. Moreover, the same order parameter is capable of locally pinpointing particles in the system with high and low mobility. We attribute the power of the local tetrahedrality for predicting local and global dynamics to the high stability of tetrahedral clusters, the most fundamental building and densest-packing building blocks for a disordered fluid.
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Affiliation(s)
- Susana Marín-Aguilar
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Henricus H Wensink
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Giuseppe Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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11
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Schrack L, Franosch T. Mode-coupling theory of the glass transition for colloidal liquids in slit geometry. PHILOSOPHICAL MAGAZINE (ABINGDON, ENGLAND) 2020; 100:1032-1057. [PMID: 32308566 PMCID: PMC7155839 DOI: 10.1080/14786435.2020.1722859] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 01/15/2020] [Indexed: 06/11/2023]
Abstract
We provide a detailed derivation of the mode-coupling equations for a colloidal liquid confined by two parallel smooth walls. We introduce irreducible memory kernels for the different relaxation channels thereby extending the projection operator technique to colloidal liquids in slit geometry. Investigating both the collective dynamics as well as the tagged-particle motion, we prove that the mode-coupling functional assumes the same form as in the Newtonian case corroborating the universality of the glass-transition singularity with respect to the microscopic dynamics.
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Affiliation(s)
- Lukas Schrack
- Institut für Theoretische Physik, Universität Innsbruck, Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Innsbruck, Austria
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12
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Elizondo-Aguilera LF, Voigtmann T. Glass-transition asymptotics in two theories of glassy dynamics: Self-consistent generalized Langevin equation and mode-coupling theory. Phys Rev E 2019; 100:042601. [PMID: 31770981 DOI: 10.1103/physreve.100.042601] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Indexed: 11/07/2022]
Abstract
We contrast the generic features of structural relaxation close to the idealized glass transition that are predicted by the self-consistent generalized Langevin equation theory (SCGLE) against those that are predicted by the mode-coupling theory of the glass transition (MCT). We present an asymptotic solution close to conditions of kinetic arrest that is valid for both theories, despite the different starting points that are adopted in deriving them. This in particular provides the same level of understanding of the asymptotic dynamics in the SCGLE as was previously done only for MCT. We discuss similarities and different predictions of the two theories for kinetic arrest in standard glass-forming models, as exemplified through the hard-sphere system. Qualitative differences are found for models where a decoupling of relaxation modes is predicted, such as the generalized Gaussian core model, or binary hard-sphere mixtures of particles with very disparate sizes. These differences, which arise in the distinct treatment of the memory kernels associated to self- and collective motion of particles, lead to distinct scenarios that are predicted by each theory for partially arrested states and in the vicinity of higher-order glass-transition singularities.
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Affiliation(s)
- L F Elizondo-Aguilera
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
| | - Th Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany.,Department of Physics, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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13
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Lázaro-Lázaro E, Perera-Burgos JA, Laermann P, Sentjabrskaja T, Pérez-Ángel G, Laurati M, Egelhaaf SU, Medina-Noyola M, Voigtmann T, Castañeda-Priego R, Elizondo-Aguilera LF. Glassy dynamics in asymmetric binary mixtures of hard spheres. Phys Rev E 2019; 99:042603. [PMID: 31108620 DOI: 10.1103/physreve.99.042603] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2018] [Indexed: 06/09/2023]
Abstract
We perform a systematic and detailed study of the glass transition in highly asymmetric binary mixtures of colloidal hard spheres, combining differential dynamic microscopy experiments, event-driven molecular dynamics simulations, and theoretical calculations, exploring the whole state diagram and determining the self-dynamics and collective dynamics of both species. Two distinct glassy states involving different dynamical arrest transitions are consistently described, namely, a double glass with the simultaneous arrest of the self-dynamics and collective dynamics of both species, and a single glass of large particles in which the self-dynamics of the small species remains ergodic. In the single-glass scenario, spatial modulations in the collective dynamics of both species occur due to the structure of the large spheres, a feature not observed in the double-glass domain. The theoretical results, obtained within the self-consistent generalized Langevin equation formalism, are in agreement with both simulations and experimental data, thus providing a stringent validation of this theoretical framework in the description of dynamical arrest in highly asymmetric mixtures. Our findings are summarized in a state diagram that classifies the various amorphous states of highly asymmetric mixtures by their dynamical arrest mechanisms.
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Affiliation(s)
- Edilio Lázaro-Lázaro
- Instituto de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, San Luis Potosí, Mexico
| | - Jorge Adrián Perera-Burgos
- CONACYT-Unidad de Ciencias del Agua, Centro de Investigación Científica de Yucatán A.C. (CICY), Calle 8, No. 39, Mz. 29, S.M. 64, 77524 Cancún, Quintana Roo, Mexico
| | - Patrick Laermann
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Tatjana Sentjabrskaja
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Gabriel Pérez-Ángel
- Departamento de Física Aplicada, Cinvestav, Unidad Mérida, Apartado Postal 73 Cordemex, 97310 Mérida, Yucatán, Mexico
| | - Marco Laurati
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Magdaleno Medina-Noyola
- Instituto de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, San Luis Potosí, Mexico
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Thomas Voigtmann
- Department of Physics, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft-und Raumfahrt (DLR), Linder Höhe 51170, Köln, Germany
| | - Ramón Castañeda-Priego
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
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Sentjabrskaja T, Jacob AR, Egelhaaf SU, Petekidis G, Voigtmann T, Laurati M. Binary colloidal glasses: linear viscoelasticity and its link to the microscopic structure and dynamics. SOFT MATTER 2019; 15:2232-2244. [PMID: 30794267 DOI: 10.1039/c8sm01349g] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We study the relation between the microscopic structure and dynamics and the macroscopic rheological response of glass-forming colloidal suspensions, namely binary colloidal hard-sphere mixtures with large size asymmetry (1 : 5) that span a large range of mixture compositions close to the glass transition. The dynamical shear moduli are measured by oscillatory rheology and the structure and dynamics on the single-particle level by confocal microscopy. The data are compared with Brownian Dynamics simulations and predictions from mode-coupling theory based on the Percus-Yevick approximation. Experiments, simulations and theory consistently observe a strong decrease of the intermediate-frequency mechanical moduli combined with faster dynamics at intermediate mixing ratios and hence a non-monotonic dependence of these parameters but a localization of the large particles which decreases monotonically as the fraction of small particles is increased. We find that the Generalized-Stokes Einstein relation applied to the mean square displacements of the two components leads to a reasonable estimate of the shear moduli of the mixtures and hence links the rheological response to the particle dynamics which in turn reflects the microscopic structure.
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15
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Mandal S, Franosch T, Voigtmann T. Glassy relaxation slows down by increasing mobility. SOFT MATTER 2018; 14:9153-9158. [PMID: 30421769 DOI: 10.1039/c8sm01581c] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We find a striking trend reversal in the relaxation dynamics of mixtures with strong dynamical asymmetry. Simulations by both Brownian and Newtonian dynamics reveal that in mixtures of fast and slow hard spheres, above a critical density, the dynamics becomes slower upon increasing the mobility of the fast particles. Below that density, the same increase in mobility speeds up the dynamics. The critical density itself can be identified with the glass transition of the mode-coupling theory that does not depend on the dynamical asymmetry. The asymptotic dynamics close to the critical density is universal, but strong pre-asymptotic effects prevail in particular when the dynamical asymmetry also involves size asymmetry. Our observations reconcile earlier findings, where a strong dependence on kinetic parameters was found for the glassy dynamics, with the paradigm that the glass transition is determined by the properties of configuration space alone.
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Affiliation(s)
- Suvendu Mandal
- Institut für Theoretische Physik, Universität Innsbruck, Austria
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16
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Thorneywork AL, Schnyder SK, Aarts DGAL, Horbach J, Roth R, Dullens RPA. Structure factors in a two-dimensional binary colloidal hard sphere system. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1492745] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Alice L. Thorneywork
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - Simon K. Schnyder
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, Japan
| | - Dirk G. A. L. Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
| | - Jürgen Horbach
- Institut für Theoretische Physik II, Heinrich-Heine Universität Düsseldorf, Düsseldorf, Germany
| | - Roland Roth
- Institut für Theoretische Physik, Universität Tübingen, Tübingen, Germany
| | - Roel P. A. Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
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17
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Wang L, Mei B, Song J, Lu Y, An L. Structural relaxation and glass transition behavior of binary hard-ellipse mixtures. Sci China Chem 2018. [DOI: 10.1007/s11426-017-9151-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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18
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The glass formation of a repulsive system with also a short range attractive potential: A re-interpretation of the free volume theory. POLYMER 2017. [DOI: 10.1016/j.polymer.2017.02.066] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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19
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Thorneywork AL, Aarts DGAL, Horbach J, Dullens RPA. Self-diffusion in two-dimensional binary colloidal hard-sphere fluids. Phys Rev E 2017; 95:012614. [PMID: 28208506 DOI: 10.1103/physreve.95.012614] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2016] [Indexed: 06/06/2023]
Abstract
We present a systematic experimental study of the dynamic behavior of monodisperse and bidisperse two-dimensional colloidal hard-sphere fluids. We consider the diffusive behavior of the two types of particles for systems with a variety of compositions and total area fractions. In particular, we measure the short- and long-time diffusion coefficients for both species independently. We find that the short-time self-diffusion coefficients show an approximately linear dependence on the area fraction and that the long-time self-diffusion coefficients are well described by an expression dependent upon only the area fraction and contact value of the radial distribution function. Finally, we consider the effect of composition change and find some variation in the long-time self-diffusion coefficients, which we ascribe to the complex packing effects exhibited by binary systems.
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Affiliation(s)
- Alice L Thorneywork
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Jürgen Horbach
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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20
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Varnik F, Franosch T. Non-monotonic effect of confinement on the glass transition. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:133001. [PMID: 26940539 DOI: 10.1088/0953-8984/28/13/133001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The relaxation dynamics of glass forming liquids and their structure are influenced in the vicinity of confining walls. This effect has mostly been observed to be a monotonic function of the slit width. Recently, a qualitatively new behaviour has been uncovered by Mittal and coworkers, who reported that the single particle dynamics in a hard-sphere fluid confined in a planar slit varies in a non-monotonic way as the slit width is decreased from five to roughly two particle diametres (Mittal et al 2008 Phys. Rev. Lett. 100 145901). In view of the great potential of this effect for applications in those fields of science and industry, where liquids occur under strong confinement (e.g. nano-technology), the number of researchers studying various aspects and consequences of this non-monotonic behaviour has been rapidly growing. This review aims at providing an overview of the research activity in this newly emerging field. We first briefly discuss how competing mechanisms such as packing effects and short-range attraction may lead to a non-monotonic glass transition scenario in the bulk. We then analyse confinement effects on the dynamics of fluids using a thermodynamic route which relates the single particle dynamics to the excess entropy. Moreover, relating the diffusive dynamics to the Widom's insertion probability, the oscillations of the local dynamics with density at moderate densities are fairly well described. At high densities belonging to the supercooled regime, however, this approach breaks down signaling the onset of strongly collective effects. Indeed, confinement introduces a new length scale which in the limit of high densities and small pore sizes competes with the short-range local order of the fluid. This gives rise to a non-monotonic dependence of the packing structure on confinement, with a corresponding effect on the dynamics of structural relaxation. This non-monotonic effect occurs also in the case of a cone-plate type channel, where the degree of confinement varies with distance from the apex. This is a very promising issue for future research with the possibility of uncovering the existence of alternating glassy and liquid-like domains.
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Affiliation(s)
- Fathollah Varnik
- Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Universitätsstraße 150, D-44780 Bochum, Germany
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21
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Robinson JF, Godfrey MJ, Moore MA. Glasslike behavior of a hard-disk fluid confined to a narrow channel. Phys Rev E 2016; 93:032101. [PMID: 27078286 DOI: 10.1103/physreve.93.032101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2015] [Indexed: 06/05/2023]
Abstract
Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks that sets in at characteristic packing fraction ϕ(d). Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event-driven molecular dynamics simulations and the time-dependent dynamical length scale has been extracted from them. The dynamical length scale increases with time and, on the equilibration time scale, it is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above ϕ(d). The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer-matrix approach.
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Affiliation(s)
- J F Robinson
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - M J Godfrey
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - M A Moore
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
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22
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Priya M, Bidhoodi N, Das SP. Qualitatively different collective and single-particle dynamics in a supercooled liquid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062308. [PMID: 26764693 DOI: 10.1103/physreve.92.062308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2014] [Indexed: 06/05/2023]
Abstract
The equations of fluctuating nonlinear hydrodynamics for a two component mixture are obtained with a proper choice of slow variables which correspond to the conservation laws in the system. Using these nonlinear equations we construct the basic equations of the mode coupling theory (MCT) and consequent ergodic-nonergodic (ENE) transition in a binary mixture. The model is also analyzed in the one component limit of the mixture to study the dynamics of a tagged particle in the sea of identical particles. According to the existing MCT, dynamics of the single-particle correlation is slaved to that of the collective density fluctuations and, hence, both correlations freeze simultaneously at the ENE transition. We show here from a nonperturbative approach that at the ENE transition, characterized by the freezing of the long time limit of the dynamic correlation of collective density fluctuations to a nonzero value, the tagged-particle correlation still decays to zero. Our result implies that the point at which simulation or experimental data of the self-diffusion constant extrapolate to zero would not correspond to the ENE transition of simple MCT.
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Affiliation(s)
- Madhu Priya
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Neeta Bidhoodi
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Shankar P Das
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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23
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Bidhoodi N, Das SP. Slow dynamics of a tagged particle in a supercooled liquid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062309. [PMID: 26764694 DOI: 10.1103/physreve.92.062309] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Indexed: 06/05/2023]
Abstract
The ergodicity-nonergodicity (ENE) transition of the self-consistent mode-coupling theory (MCT) is marked by the point at which the time correlation of collective density fluctuations is not zero in the long-time limit. The nonergodic state, reaching beyond the ENE transition of simple MCT, is characterized by a finite shear modulus. The MCT, formulated in the current set of papers, predicts that the single-particle density correlation, unlike the collective density correlation, decays to zero at long times on either side of the ENE transition. The self-diffusion coefficient remains finite. This differs from the existing MCT results in which both collective and single-particle correlations are simultaniously frozen at the ENE transition. We discuss in this paper mechanisms by which a sharp fall in self-diffusion coefficient may occur within the present model. This overdamping or the so-called adiabatic approximation for the supercooled state does not maintain microscopic momentum conservation. Within this approximation, the self-diffusion constant approaches zero at the ENE transition point. This approximate result, which is similar to the prediction of the existing MCT models, further illustrates the process of cage formation with increase of density. At a qualitative level, our analysis shows that the self-diffusion process depends on the structure as well as short-time transport properties of the supercooled liquid. We solve the integral equations for the nonergodicity parameters to analyze the full implications of the adiabatic approximation.
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Affiliation(s)
- Neeta Bidhoodi
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Shankar P Das
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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24
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Agrawal A, Yu HY, Srivastava S, Choudhury S, Narayanan S, Archer LA. Dynamics and yielding of binary self-suspended nanoparticle fluids. SOFT MATTER 2015; 11:5224-5234. [PMID: 26053059 DOI: 10.1039/c5sm00639b] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Yielding and flow transitions in bi-disperse suspensions of particles are studied using a model system comprised of self-suspended spherical nanoparticles. An important feature of the materials is that the nanoparticles are uniformly dispersed in the absence of a solvent. Addition of larger particles to a suspension of smaller ones is found to soften the suspensions, and in the limit of large size disparities, completely fluidizes the material. We show that these behaviors coincide with a speeding-up of de-correlation dynamics of all particles in the suspensions and are accompanied by a reduction in the energy dissipated at the yielding transition. We discuss our findings in terms of ligand-mediated jamming and un-jamming of hairy particle suspensions.
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Affiliation(s)
- Akanksha Agrawal
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA.
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25
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Xu WS, Duan X, Sun ZY, An LJ. Glass formation in a mixture of hard disks and hard ellipses. J Chem Phys 2015; 142:224506. [DOI: 10.1063/1.4922379] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wen-Sheng Xu
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Xiaozheng Duan
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Li-Jia An
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
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26
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Hendricks J, Capellmann R, Schofield AB, Egelhaaf SU, Laurati M. Different mechanisms for dynamical arrest in largely asymmetric binary mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032308. [PMID: 25871111 DOI: 10.1103/physreve.91.032308] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2014] [Indexed: 06/04/2023]
Abstract
Using confocal microscopy we investigate binary colloidal mixtures with large size asymmetry, in particular the formation of dynamically arrested states of the large spheres. The volume fraction of the system is kept constant, and as the concentration of small spheres is increased we observe a series of transitions of the large spheres to different arrested states: an attractive glass, a gel, and an asymmetric glass. These states are distinguished by the degree of dynamical arrest and the amount of structural and dynamical heterogeneity. The transitions between two different arrested states occur through melting and the formation of a fluid state. While a space-spanning network of bonded particles is found in both arrested and fluid states, only arrested states are characterized by the presence of a space-spanning network of dynamically arrested particles.
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Affiliation(s)
- J Hendricks
- Condensed Matter Physics Laboratory, Heinrich-Heine University, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - R Capellmann
- Condensed Matter Physics Laboratory, Heinrich-Heine University, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - A B Schofield
- SUPA, School of Physics & Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - S U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich-Heine University, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - M Laurati
- Condensed Matter Physics Laboratory, Heinrich-Heine University, Universitätsstr. 1, 40225 Düsseldorf, Germany
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27
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Ndong Mintsa E, Germain P, Amokrane S. Bond lifetime and diffusion coefficient in colloids with short-range interactions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:21. [PMID: 25813606 DOI: 10.1140/epje/i2015-15021-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2014] [Revised: 02/20/2015] [Accepted: 02/23/2015] [Indexed: 06/04/2023]
Abstract
We use molecular dynamics simulations to study the influence of short-range structures in the interaction potential between hard-sphere-like colloidal particles. Starting from model potentials and effective potentials in binary mixtures computed from the Ornstein-Zernike equations, we investigate the influence of the range and strength of a possible tail beyond the usual core repulsion or the presence of repulsive barriers. The diffusion coefficient and mean "bond" lifetimes are used as indicators of the effect of this structure on the dynamics. The existence of correlations between the variations of these quantities with the physical parameters is discussed to assess the interpretation of dynamics slowing down in terms of long-lived bonds. We also discuss the question of a universal behaviour determined by the second virial coefficient B ((2)) and the interplay of attraction and repulsion. While the diffusion coefficient follows the B ((2)) law for purely attractive tails, this is no longer true in the presence of repulsive barriers. Furthermore, the bond lifetime shows a dependence on the physical parameters that differs from that of the diffusion coefficient. This raises the question of the precise role of bonds on the dynamics slowing down in colloidal gels.
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Affiliation(s)
- E Ndong Mintsa
- Laboratoire "Physique de Liquides et Milieux Complexes", Faculté des Sciences et Technologie, Université Paris-Est, Créteil, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France
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28
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Xu WS, Sun ZY, An LJ. Relaxation dynamics in a binary hard-ellipse liquid. SOFT MATTER 2015; 11:627-634. [PMID: 25466776 DOI: 10.1039/c4sm02290d] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Structural relaxation in binary hard spherical particles has been shown recently to exhibit a wealth of remarkable features when size disparity or mixture composition is varied. In this paper, we test whether or not similar dynamical phenomena occur in glassy systems composed of binary hard ellipses. We demonstrate via event-driven molecular dynamics simulation that a binary hard-ellipse mixture with an aspect ratio of two and moderate size disparity displays characteristic glassy dynamics upon increasing density in both the translational and the rotational degrees of freedom. The rotational glass transition density is found to be close to the translational one for the binary mixtures investigated. More importantly, we assess the influence of size disparity and mixture composition on the relaxation dynamics. We find that an increase of size disparity leads, both translationally and rotationally, to a speed up of the long-time dynamics in the supercooled regime so that both the translational and the rotational glass transition shift to higher densities. By increasing the number concentration of the small particles, the time evolution of both translational and rotational relaxation dynamics at high densities displays two qualitatively different scenarios, i.e., both the initial and the final part of the structural relaxation slow down for small size disparity, while the short-time dynamics still slows down but the final decay speeds up in the binary mixture with large size disparity. These findings are reminiscent of those observed in binary hard spherical particles. Therefore, our results suggest a universal mechanism for the influence of size disparity and mixture composition on the structural relaxation in both isotropic and anisotropic particle systems.
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Affiliation(s)
- Wen-Sheng Xu
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
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29
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Sentjabrskaja T, Hermes M, Poon WCK, Estrada CD, Castañeda-Priego R, Egelhaaf SU, Laurati M. Transient dynamics during stress overshoots in binary colloidal glasses. SOFT MATTER 2014; 10:6546-6555. [PMID: 24988071 DOI: 10.1039/c4sm00577e] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate, using simultaneous rheology and confocal microscopy, the time-dependent stress response and transient single-particle dynamics following a step change in shear rate in binary colloidal glasses with large dynamical asymmetry and different mixing ratios. The transition from solid-like response to flow is characterised by a stress overshoot, whose magnitude is linked to transient superdiffusive dynamics as well as cage compression effects. These and the yield strain at which the overshoot occurs vary with the mixing ratio, and hence the prevailing caging mechanism. The yielding and stress storage are dominated by dynamics on different time and length scales, the short-time in-cage dynamics and the long-time structural relaxation respectively. These time scales and their relation to the characteristic time associated with the applied shear, namely the inverse shear rate, result in two different and distinct regimes of the shear rate dependencies of the yield strain and the magnitude of the stress overshoot.
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Affiliation(s)
- T Sentjabrskaja
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany.
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30
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Mandal S, Lang S, Gross M, Oettel M, Raabe D, Franosch T, Varnik F. Multiple reentrant glass transitions in confined hard-sphere glasses. Nat Commun 2014; 5:4435. [DOI: 10.1038/ncomms5435] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2014] [Accepted: 06/18/2014] [Indexed: 11/09/2022] Open
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31
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Das G, Gnan N, Sciortino F, Zaccarelli E. Unveiling the complex glassy dynamics of square shoulder systems: Simulations and theory. J Chem Phys 2013; 138:134501. [DOI: 10.1063/1.4795837] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Jadrich R, Schweizer KS. Theory of kinetic arrest, elasticity, and yielding in dense binary mixtures of rods and spheres. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061503. [PMID: 23367954 DOI: 10.1103/physreve.86.061503] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2012] [Indexed: 06/01/2023]
Abstract
We extend the quiescent and stressed versions of naïve mode coupling theory to treat the dynamical arrest, shear modulus, and absolute yielding of particle mixtures where one or more species is a nonrotating nonspherical object. The theory is applied in detail to dense isotropic "chemically matched" mixtures of variable aspect ratio rods and spheres that interact via repulsive and short range attractive site-site pair potentials. A remarkably rich ideal kinetic arrest behavior is predicted with up to eight "dynamical phases" emerging: an ergodic fluid, partially localized states where the spheres remain fluid but the rods can be a gel, repulsive glass or attractive glass, doubly localized glasses and gels, a porous rod gel plus sphere glass, and a narrow window where a type of rod glass and gel localization coexist. Dynamical complexity increases with rod length and the introduction of attractive forces between all species which both enhance gel network formation. Multiple dynamic reentrant features and triple points are predicted, and each dynamic phase has unique particle localization characteristics and mechanical properties. Orders of magnitude variation of the linear shear modulus and absolute yield stress are found as rod length, mixture composition and the detailed nature of interparticle attractions are varied. The interplay of total (high) mixture packing fraction and composition at fixed temperature is also briefly studied. The present work provides a foundation to study more complex rod-sphere mixtures of both biological and synthetic interest that include physical features such as interaction site size asymmetry, rod-sphere specific attractions, and/or Coulomb repulsion.
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Affiliation(s)
- Ryan Jadrich
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
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33
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Xu WS, Sun ZY, An LJ. Structure, compressibility factor, and dynamics of highly size-asymmetric binary hard-disk liquids. J Chem Phys 2012; 137:104509. [DOI: 10.1063/1.4751546] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Tchangnwa Nya F, Ayadim A, Germain P, Amokrane S. Non-ergodicity transition and multiple glasses in binary mixtures: on the accuracy of the input static structure in the mode coupling theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:325106-11. [PMID: 22766654 DOI: 10.1088/0953-8984/24/32/325106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We examine the question of the accuracy of the static correlation functions used as input in the mode coupling theory (MCT) of non-ergodic states in binary mixtures. We first consider hard-sphere mixtures and compute the static pair structure from the Ornstein-Zernike equations with the Percus-Yevick closure and more accurate ones that use bridge functions deduced from Rosenfeld's fundamental measures functional. The corresponding MCT predictions for the non-ergodicity lines and the transitions between multiple glassy states are determined from the long-time limit of the density autocorrelation functions. We find that while the non-ergodicity transition line is not very sensitive to the input static structure, up to diameter ratios D(2)/D(1) = 10, quantitative differences exist for the transitions between different glasses. The discrepancies with the more accurate closures become even qualitative for sufficiently asymmetric mixtures. They are correlated with the incorrect behavior of the PY structure at high size asymmetry. From the example of ultra-soft potential it is argued that this issue is of general relevance beyond the hard-sphere model.
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Affiliation(s)
- F Tchangnwa Nya
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France
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35
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Harrer CJ, Puertas AM, Voigtmann T, Fuchs M. Probability Densities of a Forced Probe Particle in Glass: Results from Mode Coupling Theory and Simulations of Active Microrheology. Z PHYS CHEM 2012. [DOI: 10.1524/zpch.2012.0275] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Abstract
We investigate the displacements of a probe particle inside a glass, when a strong external force is applied to the probe (active nonlinear microrheology). Calculations within mode coupling theory are presented for glasses of hard spheres and compared to Langevin and Brownian dynamics simulations. Under not too strong forces where the probe remains trapped, the probe density distribution becomes anisotropic. It is shifted towards the direction of the force, develops an enhanced tail in that direction (signalled by a positive skewness), and exhibits different variances along and perpendicular to the force direction. A simple model of an harmonically trapped probe rationalizes the low force limit, with strong strain softening setting in at forces of the order of a few thermal energies per particle radius.
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Affiliation(s)
| | - A. M. Puertas
- Universidad de Almería, Departamento de Física Aplicada, Almería, Spanien
| | - Th. Voigtmann
- Deutsches Zentrum für Luft- und Raumfahrt (DLR), Zukunftskolleg der Universität Konstanz, Cologne, Deutschland
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36
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Hunter GL, Weeks ER. The physics of the colloidal glass transition. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:066501. [PMID: 22790649 DOI: 10.1088/0034-4885/75/6/066501] [Citation(s) in RCA: 329] [Impact Index Per Article: 27.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.
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Affiliation(s)
- Gary L Hunter
- Department of Physics, Emory University, Math and Science Center 400 Dowman Dr., N201 Atlanta, GA 30322, USA
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37
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Domschke M, Marsilius M, Blochowicz T, Voigtmann T. Glassy relaxation and excess wing in mode-coupling theory: the dynamic susceptibility of propylene carbonate above and below T(c). PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:031506. [PMID: 22060378 DOI: 10.1103/physreve.84.031506] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2011] [Indexed: 05/31/2023]
Abstract
We explore the possibility of describing experimental susceptibility spectra of the glass former propylene carbonate with a two-component schematic model of mode-coupling theory (MCT) from above the melting point down to temperatures far below the critical temperature of MCT. By introducing a phenomenological time-dependent hopping rate, the spectra are reproduced in the full frequency and temperature range available. Literature data of dielectric susceptibilities and depolarized Brillouin light-scattering spectra are combined with our measurements of photon correlation spectroscopy to cover up to 18 decades in frequency of spectra for two different dynamical variables. A consistent description of all data sets is obtained by adjusting only a few physically motivated parameters. In particular the excess wing or slow β-relaxation commonly observed in the susceptibility spectra can consistently be modeled as originating from a coupling of the individual experimental probe correlator to the collective density fluctuations.
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Affiliation(s)
- Markus Domschke
- Institut für Festkörperphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
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38
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Larsen RJ, Zukoski CF. Effect of particle size on the glass transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051504. [PMID: 21728537 DOI: 10.1103/physreve.83.051504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2011] [Indexed: 05/31/2023]
Abstract
The glass transition temperature of a broad class of molecules is shown to depend on molecular size. This dependency results from the size dependence of the pair potential. A generalized equation of state is used to estimate how the volume fraction at the glass transition depends on the size of the molecule, for rigid molecule glass-formers. The model shows that at a given pressure and temperature there is a size-induced glass transition: For molecules larger than a critical size, the volume fraction required to support the effective pressure due to particle attractions is above that which characterizes the glassy state. This observation establishes the boundary between nanoparticles, which exist in liquid form only as dispersions in low molecular weight solvents and large molecules which form liquids that have viscosities below those characterized by the glassy state.
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Affiliation(s)
- Ryan J Larsen
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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39
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Larsen RJ, Zukoski CF. Molecular Mixture as an Effective Single-Component System. J Phys Chem B 2011; 115:3981-91. [DOI: 10.1021/jp1120838] [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)
- Ryan J. Larsen
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, 114 Roger Adams Laboratory, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Charles F. Zukoski
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, 114 Roger Adams Laboratory, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
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40
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Weysser F, Hajnal D. Tests of mode-coupling theory in two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:041503. [PMID: 21599165 DOI: 10.1103/physreve.83.041503] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2011] [Indexed: 05/30/2023]
Abstract
We analyze the glassy dynamics of binary mixtures of hard disks in two dimensions. Predictions of the mode-coupling theory (MCT) are tested with extensive Brownian dynamics simulations. Measuring the collective particle density correlation functions in the vicinity of the glass transition, we verify four predicted mixing effects. For instance, for large size disparities, adding a small amount of small particles at a fixed packing fraction leads to a speedup in the long-time dynamics, while for small size disparities it leads to a slowing-down. Qualitative features of the nonergodicity parameters and the β relaxation, which both depend in a nontrivial way on the mixing ratio, are found in the simulated correlators. Studying one system in detail, we are able to determine its ideal MCT glass transition point as φ(c)=0.7948 and test MCT predictions quantitatively.
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Affiliation(s)
- Fabian Weysser
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany.
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41
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Reinhardt J, Weysser F, Fuchs M. Comment on "Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition". PHYSICAL REVIEW LETTERS 2010; 105:199604-199605. [PMID: 21231206 DOI: 10.1103/physrevlett.105.199604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2009] [Revised: 07/23/2010] [Indexed: 05/30/2023]
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42
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Lang S, Boţan V, Oettel M, Hajnal D, Franosch T, Schilling R. Glass transition in confined geometry. PHYSICAL REVIEW LETTERS 2010; 105:125701. [PMID: 20867658 DOI: 10.1103/physrevlett.105.125701] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2010] [Indexed: 05/13/2023]
Abstract
Extending mode-coupling theory, we elaborate a microscopic theory for the glass transition of liquids confined between two parallel flat hard walls. The theory contains the standard mode-coupling theory equations in bulk and in two dimensions as limiting cases and requires as input solely the equilibrium density profile and the structure factors of the fluid in confinement. We evaluate the phase diagram as a function of the distance of the plates for the case of a hard sphere fluid and obtain an oscillatory behavior of the glass transition line as a result of the structural changes related to layering.
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Affiliation(s)
- Simon Lang
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, 55099 Mainz, Germany
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43
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Brader JM. Nonlinear rheology of colloidal dispersions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:363101. [PMID: 21386516 DOI: 10.1088/0953-8984/22/36/363101] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.
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Affiliation(s)
- J M Brader
- Fachbereich Physik, Universit¨at Konstanz, D-78457 Konstanz, Germany
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44
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Zhang R, Schweizer KS. Dynamic free energies, cage escape trajectories, and glassy relaxation in dense fluids of uniaxial hard particles. J Chem Phys 2010; 133:104902. [DOI: 10.1063/1.3483601] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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Roldán-Vargas S, de Vicente J, Barnadas-Rodríguez R, Quesada-Pérez M, Estelrich J, Callejas-Fernández J. Suspensions of repulsive colloidal particles near the glass transition: Time and frequency domain descriptions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:021406. [PMID: 20866808 DOI: 10.1103/physreve.82.021406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2009] [Revised: 03/19/2010] [Indexed: 05/29/2023]
Abstract
We study the relaxation of both spontaneous and shear-induced fluctuations in suspensions of charged-stabilized colloidal particles near the glass transition by dynamic light scattering and rheology. Both observations are here understood in terms of a common structural relaxation process under a hard-sphere mode-coupling formalism. For ergodic systems, we show that the descriptions of the relaxation dynamics in time and frequency domains are governed by a common set of dynamic parameters. It is further shown that the microscopic ergodicity break-up induces the emergence of the macroscopic glass elasticity.
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46
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Kramb RC, Zhang R, Schweizer KS, Zukoski CF. Glass formation and shear elasticity in dense suspensions of repulsive anisotropic particles. PHYSICAL REVIEW LETTERS 2010; 105:055702. [PMID: 20867934 DOI: 10.1103/physrevlett.105.055702] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2010] [Indexed: 05/29/2023]
Abstract
Kinetic vitrification, shear elasticity, and the approach to jamming are investigated for repulsive nonspherical colloids and contrasted with their spherical analog. Particle anisotropy dramatically increases the volume fraction for kinetic arrest. The shear modulus of all systems increases roughly exponentially with volume fraction, and a universal collapse is achieved based on either the dynamic crossover or random close packing volume fraction as the key nondimensionalizing quantity. Quantitative comparisons with recent microscopic theories are performed and good agreement demonstrated.
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Affiliation(s)
- R C Kramb
- Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana, Illinois 61801, USA
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47
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Weysser F, Puertas AM, Fuchs M, Voigtmann T. Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:011504. [PMID: 20866622 DOI: 10.1103/physreve.82.011504] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2010] [Revised: 06/26/2010] [Indexed: 05/29/2023]
Abstract
We analyze the slow glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory (MCT) of the glass transition. Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multicomponent calculation, but qualitative disagreement at small q when the system is treated as effectively monodisperse. The origin of the different small-q behavior is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantitative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behavior are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.
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Affiliation(s)
- F Weysser
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
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48
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Nonlinear Rheological Properties of Dense Colloidal Dispersions Close to a Glass Transition Under Steady Shear. ADVANCES IN POLYMER SCIENCE 2009. [DOI: 10.1007/12_2009_30] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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49
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Hajnal D, Brader JM, Schilling R. Effect of mixing and spatial dimension on the glass transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:021503. [PMID: 19792129 DOI: 10.1103/physreve.80.021503] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2009] [Indexed: 05/28/2023]
Abstract
We study the influence of composition changes on the glass transition of binary hard disk and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard disks strongly resembles the random close packing diagram. Compared to three dimensions from previous studies, the extension of the glass regime due to mixing is much more pronounced in two dimensions where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size ratio from unity.
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Affiliation(s)
- David Hajnal
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany.
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50
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Biazzo I, Caltagirone F, Parisi G, Zamponi F. Theory of amorphous packings of binary mixtures of hard spheres. PHYSICAL REVIEW LETTERS 2009; 102:195701. [PMID: 19518974 DOI: 10.1103/physrevlett.102.195701] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2009] [Revised: 03/29/2009] [Indexed: 05/27/2023]
Abstract
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical protocols can be identified with the infinite pressure limit of long-lived metastable glassy states. We test this assumption against numerical and experimental data and show that the theory correctly reproduces the variation with mixture composition of structural observables, such as the total packing fraction and the partial coordination numbers.
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Affiliation(s)
- Indaco Biazzo
- Dipartimento di Fisica, Università di Roma, La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
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