1
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Nakane T, Sasaki T. Thickness Dependence of Segmental Dynamics in Free-Standing Thin Films Predicted by a Dynamically Correlated Network Model. J Phys Chem B 2023. [PMID: 37201178 DOI: 10.1021/acs.jpcb.3c00841] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The anomalous dynamics and glass transition behaviors of supercooled liquids under nanoconfinement, such as ultrathin polymer films, have attracted much attention in recent decades. However, a complete elucidation of this mechanism has not yet been achieved. For the dynamics of bulk materials without confinement, we previously proposed a dynamically correlated network (DCN) model, which was found to agree well with the experimental data. The model assumes that segments with thermal fluctuations are dynamically correlated to their neighbors to form string-like clusters, which eventually grow into networks as temperature decreases. In this study, we applied the DCN model to nanoconfined free-standing films by using a simple cubic lattice sandwiched between two free surface layers consisting of virtual "uncorrelated" segments. The average size of DCNs at lower temperatures decreased with decreasing thickness because of confinement. This trend was associated with a decrease in the percolation temperature at which the size of DCN diverges. It was also revealed that the fractal dimension of the generated DCNs exhibits a peak with respect to temperature. The segmental relaxation time for free-standing polystyrene films was evaluated, and the predicted thickness dependence of the glass transition temperature qualitatively agreed with the experimental data. The results suggest that the concept of DCN is compatible with the dynamics of free-standing thin films.
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Affiliation(s)
- Tatsuki Nakane
- Department of Materials Science and Engineering, University of Fukui, Fukui 9108507, Japan
| | - Takashi Sasaki
- Department of Materials Science and Engineering, University of Fukui, Fukui 9108507, Japan
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2
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Laudicina CCL, Luo C, Miyazaki K, Janssen LMC. Dynamical susceptibilities near ideal glass transitions. Phys Rev E 2022; 106:064136. [PMID: 36671198 DOI: 10.1103/physreve.106.064136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Accepted: 11/28/2022] [Indexed: 06/17/2023]
Abstract
Building on the recently derived inhomogeneous mode-coupling theory, we extend the generalized mode-coupling theory of supercooled liquids to inhomogeneous environments. This provides a first-principles-based, systematic, and rigorous way of deriving high-point dynamical susceptibilities from variations of the many-body dynamic structure factors with respect to their conjugate field. This framework allows for a fully microscopic possibility to probe for collective relaxation mechanisms in supercooled liquids near the mode-coupling glass transition. The behavior of these dynamical susceptibilities is then studied in the context of simplified self-consistent relaxation models.
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Affiliation(s)
- Corentin C L Laudicina
- Soft Matter & Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | - Chengjie Luo
- Soft Matter & Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | | | - Liesbeth M C Janssen
- Soft Matter & Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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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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Szamel G. An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids. J Chem Phys 2022; 156:191102. [PMID: 35597637 DOI: 10.1063/5.0091385] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose an alternative theory for the relaxation of density fluctuations in glass-forming fluids. We derive an equation of motion for the density correlation function that is local in time and is similar in spirit to the equation of motion for the average non-uniform density profile derived within the dynamic density functional theory. We identify the Franz-Parisi free energy functional as the non-equilibrium free energy for the evolution of the density correlation function. An appearance of a local minimum of this functional leads to a dynamic arrest. Thus, the ergodicity breaking transition predicted by our theory coincides with the dynamic transition of the static approach based on the same non-equilibrium free energy functional.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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5
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Debets VE, Luo C, Ciarella S, Janssen LMC. Generalized mode-coupling theory for mixtures of Brownian particles. Phys Rev E 2021; 104:065302. [PMID: 35030832 DOI: 10.1103/physreve.104.065302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Accepted: 11/29/2021] [Indexed: 11/07/2022]
Abstract
Generalized mode-coupling theory (GMCT) has recently emerged as a promising first-principles theory to study the poorly understood dynamics of glass-forming materials. Formulated as a hierarchical extension of standard mode-coupling theory (MCT), it is able to systematically improve its predictions by including the exact dynamics of higher-order correlation functions into its hierarchy. However, in contrast to Newtonian dynamics, a fully generalized version of the theory based on Brownian dynamics is still lacking. To close this gap, we provide a detailed derivation of GMCT for colloidal mixtures obeying a many-body Smoluchowski equation. We demonstrate that a hierarchy of coupled equations can again be established and show that these, consistent with standard MCT, are identical to the ones obtained from Newtonian GMCT when taking the overdamped limit. Consequently, the nontrivial similarity between Brownian and Newtonian MCT is maintained for our multicomponent GMCT. As a proof of principle, we also solve the generalized mode-coupling equations for the binary Kob-Andersen Lennard-Jones mixture undergoing Brownian dynamics and confirm the improved predictive power of the theory upon using more levels of the GMCT hierarchy of equations.
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Affiliation(s)
- Vincent E Debets
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.,Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Chengjie Luo
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.,Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Simone Ciarella
- 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, F-75005 Paris, France
| | - Liesbeth M C Janssen
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.,Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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6
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Luo C, Janssen LMC. Glassy dynamics of sticky hard spheres beyond the mode-coupling regime. SOFT MATTER 2021; 17:7645-7661. [PMID: 34373889 PMCID: PMC8900603 DOI: 10.1039/d1sm00712b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Accepted: 08/04/2021] [Indexed: 06/13/2023]
Abstract
Sticky hard spheres, i.e., hard particles decorated with a short-ranged attractive interaction potential, constitute a relatively simple model with highly non-trivial glassy dynamics. The mode-coupling theory of the glass transition (MCT) offers a qualitative account of the complex reentrant dynamics of sticky hard spheres, but the predicted glass transition point is notoriously underestimated. Here we apply an improved first-principles-based theory, referred to as generalized mode-coupling theory (GMCT), to sticky hard spheres. This theoretical framework seeks to go beyond MCT by hierarchically expanding the dynamics in higher-order density correlation functions. We predict the phase diagrams from the first few levels of the GMCT hierarchy and the dynamics-related critical exponents, all of which are much closer to the empirical observations than MCT. Notably, the prominent reentrant glassy dynamics, the glass-glass transition, and the higher-order bifurcation singularity classes (A3 and A4) of sticky hard spheres are found to be preserved within GMCT at arbitrary order. Moreover, we demonstrate that when the hierarchical order of GMCT increases, the effect of the short-ranged attractive interactions becomes more evident in the dynamics. This implies that GMCT is more sensitive to subtle microstructural differences than MCT, and that the framework provides a promising first-principles approach to systematically go beyond the MCT regime.
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Affiliation(s)
- Chengjie Luo
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands.
| | - Liesbeth M C Janssen
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands.
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7
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Luo C, Debets VE, Janssen LMC. Tagged-particle motion of Percus-Yevick hard spheres from first principles. J Chem Phys 2021; 155:034502. [PMID: 34293894 DOI: 10.1063/5.0056257] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a first-principles-based generalized mode-coupling theory (GMCT) for the tagged-particle motion of glassy systems. This theory establishes a hierarchy of coupled integro-differential equations for self-multi-point density correlation functions, which can formally be extended up to infinite order. We use our GMCT framework to calculate the self-nonergodicity parameters and the self-intermediate scattering function for the Percus-Yevick hard-sphere system based on the first few levels of the GMCT hierarchy. We also test the scaling laws in the α- and β-relaxation regimes near the glass-transition singularity. Furthermore, we study the mean-square displacement and the Stokes-Einstein relation in the supercooled regime. We find that qualitatively our GMCT results share many similarities with the well-established predictions from standard mode-coupling theory, but the quantitative results change, and typically improve, by increasing the GMCT closure level. However, we also demonstrate on general theoretical grounds that the current GMCT framework is unable to account for violation of the Stokes-Einstein relation, underlining the need for further improvements in the first-principles description of glassy dynamics.
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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, 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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8
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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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9
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Lucco Castello F, Tolias P. Theoretical Estimate of the Glass Transition Line of Yukawa One-Component Plasmas. Molecules 2021; 26:molecules26030669. [PMID: 33525346 PMCID: PMC7865523 DOI: 10.3390/molecules26030669] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Revised: 01/07/2021] [Accepted: 01/25/2021] [Indexed: 12/04/2022] Open
Abstract
The mode coupling theory of supercooled liquids is combined with advanced closures to the integral equation theory of liquids in order to estimate the glass transition line of Yukawa one-component plasmas from the unscreened Coulomb limit up to the strong screening regime. The present predictions constitute a major improvement over the current literature predictions. The calculations confirm the validity of an existing analytical parameterization of the glass transition line. It is verified that the glass transition line is an approximate isomorphic curve and the value of the corresponding reduced excess entropy is estimated. Capitalizing on the isomorphic nature of the glass transition line, two structural vitrification indicators are identified that allow a rough estimate of the glass transition point only through simple curve metrics of the static properties of supercooled liquids. The vitrification indicators are demonstrated to be quasi-universal by an investigation of hard sphere and inverse power law supercooled liquids. The straightforward extension of the present results to bi-Yukawa systems is also discussed.
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10
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Luo C, Janssen LMC. Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres. J Chem Phys 2020; 153:214507. [PMID: 33291925 DOI: 10.1063/5.0026969] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Mode-coupling theory (MCT) constitutes one of the few first-principles-based approaches to describe the physics of the glass transition, but the theory's inherent approximations compromise its accuracy in the activated glassy regime. Here, we show that microscopic generalized mode-coupling theory (GMCT), a recently proposed hierarchical framework to systematically improve upon MCT, provides a promising pathway toward a more accurate first-principles description of glassy dynamics. We present a comprehensive numerical analysis for Percus-Yevick hard spheres by performing explicitly wavenumber- and time-dependent GMCT calculations up to sixth order. Specifically, we calculate the location of the critical point, the associated non-ergodicity parameters, and the time-dependent dynamics of the density correlators at both absolute and reduced packing fractions, and we test several universal scaling relations in the α- and β-relaxation regimes. It is found that higher-order GMCT can successfully remedy some of MCT's pathologies, including an underestimation of the critical glass transition density and an overestimation of the hard-sphere fragility. Furthermore, we numerically demonstrate that the celebrated scaling laws of MCT are preserved in GMCT and that the predicted critical exponents manifestly improve as more levels are incorporated in the GMCT hierarchy. Although formally the GMCT equations should be solved up to infinite order to reach full convergence, our finite-order GMCT calculations unambiguously reveal a uniform convergence pattern for the dynamics. We thus argue that GMCT can provide a feasible and controlled means to bypass MCT's main uncontrolled approximation, offering hope for the future development of a quantitative first-principles theory of the glass transition.
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Affiliation(s)
- Chengjie Luo
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | - Liesbeth M C Janssen
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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11
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Luo C, Janssen LMC. Generalized mode-coupling theory of the glass transition. II. Analytical scaling laws. J Chem Phys 2020; 153:214506. [PMID: 33291926 DOI: 10.1063/5.0026979] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Generalized mode-coupling theory (GMCT) constitutes a systematically correctable, first-principles theory to study the dynamics of supercooled liquids and the glass transition. It is a hierarchical framework that, through the incorporation of increasingly many particle density correlations, can remedy some of the inherent limitations of the ideal mode-coupling theory (MCT). However, despite MCT's limitations, the ideal theory also enjoys several remarkable successes, notably including the analytical scaling laws for the α- and β-relaxation dynamics. Here, we mathematically derive similar scaling laws for arbitrary-order multi-point density correlation functions obtained from GMCT under arbitrary mean-field closure levels. More specifically, we analytically derive the asymptotic and preasymptotic solutions for the long-time limits of multi-point density correlators, the critical dynamics with two power-law decays, the factorization scaling laws in the β-relaxation regime, and the time-density superposition principle in the α-relaxation regime. The two characteristic power-law-divergent relaxation times for the two-step decay and the non-trivial relation between their exponents are also obtained. The validity ranges of the leading-order scaling laws are also provided by considering the leading preasymptotic corrections. Furthermore, we test these solutions for the Percus-Yevick hard-sphere system. We demonstrate that GMCT preserves all the celebrated scaling laws of MCT while quantitatively improving the exponents, rendering the theory a promising candidate for an ultimately quantitative first-principles theory of glassy dynamics.
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Affiliation(s)
- Chengjie Luo
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | - Liesbeth M C Janssen
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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12
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Ghosh A, Schweizer KS. Microscopic theory of the influence of strong attractive forces on the activated dynamics of dense glass and gel forming fluids. J Chem Phys 2019; 151:244502. [DOI: 10.1063/1.5129941] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Ashesh Ghosh
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana-Champaign, Illinois 61801, USA
- Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana-Champaign, Illinois 61801, USA
| | - Kenneth S. Schweizer
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana-Champaign, Illinois 61801, USA
- Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana-Champaign, Illinois 61801, USA
- Department of Material Science, University of Illinois at Urbana-Champaign, Urbana-Champaign, Illinois 61801, USA
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana-Champaign, Illinois 61801, USA
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13
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Mandal S, Schrack L, Löwen H, Sperl M, Franosch T. Persistent Anti-Correlations in Brownian Dynamics Simulations of Dense Colloidal Suspensions Revealed by Noise Suppression. PHYSICAL REVIEW LETTERS 2019; 123:168001. [PMID: 31702351 DOI: 10.1103/physrevlett.123.168001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Revised: 08/28/2019] [Indexed: 06/10/2023]
Abstract
Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals persistent anti-correlations manifested by a negative algebraic power-law tail t^{-5/2} at all densities. At small packing fractions the simulations fully agree with the analytic low-density prediction, yet the amplitude of the tail becomes dramatically suppressed as the packing fraction is increased. The mode-coupling theory of the glass transition provides a qualitative explanation for the strong variation in terms of the static compressibility as well as the slowing down of the structural relaxation.
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Affiliation(s)
- Suvendu Mandal
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Lukas Schrack
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Matthias Sperl
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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14
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Germain P, Amokrane S. Glass transition and reversible gelation in asymmetric binary mixtures: A study by mode coupling theory and molecular dynamics. Phys Rev E 2019; 100:042614. [PMID: 31770885 DOI: 10.1103/physreve.100.042614] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2019] [Indexed: 06/10/2023]
Abstract
The glass transition and the binodals of asymmetric binary mixtures are investigated from the effective fluid approach in the mode coupling theory and by molecular dynamics. Motivated by previous theoretical predictions, the hard-sphere mixture and the Asakura-Oosawa models are used to analyze experimental results from the literature, relative to polystyrene spheres mixed either with linear polymers or with dense microgel particles. In agreement with the experimental observations, the specificity of the depletant particles is shown to favor lower density gels. It further favors equilibrium gelation by reducing also the tendency of the system to phase separate. These results are confirmed by a phenomenological modification of the mode coupling theory in which the vertex functions are computed at an effective density lower than the actual one. A model effective potential in asymmetric mixtures of hard particles is used to further check this phenomenological modification against molecular dynamics simulation.
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Affiliation(s)
- Ph Germain
- 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
| | - S Amokrane
- 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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15
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Amokrane S, Germain P. α-relaxation, shear viscosity, and elastic moduli of hard-particle fluids from a mode-coupling theory with a retarded vertex. Phys Rev E 2019; 99:052120. [PMID: 31212463 DOI: 10.1103/physreve.99.052120] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 06/09/2023]
Abstract
The recently proposed modification of the mode-coupling theory (MCT) in which the static structure used in the vertex is computed at a lower density than the actual one is tested on several dynamics-related properties. The predictions from this modified version of MCT calibrated on the one-component hard-sphere fluid are found in very good agreement with simulation data for one-component and binary hard-sphere fluids. They are also relevant for the stress moduli for models with attractive tails beyond the hard core. The clear improvement observed on several properties should give a new impetus to the use of MCT as a quantitative tool.
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Affiliation(s)
- S Amokrane
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Av. du Général de Gaulle, 94010 Créteil Cedex, France
| | - Ph Germain
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Av. du Général de Gaulle, 94010 Créteil Cedex, France
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16
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Amokrane S, Tchangnwa Nya F, Ndjaka JM. Glass transition in hard-core fluids and beyond, using an effective static structure in the mode coupling theory. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:17. [PMID: 28210959 DOI: 10.1140/epje/i2017-11506-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2016] [Accepted: 01/26/2017] [Indexed: 06/06/2023]
Abstract
The dynamical arrest in classical fluids is studied using a simple modification of the mode coupling theory (MCT) aimed at correcting its overestimation of the tendency to glass formation while preserving its overall structure. As in previous attempts, the modification is based on the idea of tempering the static pair correlations used as input. It is implemented in this work by computing the static structure at a different state point than the one used to solve the MCT equation for the intermediate scattering function, using the pure hard-sphere glass for calibration. The location of the glass transition predicted from this modification is found to agree with simulations data for a variety of systems --pure fluids and mixtures with either purely repulsive interaction potentials or ones with attractive contributions. Besides improving the predictions in the long-time limit, and so reducing the non-ergodicity domain, the same modification works as well for the time-dependent correlators.
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Affiliation(s)
- S Amokrane
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Av. du Général de Gaulle, 94010, Créteil Cedex, France.
| | - F Tchangnwa Nya
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Av. du Général de Gaulle, 94010, Créteil Cedex, France
- Département de Physique, Faculté des Sciences, Université de Maroua, BP 814, Maroua, Cameroon
| | - J M Ndjaka
- Département de Physique, Faculté des Sciences, Université de Yaoundé, I. B.P. 812, Yaoundé, Cameroon
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Janssen LMC, Reichman DR. Microscopic Dynamics of Supercooled Liquids from First Principles. PHYSICAL REVIEW LETTERS 2015; 115:205701. [PMID: 26613452 DOI: 10.1103/physrevlett.115.205701] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2015] [Indexed: 06/05/2023]
Abstract
The transition from a liquid to a glass remains one of the most poorly understood phenomena in condensed matter physics, and still no fully microscopic theory exists that can describe the dynamics of supercooled liquids in a quantitative manner over all relevant time scales. Here, we present a theoretical framework that yields near-quantitative accuracy for the time-dependent correlation functions of a glass-forming system over a broad density range. Our approach requires only simple static structural information as input and is based entirely on first principles. Owing to its ab initio nature, the framework offers a unique platform to study the relation between structure and dynamics in glass-forming matter, and paves the way towards a systematically correctable and ultimately fully quantitative theory of microscopic glassy dynamics.
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Affiliation(s)
- Liesbeth M C Janssen
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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18
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Götze W, Schilling R. Glass transitions and scaling laws within an alternative mode-coupling theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042117. [PMID: 25974449 DOI: 10.1103/physreve.91.042117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2015] [Indexed: 06/04/2023]
Abstract
Idealized glass transitions are discussed within an alternative mode-coupling theory (TMCT) proposed by Tokuyama [Physica A 395, 31 (2014)]. This is done in order to identify common ground with and differences from the conventional mode-coupling theory (MCT). It is proven that both theories imply the same scaling laws for the transition dynamics, which are characterized by two power-law decay functions and two diverging power-law time scales. However, the values for the corresponding anomalous exponents calculated within both theories differ from each other. It is proven that the TMCT, contrary to the MCT, does not describe transitions with continuously vanishing arrested parts of the correlation functions. It is also demonstrated for a schematic model that the TMCT does not lead to the MCT scenarios either for transition-line crossings or for the appearance of higher-order glass-transition singularities.
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Affiliation(s)
- Wolfgang Götze
- Physik Department, Technische Universität München, James-Franck-Straße 1, D-85747 Garching, Germany
| | - Rolf Schilling
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 9, D-55099 Mainz, Germany
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Janssen LMC, Mayer P, Reichman DR. Relaxation patterns in supercooled liquids from generalized mode-coupling theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052306. [PMID: 25493795 DOI: 10.1103/physreve.90.052306] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Indexed: 06/04/2023]
Abstract
The mode-coupling theory of the glass transition treats the dynamics of supercooled liquids in terms of two-point density correlation functions. Here we consider a generalized, hierarchical formulation of schematic mode-coupling equations in which the full basis of multipoint density correlations is taken into account. By varying the parameters that control the effective contributions of higher-order correlations, we show that infinite hierarchies can give rise to both sharp and avoided glass transitions. Moreover, small changes in the form of the coefficients result in different scaling behaviors of the structural relaxation time, providing a means to tune the fragility in glass-forming materials. This demonstrates that the infinite-order construct of generalized mode-coupling theory constitutes a powerful and unifying framework for kinetic theories of the glass transition.
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Affiliation(s)
- Liesbeth M C Janssen
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Peter Mayer
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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20
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Ayadim A, Germain P, Amokrane S. Mode-coupling theory for the glass transition: test of the convolution approximation for short-range interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:061502. [PMID: 22304092 DOI: 10.1103/physreve.84.061502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2011] [Indexed: 05/31/2023]
Abstract
We reexamine the convolution approximation commonly used in the mode-coupling theory (MCT) of nonergodic states of classical fluids. This approximation concerns the static correlation functions used as input in the MCT treatment of the dynamics. Besides the hard-sphere model, we consider interaction potentials that present a short-range tail, either attractive or repulsive, beyond the hard core. By using accurate static correlation functions obtained from the fundamental measures functional for hard spheres, we show that the role of three-body direct correlations can be more significant than what is inferred from previous simple ansatzs for pure hard spheres. This may in particular impact the location of the glass transition line and the nonergodicity parameter.
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Affiliation(s)
- A Ayadim
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est, Créteil, 61 Avenue du Général de Gaulle, FR-94010 Créteil Cedex, France
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21
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Coslovich D. Locally preferred structures and many-body static correlations in viscous liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051505. [PMID: 21728538 DOI: 10.1103/physreve.83.051505] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2011] [Indexed: 05/31/2023]
Abstract
The influence of static correlations beyond the pair level on the dynamics of selected model glass formers is investigated. The pair structure, angular distribution functions, and statistics of Voronoi polyhedra of two well-known Lennard-Jones mixtures as well as of the corresponding Weeks-Chandler-Andersen variants, in which the attractive part of the potential is truncated, are compared. By means of the Voronoi construction, the atomic arrangements corresponding to the locally preferred structures of the models are identified. It is found that the growth of domains formed by interconnected locally preferred structures signals the onset of the slow-dynamics regime and allows the rationalization of the different dynamic behaviors of the models. At low temperature, the spatial extension of the structurally correlated domains, evaluated at fixed relaxation time, increases with the fragility of the models and is systematically reduced by truncating the attractions. In view of these results, proper inclusion of many-body static correlations in theories of the glass transition appears crucial for the description of the dynamics of fragile glass formers.
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Affiliation(s)
- Daniele Coslovich
- Laboratoire Charles Coulomb UMR 5221, Université Montpellier 2 and CNRS, Montpellier, France.
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Di Cola E, Moussaïd A, Sztucki M, Narayanan T, Zaccarelli E. Correlation between structure and rheology of a model colloidal glass. J Chem Phys 2009; 131:144903. [DOI: 10.1063/1.3240345] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Nishino TH, Hayakawa H. Fluctuation-dissipation-relation-preserving field theory of the glass transition in terms of fluctuating hydrodynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:061502. [PMID: 19256841 DOI: 10.1103/physreve.78.061502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2008] [Revised: 06/25/2008] [Indexed: 05/27/2023]
Abstract
A field theoretical method for fluctuating hydrodynamics with preserved fluctuation-dissipation relations is reformulated. By assuming that the correlations including momentum are irrelevant in the long time region, we demonstrate that the equation obtained from the first-order perturbation is reduced to that for standard mode-coupling theory.
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Affiliation(s)
- Taka H Nishino
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
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Juárez-Maldonado R, Medina-Noyola M. Theory of dynamic arrest in colloidal mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051503. [PMID: 18643070 DOI: 10.1103/physreve.77.051503] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2007] [Revised: 02/18/2008] [Indexed: 05/26/2023]
Abstract
We present a first-principles theory of dynamic arrest in colloidal mixtures based on the multicomponent self-consistent generalized Langevin equation theory of colloid dynamics [M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E 72, 031107 (2005); M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E76, 039902 (2007)]. We illustrate its application with a description of dynamic arrest in two simple model colloidal mixtures: namely, hard-sphere and repulsive Yukawa binary mixtures. Our results include observation of the two patterns of dynamic arrest, one in which both species become simultaneously arrested and the other involving the sequential arrest of the two species. The latter case gives rise to mixed states in which one species is arrested while the other species remains mobile. We also derive the ("bifurcation" or fixed-point") equations for the nonergodic parameters of the system, which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species. The solution of this system of equations indicates unambiguously which species is arrested (finite localization length) and which species remains ergodic (infinite localization length). As a result, we are able to draw the entire ergodic-nonergodic phase diagram of the binary hard-sphere mixture.
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Affiliation(s)
- R Juárez-Maldonado
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, SLP, México
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25
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Yeomans-Reyna L, Chávez-Rojo MA, Ramírez-González PE, Juárez-Maldonado R, Chávez-Páez M, Medina-Noyola M. Dynamic arrest within the self-consistent generalized Langevin equation of colloid dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:041504. [PMID: 17994991 DOI: 10.1103/physreve.76.041504] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2007] [Revised: 07/26/2007] [Indexed: 05/25/2023]
Abstract
This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.
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Affiliation(s)
- L Yeomans-Reyna
- Departamento de Física, Universidad de Sonora, Boulevard Luis Encinas y Rosales, 83000, Hermosillo, Sonora, Mexico
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26
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Szamel G. Dynamics of interacting Brownian particles: A diagrammatic formulation. J Chem Phys 2007; 127:084515. [PMID: 17764277 DOI: 10.1063/1.2759487] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion, we introduce a basis that consists of orthogonalized many-particle density fluctuations. We obtain an exact hierarchy of equations of motion for time-dependent correlations of orthogonalized density fluctuations. To simplify this hierarchy we neglect contributions to the vertices from higher-order cluster expansion terms. An iterative solution of the resulting equations can be represented by diagrams with three- and four-leg vertices. We analyze the structure of the diagrammatic series for the time-dependent density correlation function and obtain a diagrammatic interpretation of reducible and irreducible memory functions. The one-loop self-consistent approximation for the latter function coincides with mode-coupling approximation for Brownian systems that was derived previously using a projection operator approach.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80525, USA
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27
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Mayer P, Miyazaki K, Reichman DR. Cooperativity beyond caging: Generalized mode-coupling theory. PHYSICAL REVIEW LETTERS 2006; 97:095702. [PMID: 17026376 DOI: 10.1103/physrevlett.97.095702] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2006] [Indexed: 05/12/2023]
Abstract
The validity of mode-coupling theory (MCT) is restricted by an uncontrolled factorization approximation of density correlations. The factorization can be delayed and ultimately avoided, however, by explicitly including higher order correlations. We explore this approach within a microscopically motivated schematic model. Analytic tractability allows us to discuss in great detail the impact of factorization at arbitrary order, including the limit of avoided factorization. Our results indicate a coherent picture for the capabilities as well as limitations of MCT. Moreover, including higher order correlations systematically defers the transition and ultimately restores ergodicity. Power-law divergence of the relaxation time is then replaced by continuous but exponential growth.
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Affiliation(s)
- Peter Mayer
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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