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Pareek P, Adhikari M, Dasgupta C, Nandi SK. Different glassy characteristics are related to either caging or dynamical heterogeneity. J Chem Phys 2023; 159:174503. [PMID: 37916596 DOI: 10.1063/5.0166404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 10/09/2023] [Indexed: 11/03/2023] Open
Abstract
Despite the enormous theoretical and application interests, a fundamental understanding of the glassy dynamics remains elusive. The static properties of glassy and ordinary liquids are similar, but their dynamics are dramatically different. What leads to this difference is the central puzzle of the field. Even the primary defining glassy characteristics, their implications, and if they are related to a single mechanism remain unclear. This lack of clarity is a severe hindrance to theoretical progress. Here, we combine analytical arguments and simulations of various systems in different dimensions and address these questions. Our results suggest that the myriad of glassy features are manifestations of two distinct mechanisms. Particle caging controls the mean, and coexisting slow- and fast-moving regions govern the distribution of particle displacements. All the other glassy characteristics are manifestations of these two mechanisms; thus, the Fickian yet non-Gaussian nature of glassy liquids is not surprising. We discover a crossover, from stretched exponential to a power law, in the behavior of the overlap function. This crossover is prominent in simulation data and forms the basis of our analyses. Our results have crucial implications on how the glassy dynamics data are analyzed, challenge some recent suggestions on the mechanisms governing glassy dynamics, and impose strict constraints that a correct theory of glasses must have.
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Affiliation(s)
- Puneet Pareek
- Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Monoj Adhikari
- Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Chandan Dasgupta
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
- International Centre for Theoretical Sciences, TIFR, Bangalore 560089, India
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Mendoza-Méndez P, Peredo-Ortiz R, Lázaro-Lázaro E, Chávez-Paez M, Ruiz-Estrada H, Pacheco-Vázquez F, Medina-Noyola M, Elizondo-Aguilera LF. Structural relaxation, dynamical arrest, and aging in soft-sphere liquids. J Chem Phys 2022; 157:244504. [PMID: 36586975 DOI: 10.1063/5.0121224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
We investigate the structural relaxation of a soft-sphere liquid quenched isochorically (ϕ = 0.7) and instantaneously to different temperatures Tf above and below the glass transition. For this, we combine extensive Brownian dynamics simulations and theoretical calculations based on the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory. The response of the liquid to a quench generally consists of a sub-linear increase of the α-relaxation time with system's age. Approaching the ideal glass-transition temperature from above (Tf > Ta), sub-aging appears as a transient process describing a broad equilibration crossover for quenches to nearly arrested states. This allows us to empirically determine an equilibration timescale teq(Tf) that becomes increasingly longer as Tf approaches Ta. For quenches inside the glass (Tf ≤ Ta), the growth rate of the structural relaxation time becomes progressively larger as Tf decreases and, unlike the equilibration scenario, τα remains evolving within the whole observation time-window. These features are consistently found in theory and simulations with remarkable semi-quantitative agreement and coincide with those revealed in a previous and complementary study [P. Mendoza-Méndez et al., Phys. Rev. 96, 022608 (2017)] that considered a sequence of quenches with fixed final temperature Tf = 0 but increasing ϕ toward the hard-sphere dynamical arrest volume fraction ϕHS a=0.582. The NE-SCGLE analysis, however, unveils various fundamental aspects of the glass transition, involving the abrupt passage from the ordinary equilibration scenario to the persistent aging effects that are characteristic of glass-forming liquids. The theory also explains that, within the time window of any experimental observation, this can only be observed as a continuous crossover.
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Affiliation(s)
- P Mendoza-Méndez
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, CP 72570 Puebla, Mexico
| | - R Peredo-Ortiz
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, CP 72570 Puebla, Mexico
| | - E Lázaro-Lázaro
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, CP 72570 Puebla, Mexico
| | - M Chávez-Paez
- Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - H Ruiz-Estrada
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, CP 72570 Puebla, Mexico
| | - F Pacheco-Vázquez
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla, Mexico
| | - M Medina-Noyola
- Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - L F Elizondo-Aguilera
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla, Mexico
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Dubey V, Dueby S, Daschakraborty S. Breakdown of the Stokes-Einstein relation in supercooled water: the jump-diffusion perspective. Phys Chem Chem Phys 2021; 23:19964-19986. [PMID: 34515269 DOI: 10.1039/d1cp02202d] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Although water is the most ubiquitous liquid it shows many thermodynamic and dynamic anomalies. Some of the anomalies further intensify in the supercooled regime. While many experimental and theoretical studies have focused on the thermodynamic anomalies of supercooled water, fewer studies explored the dynamical anomalies very extensively. This is due to the intricacy of the experimental measurement of the dynamical properties of supercooled water. Violation of the Stokes-Einstein relation (SER), an important relation connecting the diffusion of particles with the viscosity of the medium, is one of the major dynamical anomalies. In absence of experimentally measured viscosity, researchers used to check the validity of SER indirectly using average translational relaxation time or α-relaxation time. Very recently, the viscosity of supercooled water was accurately measured at a wide range of temperatures and pressures. This allowed direct verification of the SER at different temperature-pressure thermodynamic state points. An increasing breakdown of the SER was observed with decreasing temperature. Increasing pressure reduces the extent of breakdown. Although some well-known theories explained the above breakdown, a detailed molecular mechanism was still elusive. Recently, a translational jump-diffusion (TJD) approach has been able to quantitatively explain the breakdown of the SER in pure supercooled water and an aqueous solution of methanol. The objective of this article is to present a detailed and state-of-the-art analysis of the past and present works on the breakdown of SER in supercooled water with a specific focus on the new TJD approach for explaining the breakdown of the SER.
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Affiliation(s)
- Vikas Dubey
- Department of Chemistry, Indian Institute of Technology Patna, Bihar 801106, India.
| | - Shivam Dueby
- Department of Chemistry, Indian Institute of Technology Patna, Bihar 801106, India.
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4
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Hodge SR, Berg MA. Nonlinear measurements of kinetics and generalized dynamical modes. I. Extracting the one-dimensional Green's function from a time series. J Chem Phys 2021; 155:024122. [PMID: 34266246 DOI: 10.1063/5.0053422] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion. Here, these ideas are generalized to other observables. A set of correlation functions of nonlinear functions of an observable is used to extract the corresponding Green's function. Although this paper focuses on nonlinear correlation functions of an equilibrium time series, the results are directly connected to other types of nonlinear kinetics, including perturbation-response experiments with strong fields. Generalized modes are defined as the orthogonal polynomials associated with the equilibrium distribution. A matrix of mode-correlation functions can be transformed to the complete, single-time-interval (1D) Green's function. Diagonalizing this matrix finds the eigendecays. To understand the advantages and limitation of this approach, Green's functions are calculated for a number of models of complex dynamics within a Gaussian probability distribution. Examples of non-diffusive motion, rate heterogeneity, and range heterogeneity are examined. General arguments are made that a full set of nonlinear 1D measurements is necessary to extract all the information available in a time series. However, when a process is neither dynamically Gaussian nor Markovian, they are not sufficient. In those cases, additional multidimensional measurements are needed.
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Affiliation(s)
- Stuart R Hodge
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - Mark A Berg
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
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Mendoza-Méndez P, Lázaro-Lázaro E, Sánchez-Díaz LE, Ramírez-González PE, Pérez-Ángel G, Medina-Noyola M. Crossover from equilibration to aging: Nonequilibrium theory versus simulations. Phys Rev E 2017; 96:022608. [PMID: 28950613 DOI: 10.1103/physreve.96.022608] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2015] [Indexed: 06/07/2023]
Abstract
Understanding glasses and the glass transition requires comprehending the nature of the crossover from the ergodic (or equilibrium) regime, in which the stationary properties of the system have no history dependence, to the mysterious glass transition region, where the measured properties are nonstationary and depend on the protocol of preparation. In this work we use nonequilibrium molecular dynamics simulations to test the main features of the crossover predicted by the molecular version of the recently developed multicomponent nonequilibrium self-consistent generalized Langevin equation theory. According to this theory, the glass transition involves the abrupt passage from the ordinary pattern of full equilibration to the aging scenario characteristic of glass-forming liquids. The same theory explains that this abrupt transition will always be observed as a blurred crossover due to the unavoidable finiteness of the time window of any experimental observation. We find that within their finite waiting-time window, the simulations confirm the general trends predicted by the theory.
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Affiliation(s)
- P Mendoza-Méndez
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, SLP, México
| | - E Lázaro-Lázaro
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, SLP, México
| | - L E Sánchez-Díaz
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - P E Ramírez-González
- CONACYT-Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, SLP, México
| | - G Pérez-Ángel
- Departamento de Física Aplicada CINVESTAV-IPN, Unidad Mérida Apartado Postal 73 Cordemex, 97310 Mérida, Yuc., México
| | - M Medina-Noyola
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, SLP, México
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6
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Berg MA, Kaur H. Nonparametric analysis of nonexponential and multidimensional kinetics. I. Quantifying rate dispersion, rate heterogeneity, and exchange dynamics. J Chem Phys 2017; 146:054104. [DOI: 10.1063/1.4974508] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Mark A. Berg
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - Harveen Kaur
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
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7
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Berg MA, Darvin JR. Measuring a hidden coordinate: Rate-exchange kinetics from 3D correlation functions. J Chem Phys 2016; 145:054119. [DOI: 10.1063/1.4960186] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mark A. Berg
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - Jason R. Darvin
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
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8
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Dinkgreve M, Paredes J, Michels MAJ, Bonn D. Universal rescaling of flow curves for yield-stress fluids close to jamming. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012305. [PMID: 26274160 DOI: 10.1103/physreve.92.012305] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Indexed: 06/04/2023]
Abstract
The experimental flow curves of four different yield-stress fluids with different interparticle interactions are studied near the jamming concentration. By appropriate scaling with the distance to jamming all rheology data can be collapsed onto master curves below and above jamming that meet in the shear-thinning regime and satisfy the Herschel-Bulkley and Cross equations, respectively. In spite of differing interactions in the different systems, master curves characterized by universal scaling exponents are found for the four systems. A two-state microscopic theory of heterogeneous dynamics is presented to rationalize the observed transition from Herschel-Bulkley to Cross behavior and to connect the rheological exponents to microscopic exponents for the divergence of the length and time scales of the heterogeneous dynamics. The experimental data and the microscopic theory are compared with much of the available literature data for yield-stress systems.
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Affiliation(s)
- M Dinkgreve
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Science Park 904, 1018 XH Amsterdam, The Netherlands
| | - J Paredes
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Science Park 904, 1018 XH Amsterdam, The Netherlands
| | - M A J Michels
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - D Bonn
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Science Park 904, 1018 XH Amsterdam, The Netherlands
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9
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Ono J, Takada S, Saito S. Couplings between hierarchical conformational dynamics from multi-time correlation functions and two-dimensional lifetime spectra: Application to adenylate kinase. J Chem Phys 2015; 142:212404. [DOI: 10.1063/1.4914328] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Affiliation(s)
- Junichi Ono
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan
| | - Shoji Takada
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan
- Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Shinji Saito
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan
- The Graduate University for Advanced Studies, Okazaki 444-8585, Japan
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10
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Park SW, Kim S, Jung Y. Time scale of dynamic heterogeneity in model ionic liquids and its relation to static length scale and charge distribution. Phys Chem Chem Phys 2015; 17:29281-92. [DOI: 10.1039/c5cp03390j] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We find a general power-law behavior: , where ζdh ≈ 1.2 for all the ionic liquid models, regardless of charges and the length scale of structural relaxation.
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Affiliation(s)
- Sang-Won Park
- Department of Chemistry
- Seoul National University
- Seoul 08826
- Korea
| | - Soree Kim
- Department of Chemistry
- Seoul National University
- Seoul 08826
- Korea
| | - YounJoon Jung
- Department of Chemistry
- Seoul National University
- Seoul 08826
- Korea
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Paredes J, Michels MAJ, Bonn D. Rheology across the zero-temperature jamming transition. PHYSICAL REVIEW LETTERS 2013; 111:015701. [PMID: 23863014 DOI: 10.1103/physrevlett.111.015701] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2013] [Indexed: 06/02/2023]
Abstract
Many soft-matter systems show a transition between fluidlike and mechanically solidlike states when the volume fraction of the material, e.g., particles, drops, or bubbles is increased. Using an emulsion as a model system with a precisely controllable volume fraction, we show that the entire mechanical behavior in the vicinity of the jamming point can be understood if the mechanical transition is assumed to be analogous to a phase transition. We find power-law scalings in the distance to the jamming point, in which the parameters and exponents connect the behavior above and below jamming. We propose a simple two-state model with heterogeneous dynamics to describe the transition between jammed and mobile states. The model reproduces the steady-state and creep rheology and relates the power-law exponents to diverging microscopic time scales.
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Affiliation(s)
- José Paredes
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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12
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Furukawa A. Simple picture of supercooled liquid dynamics: dynamic scaling and phenomenology based on clusters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062321. [PMID: 23848689 DOI: 10.1103/physreve.87.062321] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2012] [Revised: 03/10/2013] [Indexed: 06/02/2023]
Abstract
Although it is now well established that in glassy liquids, slow structural relaxation accompanies a correlated structural rearrangement, the role of such a correlation in the transport anomaly, and thus in the slow dynamics, remains unclear. In this paper, we argue from a hydrodynamic viewpoint that a correlated structure (cluster) with a characteristic size ξ sustains the long-lived stress and dynamically couples with the hydrodynamic fluctuations; therefore, the dynamics of this cluster is the origin of the mesoscopic nature of anomalous hydrodynamic transport. Based on this argument, we derive a dynamic scaling law for τ(α) (or η, where η is the macroscopic shear viscosity) as a function of ξ: τ(α)([proportionality]η)[proportionality]ξ(4). We provide a simple explanation for basic features of anomalous transport, such as the breakdown of the Stokes-Einstein relation and the length-scale-dependent decoupling between viscosity and diffusion. The present study further suggests a different physical picture: Through the coarse graining of smaller-scale fluctuations (</~ξ), the supercooled liquid dynamics can be regarded as the dynamics of normal (cluster) liquids composed of units with a typical size of ξ. Although the correlation length of hydrodynamic transport ξ and the dynamic heterogeneity size ξ(DH), which is determined by the usual four-point correlation function, reflect some aspects of the cooperative effects, the correspondence between ξ and ξ(DH) is not one to one. We highlight the possibility that ξ(DH) overestimates the actual collective transport range at a low degree of supercooling.
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Affiliation(s)
- Akira Furukawa
- Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan.
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Sánchez-Díaz LE, Ramírez-González P, Medina-Noyola M. Equilibration and aging of dense soft-sphere glass-forming liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052306. [PMID: 23767539 DOI: 10.1103/physreve.87.052306] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2012] [Revised: 03/20/2013] [Indexed: 06/02/2023]
Abstract
The recently developed nonequilibrium extension of the self-consistent generalized Langevin equation theory of irreversible relaxation [Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061503 (2010); Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061504 (2010)] is applied to the description of the irreversible process of equilibration and aging of a glass-forming soft-sphere liquid that follows a sudden temperature quench, within the constraint that the local mean particle density remains uniform and constant. For these particular conditions, this theory describes the nonequilibrium evolution of the static structure factor S(k;t) and of the dynamic properties, such as the self-intermediate scattering function F(S)(k,τ;t), where τ is the correlation delay time and t is the evolution or waiting time after the quench. Specific predictions are presented for the deepest quench (to zero temperature). The predicted evolution of the α-relaxation time τ(α)(t) as a function of t allows us to define the equilibration time t(eq)(φ), as the time after which τ(α)(t) has attained its equilibrium value τ(α)(eq)(φ). It is predicted that both, t(eq)(φ) and τ(α)(eq)(φ), diverge as φ→φ((a)), where φ((a)) is the hard-sphere dynamic-arrest volume fraction φ((a))(≈0.582), thus suggesting that the measurement of equilibrium properties at and above φ((a)) is experimentally impossible. The theory also predicts that for fixed finite waiting times t, the plot of τ(α)(t;φ) as a function of φexhibits two regimes, corresponding to samples that have fully equilibrated within this waiting time (φ≤φ((c))(t)), and to samples for which equilibration is not yet complete (φ≥φ((c))(t)). The crossover volume fraction φ((c))(t) increases with t but saturates to the value φ((a)).
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Affiliation(s)
- Luis Enrique Sánchez-Díaz
- Instituto de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, San Luis Potosí, México
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Kim K, Saito S. Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations. J Chem Phys 2013; 138:12A506. [DOI: 10.1063/1.4769256] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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15
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Saito S, Ohmine I, Bagchi B. Frequency dependence of specific heat in supercooled liquid water and emergence of correlated dynamics. J Chem Phys 2013; 138:094503. [DOI: 10.1063/1.4793555] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Tatsumi S, Aso S, Yamamuro O. Thermodynamic study of simple molecular glasses: universal features in their heat capacity and the size of the cooperatively rearranging regions. PHYSICAL REVIEW LETTERS 2012; 109:045701. [PMID: 23006098 DOI: 10.1103/physrevlett.109.045701] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2011] [Indexed: 06/01/2023]
Abstract
We have obtained some universal thermodynamic properties on glass transitions of molecular liquids. The heat capacity C(p) of glassy propene, which was vitrified by using a vapor-deposition technique, was measured with a newly developed adiabatic calorimeter. Propene has the lowest glass transition temperature (T(g)=56 K), the largest C(p) jump at T(g) (C(p)(lq)/C(p)(gl)~2.5), and the lowest residual entropy (S(res)~Rln2) compared with glass-forming molecules measured before. We have analyzed the present data with other hydrocarbon molecules vitrified by liquid quenching and obtained the following results: (1) The excess heat capacities are scaled well by using a Kauzmann temperature T(K), (2) The size of the cooperative rearrangement region (CRR) frozen at T(g) increases with decreasing the temperature difference between T(g) and T(K) (Kauzmann temperature), and (3) The simpler the molecule is, the larger the frozen CRR becomes. These are all supporting the validity of the Adam-Gibbs theory.
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Affiliation(s)
- Soichi Tatsumi
- Neutron Science Laboratory, Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan.
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Mizuno H, Yamamoto R. Dynamical heterogeneity in a highly supercooled liquid under a sheared situation. J Chem Phys 2012; 136:084505. [DOI: 10.1063/1.3688227] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
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18
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Yagasaki T, Saito S. Energy relaxation of intermolecular motions in supercooled water and ice: A molecular dynamics study. J Chem Phys 2011; 135:244511. [DOI: 10.1063/1.3671993] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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Mizuno H, Yamamoto R. Dynamical heterogeneity in a highly supercooled liquid: consistent calculations of correlation length, intensity, and lifetime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011506. [PMID: 21867177 DOI: 10.1103/physreve.84.011506] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2010] [Revised: 05/16/2011] [Indexed: 05/31/2023]
Abstract
We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length ξ(4), intensity χ(4), and lifetime τ(hetero). We evaluated all three quantities consistently from a single order parameter. In a previous study [H. Mizuno and R. Yamamoto, Phys. Rev. E 82, 030501(R) (2010)], we examined the lifetime τ(hetero)(t) in two time intervals t = τ(α) and τ(ngp), where τ(α) is the α-relaxation time and τ(ngp) is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime τ(hetero)(t), we evaluated the correlation length ξ(4)(t) and the intensity χ({4)(t) from the same order parameter used for the lifetime τ(hetero)(t). We found that as the temperature decreases, the lifetime τ(hetero)(t) grows dramatically, whereas the correlation length ξ(4)(t) and the intensity χ(4)(t) increase slowly compared to τ(hetero)(t) or plateaus. Furthermore, we investigated the lifetime τ(hetero)(t) in more detail. We examined the time-interval dependence of the lifetime τ(hetero)(t) and found that as the time interval t increases, τ(hetero)(t) monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which τ(hetero)(t) plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.
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Affiliation(s)
- Hideyuki Mizuno
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan.
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Pérez-Ángel G, Sánchez-Díaz LE, Ramírez-González PE, Juárez-Maldonado R, Vizcarra-Rendón A, Medina-Noyola M. Equilibration of concentrated hard-sphere fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:060501. [PMID: 21797290 DOI: 10.1103/physreve.83.060501] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2010] [Revised: 01/31/2011] [Indexed: 05/31/2023]
Abstract
We report a systematic molecular dynamics study of the isochoric equilibration of hard-sphere fluids in their metastable regime close to the glass transition. The thermalization process starts with the system prepared in a nonequilibrium state with the desired final volume fraction ϕ for which we can obtain a well-defined nonequilibrium static structure factor S(0)(k;ϕ). The evolution of the α-relaxation time τ(α)(k) and long-time self-diffusion coefficient D(L) as a function of the evolution time t(w) is then monitored for an array of volume fractions. For a given waiting time the plot of τ(α)(k;ϕ,t(w)) as a function of ϕ exhibits two regimes corresponding to samples that have fully equilibrated within this waiting time [ϕ≤ϕ(c)(t(w))] and to samples for which equilibration is not yet complete [ϕ≥ϕ(c)(t(w))]. The crossover volume fraction ϕ(c)(t(w)) increases with t(w) but seems to saturate to a value ϕ(a)≡ϕ(c)(t(w)→∞)≈0.582. We also find that the waiting time t(w)(eq)(ϕ) required to equilibrate a system grows faster than the corresponding equilibrium relaxation time, t(w)(eq)(ϕ)≈0.27[τ(α)(eq)(k;ϕ)](1.43), and that both characteristic times increase strongly as ϕ approaches ϕ(a), thus suggesting that the measurement of equilibrium properties at and above ϕ(a) is experimentally impossible.
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Affiliation(s)
- Gabriel Pérez-Ángel
- Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Unidad Mérida, Mérida, Yucatán, Mexico
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Mizuno H, Yamamoto R. Lifetime of dynamical heterogeneity in a highly supercooled liquid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:030501. [PMID: 21230016 DOI: 10.1103/physreve.82.030501] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2010] [Indexed: 05/30/2023]
Abstract
We numerically examine dynamical heterogeneity in a highly supercooled three-dimensional liquid via molecular-dynamics simulations. To define the local dynamics, we consider two time intervals: τ(α) and τ(ngp). τ(α) is the α relaxation time, and τ(ngp) is the time at which non-gaussian parameter of the Van Hove self-correlation function is maximized. We determine the lifetimes of the heterogeneous dynamics in these two different time intervals, τ(hetero)(τ(α)) and τ(hetero)(τ(ngp)), by calculating the time correlation function of the particle dynamics, i.e., the four-point correlation function. We find that the difference between τ(hetero)(τ(α)) and τ(hetero)(τ(ngp)) increases with decreasing temperature. At low temperatures, τ(hetero)(τ(α)) is considerably larger than τ(α), while τ(hetero)(τ(ngp)) remains comparable to τ(α). Thus, the lifetime of the heterogeneous dynamics depends strongly on the time interval.
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Affiliation(s)
- Hideyuki Mizuno
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan.
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Kim K, Saito S. Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime. J Chem Phys 2010; 133:044511. [DOI: 10.1063/1.3464331] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
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Berg MA. Hilbert-space treatment of incoherent, time-resolved spectroscopy. I. Formalism, a tensorial classification of high-order orientational gratings and generalized MUPPETS “echoes”. J Chem Phys 2010; 132:144105. [DOI: 10.1063/1.3327760] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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