1
|
Luo P, Zhai Y, Falus P, García Sakai V, Hartl M, Kofu M, Nakajima K, Faraone A, Z Y. Q-dependent collective relaxation dynamics of glass-forming liquid Ca 0.4K 0.6(NO 3) 1.4 investigated by wide-angle neutron spin-echo. Nat Commun 2022; 13:2092. [PMID: 35440658 PMCID: PMC9018732 DOI: 10.1038/s41467-022-29778-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 03/29/2022] [Indexed: 11/30/2022] Open
Abstract
The relaxation behavior of glass formers exhibits spatial heterogeneity and dramatically changes upon cooling towards the glass transition. However, the underlying mechanisms of the dynamics at different microscopic length scales are not fully understood. Employing the recently developed wide-angle neutron spin-echo spectroscopy technique, we measured the Q-dependent coherent intermediate scattering function of a prototypical ionic glass former Ca0.4K0.6(NO3)1.4, in the highly viscous liquid state. In contrast to the structure modulated dynamics for Q < 2.4 Å−1, i.e., at and below the structure factor main peak, for Q > 2.4 Å−1, beyond the first minimum above the structure factor main peak, the stretching exponent exhibits no temperature dependence and concomitantly the relaxation time shows smaller deviations from Arrhenius behavior. This finding indicates a change in the dominant relaxation mechanisms around a characteristic length of 2π/(2.4 Å−1) ≈ 2.6 Å, below which the relaxation process exhibits a temperature independent distribution and more Arrhenius-like behavior. Length scale dependence is important for understanding the collective relaxation dynamics in glass-forming liquids. Here, the authors find in liquid Ca0.4K0.6(NO3)1.4 a change in the dominant relaxation mechanisms around 2.6 Å, below which the relaxation process exhibits a temperature independent distribution and more Arrhenius-like behavior.
Collapse
Affiliation(s)
- Peng Luo
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Yanqin Zhai
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA.,Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Peter Falus
- Institut Laue-Langevin (ILL), 38042, Grenoble, France
| | - Victoria García Sakai
- ISIS Neutron and Muon Facility, Rutherford Appleton Laboratory, Science & Technology Facilities Council, Didcot, OX11 0QX, UK
| | - Monika Hartl
- European Spallation Source, SE-221 00, Lund, Sweden
| | - Maiko Kofu
- J-PARC Center, Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan
| | - Kenji Nakajima
- J-PARC Center, Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan
| | - Antonio Faraone
- NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD, 20899-1070, USA.
| | - Y Z
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA. .,Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA. .,Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA.
| |
Collapse
|
2
|
Das R, Tah I, Karmakar S. Possible universal relation between short timeβ-relaxation and long timeα-relaxation in glass-forming liquids. J Chem Phys 2018; 149:024501. [DOI: 10.1063/1.5033555] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Affiliation(s)
- Rajsekhar Das
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad 500107, India
| | - Indrajit Tah
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad 500107, India
| | - Smarajit Karmakar
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad 500107, India
| |
Collapse
|
3
|
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.
Collapse
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
| |
Collapse
|
4
|
McCowan DD. Numerical study of long-time dynamics and ergodic-nonergodic transitions in dense simple fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022107. [PMID: 26382344 DOI: 10.1103/physreve.92.022107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2014] [Indexed: 06/05/2023]
Abstract
Since the mid-1980s, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the transition from the fluid state to the glassy state. MCT, however, is limited by the approximations used in its construction and lacks an unambiguous mechanism to institute corrections. We use recent results from a new theoretical framework--developed from first principles via a self-consistent perturbation expansion in terms of an effective two-body potential--to numerically explore the kinetics of systems of classical particles, specifically hard spheres governed by Smoluchowski dynamics. We present here a full solution for such a system to the kinetic equation governing the density-density time correlation function and show that the function exhibits the characteristic two-step decay of supercooled fluids and an ergodic-nonergodic transition to a dynamically arrested state. Unlike many previous numerical studies--and in stark contrast to experiment--we have access to the full time and wave-number range of the correlation function with great precision and are able to track the solution unprecedentedly close to the transition, covering nearly 15 decades in scaled time. Using asymptotic approximation techniques analogous to those developed for MCT, we fit the solution to predicted forms and extract critical parameters. We find complete qualitative agreement with known glassy behavior (e.g. power-law divergence of the α-relaxation time scale in the ergodic phase and square-root growth of the glass form factors in the nonergodic phase), as well as some limited quantitative agreement [e.g. the transition at packing fraction η*=0.60149761(10)], consistent with previous static solutions under this theory and with comparable colloidal suspension experiments. However, most importantly, we establish that this new theory is able to reproduce the salient features seen in other theories, experiments, and simulations but has the advantages of being derived from first principles and possessing a clear mechanism for making systematic corrections.
Collapse
Affiliation(s)
- David D McCowan
- The James Franck Institute and the Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
| |
Collapse
|
5
|
Bidhoodi N, Das SP. Renormalized dynamics of the Dean-Kawasaki model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012325. [PMID: 26274179 DOI: 10.1103/physreve.92.012325] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2015] [Indexed: 06/04/2023]
Abstract
We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ(x,t) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ. The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ,θ}, linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D(0) to D(R) is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997)]. D(R) sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with D(R)=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.
Collapse
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
| |
Collapse
|
6
|
Jacquin H, Kim B, Kawasaki K, van Wijland F. Brownian dynamics: from glassy to trivial. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022130. [PMID: 25768481 DOI: 10.1103/physreve.91.022130] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2014] [Indexed: 06/04/2023]
Abstract
We endow a system of interacting particles with two distinct, local, Markovian, and reversible microscopic dynamics that both converge to the Boltzmann-Gibbs equilibrium of standard liquids. While the first, standard, one leads to glassy dynamics, we use field-theoretical techniques to show that the latter displays no sign of glassiness. The approximations we use, akin to the mode-coupling approximation, are famous for magnifying glassy aspects of the dynamics, supposedly through the neglect of activated events. Despite this, the modified dynamics seem to stick to standard liquid relaxation. This finding singles out as applying to a realistic system of interacting particles in low dimensions and questions the role of the dynamical rules used to explore a given static free-energy landscape. Moreover, our peculiar choice of dynamical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.
Collapse
Affiliation(s)
- Hugo Jacquin
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
| | - Bongsoo Kim
- Department of Physics and Institute for Soft and Bio Matter Science, Changwon National University, Changwon 641-773, Korea
| | - Kyozi Kawasaki
- Department of Physics, Faculty of Science, Kyushu University, Fukuoka 812-8581, Japan
| | - Frédéric van Wijland
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
| |
Collapse
|
7
|
|
8
|
Gross M, Varnik F. Critical dynamics of an isothermal compressible nonideal fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061119. [PMID: 23367905 DOI: 10.1103/physreve.86.061119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2012] [Revised: 08/23/2012] [Indexed: 06/01/2023]
Abstract
A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible nonideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.
Collapse
Affiliation(s)
- Markus Gross
- Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum, Universitätsstr 90a, 44789 Bochum, Germany.
| | | |
Collapse
|
9
|
Berthier L, Tarjus G. Critical test of the mode-coupling theory of the glass transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031502. [PMID: 21230078 DOI: 10.1103/physreve.82.031502] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2010] [Revised: 07/06/2010] [Indexed: 05/30/2023]
Abstract
In its common implementation, the mode-coupling theory of the glass transition predicts the time evolution of the intermediate scattering functions in viscous liquids on the sole basis of the structural information encoded in two-point density correlations. We provide a critical test of this property and show that the theory fails to describe the strong differences of dynamical behavior seen in two model liquids characterized by very similar pair-correlation functions. Because we use "exact" static information provided by numerical simulations, our results are a direct indication that some important information about the dynamics of viscous liquids is not captured by pair correlations and is thus not described by the mode-coupling theory, even in the temperature regime where the theory is usually applied.
Collapse
Affiliation(s)
- Ludovic Berthier
- Laboratoire des Colloïdes, Verres et Nanomatériaux, Université Montpellier II and UMR 5587 CNRS, 34095 Montpellier, France
| | | |
Collapse
|
10
|
Bartsch E, Debus O, Fujara F, Kiebel M, Sillescu H, Petry W. Dynamic Anomalies and their Relation to the Glass Transition: A Neutron Scattering Study of the Glass Forming Van der Waals Liquid Ortho-terphenyl. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19910950938] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
|
11
|
Mezei F. Scaling Behaviour of Structural Relaxation near the Glass Transition: A Critical Analysis. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19910950932] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
|
12
|
Yeo J. Density nonlinearities in field theories for a toy model of fluctuating nonlinear hydrodynamics of supercooled liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:051501. [PMID: 20364986 DOI: 10.1103/physreve.80.051501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2009] [Indexed: 05/29/2023]
Abstract
We study a zero-dimensional version of the fluctuating nonlinear hydrodynamics (FNH) of supercooled liquids originally investigated by Das and Mazenko (DM) [Shankar P. Das and Gene F. Mazenko Phys. Rev. A 34, 2265 (1986)]. The time-dependent density-like and momentum-like variables are introduced with no spatial degrees of freedom in this toy model. The structure of nonlinearities takes the similar form to the original FNH, which allows one to study in a simpler setting the issues raised recently regarding the field theoretical approaches to glass forming liquids. We study the effects of density nonlinearities on the time evolution of correlation and response functions by developing field theoretic formulations in two different ways: first by following the original prescription of DM and then by constructing a dynamical action which possesses a linear time-reversal symmetry as proposed recently. We show explicitly that, at the one-loop order of the perturbation theory, the DM-type field theory does not support a sharp ergodic-nonergodic transition, while the other admits one. The simple nature of the toy model in the DM formulation allows us to develop numerical solutions to a complete set of coupled dynamical equations for the correlation and response functions at the one-loop order.
Collapse
Affiliation(s)
- Joonhyun Yeo
- Division of Quantum Phases and Devices, School of Physics, Konkuk University, Seoul 143-701, Korea.
| |
Collapse
|
13
|
Das SP, Mazenko GF. Fluctuating nonlinear hydrodynamics does not support an ergodic-nonergodic transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:021504. [PMID: 19391752 DOI: 10.1103/physreve.79.021504] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2008] [Revised: 08/08/2008] [Indexed: 05/27/2023]
Abstract
Despite its appeal, real and simulated glass forming systems do not undergo an ergodic-nonergodic (ENE) transition. We reconsider whether the fluctuating nonlinear hydrodynamics (FNH) model for this system, introduced by us in 1986, supports an ENE transition. Using nonperturbative arguments, with no reference to the hydrodynamic regime, we show that the FNH model does not support an ENE transition. Our results support the findings in the original paper. Assertions in the literature questioning the validity of the original work are shown to be in error.
Collapse
Affiliation(s)
- Shankar P Das
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | | |
Collapse
|
14
|
Archer AJ. Dynamical density functional theory for molecular and colloidal fluids: A microscopic approach to fluid mechanics. J Chem Phys 2009; 130:014509. [DOI: 10.1063/1.3054633] [Citation(s) in RCA: 104] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
15
|
Mazenko GF. Random diffusion model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:031123. [PMID: 18851009 DOI: 10.1103/physreve.78.031123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2007] [Revised: 08/25/2008] [Indexed: 05/26/2023]
Abstract
We study the random diffusion model. This is a continuum model for a conserved scalar density field varphi driven by diffusive dynamics. The interesting feature of the dynamics is that the bare diffusion coefficient D is density dependent. In the simplest case, D=D[over ]+D_{1}deltavarphi , where D[over ] is the constant average diffusion constant. In the case where the driving effective Hamiltonian is quadratic, the model can be treated using perturbation theory in terms of the single nonlinear coupling D1 . We develop perturbation theory to fourth order in D1 . The are two ways of analyzing this perturbation theory. In one approach, developed by Kawasaki, at one-loop order one finds mode-coupling theory with an ergodic-nonergodic transition. An alternative more direct interpretation at one-loop order leads to a slowing down as the nonlinear coupling increases. Eventually one hits a critical coupling where the time decay becomes algebraic. Near this critical coupling a weak peak develops at a wave number well above the peak at q=0 associated with the conservation law. The width of this peak in Fourier space decreases with time and can be identified with a characteristic kinetic length which grows with a power law in time. For stronger coupling the system becomes metastable and then unstable. At two-loop order it is shown that the ergodic-nonergodic transition is not supported. It is demonstrated that the critical properties of the direct approach survive, going to higher order in perturbation theory.
Collapse
Affiliation(s)
- Gene F Mazenko
- The James Franck Institute and the Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
| |
Collapse
|
16
|
Dong H, Evans GT. Effective separation of forces in a mode coupling theory of self-diffusion. J Chem Phys 2007; 127:054502. [PMID: 17688344 DOI: 10.1063/1.2754266] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A mode coupling theory (MCT) expression for the self-diffusion coefficient follows simply when the soft fluctuating intermolecular forces are projected along a collective densitylike variable. The projected forces separate into two parts: from the gradient of the direct correlation function (dcf), and from the short range forces. The time correlation function of the dcf-derived forces is related to the excess entropy, as shown by Ali [J. Chem. Phys. 124, 144504 (2006)], and this relationship is evaluated for two variations of MCT. As for hard spheres, the derivation of an analogous MCT is beset by a number of singularities that kinetic theory could not remove. A justifiable MCT for hard sphere fluids may not exist.
Collapse
Affiliation(s)
- H Dong
- Department of Chemistry, Oregon State University, Corvallis, Oregon 97331, USA
| | | |
Collapse
|
17
|
Fluctuating Nonlinear Hydrodynamics, Dense Fluids, and the Glass Transition. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141274.ch3] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/14/2023]
|
18
|
BIRGE NORMANO, JEONG YOONH, NAGEL SIDNEYR. Specific Heat and Ultrasonics as Dynamic Probes of the Glass Transitiona. Ann N Y Acad Sci 2006. [DOI: 10.1111/j.1749-6632.1986.tb49565.x] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
19
|
|
20
|
|
21
|
Affiliation(s)
- Gene F. Mazenko
- a The James Franck Institute and Department of Physics, University of Chicago , Chicago , IL , 60637 , U.S.A
| | - Joonhyun Yeo
- b Department of Physics , University of Manchester , Manchester , M13 9PL , U.K
| |
Collapse
|
22
|
Pathmanathan K, Johari GP. Temperature dependence of molecular relaxation rates and of viscosity of glass-forming liquids. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/13642819008226988] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- K. Pathmanathan
- a Department of Materials Science and Engineering , McMaster University , Hamilton , Ontario , Canada , L8S 4L7
| | - G. P. Johari
- a Department of Materials Science and Engineering , McMaster University , Hamilton , Ontario , Canada , L8S 4L7
| |
Collapse
|
23
|
Cates ME, Ramaswamy S. Do current-density nonlinearities cut off the glass transition? PHYSICAL REVIEW LETTERS 2006; 96:135701. [PMID: 16712000 DOI: 10.1103/physrevlett.96.135701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2005] [Indexed: 05/09/2023]
Abstract
Extended mode-coupling theories for dense fluids predict that nonlinear current-density couplings cut off the singular "ideal glass transition" present in the standard mode-coupling theory where such couplings are ignored. We suggest here that, rather than allowing for activated processes as sometimes supposed, contributions from current-density couplings are always negligible close to a glass transition. We discuss in schematic terms how activated processes can nonetheless cut off the transition by causing the memory function to become linear in correlators at late times.
Collapse
Affiliation(s)
- M E Cates
- SUPA, School of Physics, University of Edinburgh, JCMB Kings Buildings, Edinburgh EH9 3JZ, United Kingdom
| | | |
Collapse
|
24
|
Miyazaki K, Reichman DR, Yamamoto R. Supercooled liquids under shear: theory and simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:011501. [PMID: 15324050 DOI: 10.1103/physreve.70.011501] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2004] [Indexed: 05/24/2023]
Abstract
We analyze the behavior of supercooled fluids under shear both theoretically and numerically. Theoretically, we generalize the mode-coupling theory of supercooled fluids to systems under stationary shear flow. Our starting point is the set of generalized fluctuating hydrodynamic equations with a convection term. A nonlinear integrodifferential equation for the intermediate scattering function is constructed. This theory is applied to a two-dimensional colloidal suspension. The shear rate dependence of the intermediate scattering function and the shear viscosity is analyzed. We have also performed extensive numerical simulations of a two-dimensional binary liquid with soft-core interactions near, but above, the glass transition temperature. Both theoretical and numerical results show the following. (i) A drastic reduction of the structural relaxation time and the shear viscosity due to shear. Both the structural relaxation time and the viscosity decrease as gamma(-nu) with an exponent nu< or =1, where gamma; is the shear rate. (ii) Almost isotropic dynamics regardless of the strength of the anisotropic shear flow.
Collapse
Affiliation(s)
- Kunimasa Miyazaki
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, USA
| | | | | |
Collapse
|
25
|
Dean DS, Lefèvre A. Self-diffusion in a system of interacting Langevin particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061111. [PMID: 15244544 DOI: 10.1103/physreve.69.061111] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2004] [Indexed: 05/24/2023]
Abstract
The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature beta and the particle density rho. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small beta and rhobeta constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.
Collapse
Affiliation(s)
- D S Dean
- DAMTP, CMS, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | | |
Collapse
|
26
|
|
27
|
Raedt HD, Gotze W. Scaling properties of correlation functions at the liquid-glass transition. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/19/15/007] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
28
|
Thirumalai D, Mountain RD. Relaxation of anisotropic correlations in (two-component) supercooled liquids. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/20/19/005] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
29
|
|
30
|
Thakur JS, Neilson D. Frozen electron solid in the presence of small concentrations of defects. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:7674-7677. [PMID: 9984433 DOI: 10.1103/physrevb.54.7674] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
31
|
Das SP. Fluctuating hydrodynamic models for supercooled liquids and development of long relaxation times. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:1715-1719. [PMID: 9965248 DOI: 10.1103/physreve.54.1715] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
32
|
Ahluwalia R, Das SP. Mode-coupling effects on self-diffusion in a simple fluid at freezing. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:463-466. [PMID: 9965090 DOI: 10.1103/physreve.54.463] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
33
|
|
34
|
Kob W, Andersen HC. Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:4626-4641. [PMID: 9963176 DOI: 10.1103/physreve.51.4626] [Citation(s) in RCA: 690] [Impact Index Per Article: 23.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
|
35
|
Lewis LJ, Wahnström G. Molecular-dynamics study of supercooled ortho-terphenyl. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:3865-3877. [PMID: 9962441 DOI: 10.1103/physreve.50.3865] [Citation(s) in RCA: 72] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
36
|
Das SP, Schilling R. Fluctuating hydrodynamics and diffusion in amorphous solids. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:1265-1273. [PMID: 9962088 DOI: 10.1103/physreve.50.1265] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
37
|
DUFTY JAMESW, SCHMITZ RUDI, DE PIALI. Stochastic Fluid Dynamics and Broken Ergodicity. Ann N Y Acad Sci 1993. [DOI: 10.1111/j.1749-6632.1993.tb24690.x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
38
|
Kob W, Andersen HC. Kinetic lattice-gas model of cage effects in high-density liquids and a test of mode-coupling theory of the ideal-glass transition. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:4364-4377. [PMID: 9961118 DOI: 10.1103/physreve.48.4364] [Citation(s) in RCA: 69] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
39
|
De P, Pelcovits RA, Vogel E, Vogel J. Supercooling of a nematic liquid crystal. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:1824-1835. [PMID: 9960205 DOI: 10.1103/physreve.47.1824] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
40
|
Das SP. Scaling behavior near glass instability in mode‐coupling model for dense fluids. J Chem Phys 1993. [DOI: 10.1063/1.464104] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
41
|
Sinha S, Marchetti MC. Mode-coupling theory of the stress-tensor autocorrelation function of a dense binary fluid mixture. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:4942-4953. [PMID: 9908714 DOI: 10.1103/physreva.46.4942] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
42
|
Bartsch E, Antonietti M, Schupp W, Sillescu H. Dynamic light scattering study of concentrated microgel solutions as mesoscopic model of the glass transition in quasiatomic fluids. J Chem Phys 1992. [DOI: 10.1063/1.462934] [Citation(s) in RCA: 132] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
43
|
Silence SM, Duggal AR, Dhar L, Nelson KA. Structural and orientational relaxation in supercooled liquid triphenylphosphite. J Chem Phys 1992. [DOI: 10.1063/1.462728] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
44
|
Kim B, Mazenko GF. Mode coupling, universality, and the glass transition. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:2393-2398. [PMID: 9907261 DOI: 10.1103/physreva.45.2393] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
45
|
Miyagawa H, Hiwatari Y. Molecular-dynamics study of the glass transition in a binary soft-sphere model. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:8278-8288. [PMID: 9905982 DOI: 10.1103/physreva.44.8278] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
46
|
Lewis LJ. Atomic dynamics through the glass transition. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:4245-4254. [PMID: 10000072 DOI: 10.1103/physrevb.44.4245] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
47
|
Thakur JS, Bosse J. Glass transition of two-component liquids. II. The Lamb-Mössbauer factors. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:4388-4395. [PMID: 9905542 DOI: 10.1103/physreva.43.4388] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
48
|
Thakur JS, Bosse J. Glass transition of two-component liquids. I. The Debye-Waller factors. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:4378-4387. [PMID: 9905541 DOI: 10.1103/physreva.43.4378] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
49
|
Tao NJ, Li G, Cummins HZ. Self-similar light-scattering spectra of beta relaxation near the liquid-glass transition. PHYSICAL REVIEW LETTERS 1991; 66:1334-1337. [PMID: 10043179 DOI: 10.1103/physrevlett.66.1334] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
50
|
Bagchi B, Chandra A, Rice SA. An interpretation of the bifurcation of orientational relaxation processes in a supercooled liquid. J Chem Phys 1990. [DOI: 10.1063/1.459239] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|