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Rössler EA, Becher M. Glass spectrum, excess wing phenomenon, and master curves in molecular glass formers: A multi-method approach. J Chem Phys 2024; 160:074501. [PMID: 38364007 DOI: 10.1063/5.0181187] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2023] [Accepted: 01/18/2024] [Indexed: 02/18/2024] Open
Abstract
The relaxation spectra of glass formers solely displaying an α-peak and excess wing contribution collected by various methods are reanalyzed to pin down their different spectral evolution. We show that master curve construction encompassing both α-peak and emerging excess wing works for depolarized light scattering (DLS) and nuclear magnetic resonance (NMR) relaxometry. It reveals the self-part of the slow dynamics' spectrum. Master curves are to be understood as a result of a more extensive scaling covering all temperatures instead of strict frequency-temperature superposition. DLS and NMR display identical relaxation spectra; yet, comparing different systems, we do not find a generic structural relaxation at variance with recent claims. Dielectric spectroscopy (DS) spectra show particularities, which render master curve construction obsolete. The DS α-peak is enhanced or suppressed with respect to that of DLS or NMR, yet, not correlated to the polarity of the liquid. Attempting to single out the excess wing from the overall spectrum discloses a stronger exponential temperature dependence of its amplitude compared to that below Tg and a link between its exponent and that of the fast dynamics' spectrum. Yet, such a decomposition of α-peak and excess wing appears to be unphysical. Among many different glasses, the amplitude of the excess wing power-law spectrum is found to be identical at Tg, interpreted as a relaxation analog to the Lindemann criterion.
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Affiliation(s)
- Ernst A Rössler
- Nordbayerisches NMR Zentrum, Universität Bayreuth, 95440 Bayreuth, Germany
| | - Manuel Becher
- Nordbayerisches NMR Zentrum, Universität Bayreuth, 95440 Bayreuth, Germany
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2
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Nguyen V, Song X. Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via implementation of machine learning. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:465401. [PMID: 37531967 DOI: 10.1088/1361-648x/acecef] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Accepted: 08/02/2023] [Indexed: 08/04/2023]
Abstract
A computational approach by an implementation of the principle component analysis (PCA) withK-means and Gaussian mixture (GM) clustering methods from machine learning algorithms to identify structural and dynamical heterogeneities of supercooled liquids is developed. In this method, a collection of the average weighted coordination numbers (WCNs‾) of particles calculated from particles' positions are used as an order parameter to build a low-dimensional representation of feature (structural) space forK-means clustering to sort the particles in the system into few meso-states using PCA. Nano-domains or aggregated clusters are also formed in configurational (real) space from a direct mapping using associated meso-states' particle identities with some misclassified interfacial particles. These classification uncertainties can be improved by a co-learning strategy which utilizes the probabilistic GM clustering and the information transfer between the structural space and configurational space iteratively until convergence. A final classification of meso-states in structural space and domains in configurational space are stable over long times and measured to have dynamical heterogeneities. Armed with such a classification protocol, various studies over the thermodynamic and dynamical properties of these domains indicate that the observed heterogeneity is the result of liquid-liquid phase separation after quenching to a supercooled state.
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Affiliation(s)
- Viet Nguyen
- Ames Laboratory and Department of Chemistry, Iowa State University, Ames, IA, United States of America
| | - Xueyu Song
- Ames Laboratory and Department of Chemistry, Iowa State University, Ames, IA, United States of America
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3
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Malik S, Debnath A. Dehydration induced dynamical heterogeneity and ordering mechanism of lipid bilayers. J Chem Phys 2021; 154:174904. [PMID: 34241050 DOI: 10.1063/5.0044614] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Understanding the influence of dehydration on the membrane structure is crucial to control membrane functionality related to domain formation and cell fusion under anhydrobiosis conditions. To this end, we perform all-atom molecular dynamic simulations of 1,2-dimyristoyl-sn-glycero-3-phosphocholine dimyristoylphosphatidylcholine lipid membranes at different hydration levels at 308 K. As dehydration increases, the lipid area per head group decreases with an increase in bilayer thickness and lipid order parameters indicating bilayer ordering. Concurrently, translational and rotational dynamics of interfacial water (IW) molecules near membranes slow down. On the onset of bilayer ordering, the IW molecules exhibit prominent features of dynamical heterogeneity evident from non-Gaussian parameters and one-dimensional van Hove correlation functions. At a fully hydrated state, diffusion constants (D) of the IW follow a scaling relation, D∼τα -1, where the α relaxation time (τα) is obtained from self-intermediate scattering functions. However, upon dehydration, the relation breaks and the D of the IW follows a power law behavior as D∼τα -0.57, showing the signature of glass dynamics. τα and hydrogen bond lifetime calculated from intermittent hydrogen bond auto-correlation functions undergo a similar crossover in association with bilayer ordering on dehydration. The bilayer ordering is accompanied with an increase in fraction of caged lipids spanned over the bilayer surface and a decrease in fraction of mobile lipids due to the non-diffusive dynamics. Our analyses reveal that the microscopic mechanism of lipid ordering by dehydration is governed by dynamical heterogeneity. The fundamental understanding from this study can be applied to complex bio-membranes to trap functionally relevant gel-like domains at room temperature.
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Affiliation(s)
- Sheeba Malik
- Department of Chemistry, Indian Institute of Technology Jodhpur, Karwad, Rajasthan, India
| | - Ananya Debnath
- Department of Chemistry, Indian Institute of Technology Jodhpur, Karwad, Rajasthan, India
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4
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Scalliet C, Guiselin B, Berthier L. Excess wings and asymmetric relaxation spectra in a facilitated trap model. J Chem Phys 2021; 155:064505. [PMID: 34391365 DOI: 10.1063/5.0060408] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
In a recent computer study, we have shown that the combination of spatially heterogeneous dynamics and kinetic facilitation provides a microscopic explanation for the emergence of excess wings in deeply supercooled liquids. Motivated by these findings, we construct a minimal empirical model to describe this physics and introduce dynamic facilitation in the trap model, which was initially developed to capture the thermally activated dynamics of glassy systems. We fully characterize the relaxation dynamics of this facilitated trap model varying the functional form of energy distributions and the strength of dynamic facilitation, combining numerical results and analytic arguments. Dynamic facilitation generically accelerates the relaxation of the deepest traps, thus making relaxation spectra strongly asymmetric, with an apparent "excess" signal at high frequencies. For well-chosen values of the parameters, the obtained spectra mimic experimental results for organic liquids displaying an excess wing. Overall, our results identify the minimal physical ingredients needed to describe excess processes in the relaxation spectra of supercooled liquids.
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Affiliation(s)
- Camille Scalliet
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Benjamin Guiselin
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
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5
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Berthier L, Ediger MD. How to "measure" a structural relaxation time that is too long to be measured? J Chem Phys 2020; 153:044501. [PMID: 32752666 DOI: 10.1063/5.0015227] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It has recently become possible to prepare ultrastable glassy materials characterized by structural relaxation times, which vastly exceed the duration of any feasible experiment. Similarly, new algorithms have led to the production of ultrastable computer glasses. Is it possible to obtain a reliable estimate of a structural relaxation time that is too long to be measured? We review, organize, and critically discuss various methods to estimate very long relaxation times. We also perform computer simulations of three dimensional ultrastable hard spheres glasses to test and quantitatively compare some of these methods for a single model system. The various estimation methods disagree significantly, and non-linear and non-equilibrium methods lead to a strong underestimate of the actual relaxation time. It is not yet clear how to accurately estimate extremely long relaxation times.
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Affiliation(s)
- L Berthier
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - M D Ediger
- Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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Berthier L, Biroli G, Bouchaud JP, Tarjus G. Can the glass transition be explained without a growing static length scale? J Chem Phys 2019; 150:094501. [DOI: 10.1063/1.5086509] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), University of Montpellier, CNRS, Montpellier, France
| | - Giulio Biroli
- Institut de physique théorique, Université Paris Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette, France
- Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, PSL Research University, Sorbonne Université, 75005 Paris, France
| | | | - Gilles Tarjus
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Pl. Jussieu, 75005 Paris, France
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7
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Koperwas K, Grzybowski A, Grzybowska K, Wojnarowska Z, Sokolov AP, Paluch M. Effect of temperature and density fluctuations on the spatially heterogeneous dynamics of glass-forming Van der Waals liquids under high pressure. PHYSICAL REVIEW LETTERS 2013; 111:125701. [PMID: 24093275 DOI: 10.1103/physrevlett.111.125701] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Indexed: 06/02/2023]
Abstract
In this Letter, we show how temperature and density fluctuations affect the spatially heterogeneous dynamics at ambient and elevated pressures. By using high-pressure experimental data for van der Waals liquids, we examine contributions of the temperature and density fluctuations to the dynamics heterogeneity. We show that the dynamic heterogeneity decreases significantly with increasing pressure at a constant structural relaxation time (isochronal condition), while the broadening of the relaxation spectrum remains constant. This observation questions the relationship between spectral broadening and dynamic heterogeneity.
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Affiliation(s)
- K Koperwas
- Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland
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8
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Vargheese KD, Tandia A, Mauro JC. Origin of dynamical heterogeneities in calcium aluminosilicate liquids. J Chem Phys 2010; 132:194501. [DOI: 10.1063/1.3429880] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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9
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Kearns KL, Swallen SF, Ediger MD, Wu T, Sun Y, Yu L. Hiking down the Energy Landscape: Progress Toward the Kauzmann Temperature via Vapor Deposition. J Phys Chem B 2008; 112:4934-42. [DOI: 10.1021/jp7113384] [Citation(s) in RCA: 183] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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10
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Ediger MD, Harrowell P, Yu L. Crystal growth kinetics exhibit a fragility-dependent decoupling from viscosity. J Chem Phys 2008; 128:034709. [DOI: 10.1063/1.2815325] [Citation(s) in RCA: 236] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Dalle-Ferrier C, Thibierge C, Alba-Simionesco C, Berthier L, Biroli G, Bouchaud JP, Ladieu F, L'Hôte D, Tarjus G. Spatial correlations in the dynamics of glassforming liquids: experimental determination of their temperature dependence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:041510. [PMID: 17994997 DOI: 10.1103/physreve.76.041510] [Citation(s) in RCA: 94] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2007] [Indexed: 05/25/2023]
Abstract
We use recently introduced three-point dynamic susceptibilities to obtain an experimental determination of the temperature evolution of the number of molecules Ncorr that are dynamically correlated during the structural relaxation of supercooled liquids. We first discuss in detail the physical content of three-point functions that relate the sensitivity of the averaged two-time dynamics to external control parameters (such as temperature or density), as well as their connection to the more standard four-point dynamic susceptibility associated with dynamical heterogeneities. We then demonstrate that these functions can be experimentally determined with good precision. We gather available data to obtain the temperature dependence of Ncorr for a large number of supercooled liquids over a wide range of relaxation time scales from the glass transition up to the onset of slow dynamics. We find that Ncorr systematically grows when approaching the glass transition. It does so in a modest manner close to the glass transition, which is consistent with an activation-based picture of the dynamics in glassforming materials. For higher temperatures, there appears to be a regime where Ncorr behaves as a power-law of the relaxation time. Finally, we find that the dynamic response to density, while being smaller than the dynamic response to temperature, behaves similarly, in agreement with theoretical expectations.
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Affiliation(s)
- C Dalle-Ferrier
- Laboratoire de Chimie Physique, UMR 8000, Université Paris Sud and CNRS, Bâtiment 349, 91405 Orsay, France
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12
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Puzenko A, Ishai PB, Paluch M. Non-Debye response for the structural relaxation in glass-forming liquids: Test of the Avramov model. J Chem Phys 2007; 127:094503. [PMID: 17824744 DOI: 10.1063/1.2768962] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The experimentally observed characteristic features of the alpha-relaxation process in glass-forming liquids are the non-Arrhenius behavior of the structural relaxation times and the non-Debye character of the macroscopic relaxation function. The Avramov model in which relaxation is considered as an energy activation process of surmounting random barriers in liquid energy landscape was successfully applied to describe the temperature and pressure dependences of the macroscopic relaxation times or viscosity. In this paper, we consider the dielectric spectrum associated with Avramov model. The asymmetrical broadening of the loss spectra was found to be related directly to dispersion of the energy barrier distribution. However, it turns out that temperature dependence of the spectrum broadening as predicted by the Avromov model is at odds to experimental observation in glass-forming liquids.
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Affiliation(s)
- Alexander Puzenko
- Department of Applied Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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13
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Berthier L, Biroli G, Bouchaud JP, Kob W, Miyazaki K, Reichman DR. Spontaneous and induced dynamic fluctuations in glass formers. I. General results and dependence on ensemble and dynamics. J Chem Phys 2007; 126:184503. [PMID: 17508807 DOI: 10.1063/1.2721554] [Citation(s) in RCA: 214] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We study theoretically and numerically a family of multipoint dynamic susceptibilities that quantify the strength and characteristic length scales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments (fluctuation-dissipation relations and symmetries of relevant dynamical field theories) to relate the sensitivity of averaged two-time correlators to temperature and density to spontaneous fluctuations of the local dynamics. Our theoretical results are then compared to molecular dynamics simulations of the Newtonian, Brownian, and Monte Carlo dynamics of two representative glass-forming liquids, a fragile binary Lennard-Jones mixture, and a model for the strong glass-former silica. We justify in detail the claim made by Berthier et al. [Science 310, 1797 (2005)] that the temperature dependence of correlation functions allows one to extract useful information on dynamic length scales in glassy systems. We also discuss some subtle issues associated with the choice of microscopic dynamics and of statistical ensemble through conserved quantities, which are found to play an important role in determining dynamic correlations.
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Affiliation(s)
- L Berthier
- Laboratoire des Colloïdes, Verres et Nanomatériaux, UMR 5587, Université Montpellier II-CNRS, 34095 Montpellier, France
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14
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Berthier L, Biroli G, Bouchaud JP, Kob W, Miyazaki K, Reichman DR. Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations. J Chem Phys 2007; 126:184504. [PMID: 17508808 DOI: 10.1063/1.2721555] [Citation(s) in RCA: 146] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study in detail the predictions of various theoretical approaches, in particular, mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wave vector dependence of multipoint correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multipoint correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular, explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multipoint correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.
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Affiliation(s)
- L Berthier
- Laboratoire des Colloïdes, Verres et Nanomatériaux, UMR 5587, Université Montpellier II and CNRS, 34095 Montpellier, France
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15
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Tarzia M, Coniglio A. Lamellar order, microphase structures, and glassy phase in a field theoretic model for charged colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:011410. [PMID: 17358153 DOI: 10.1103/physreve.75.011410] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2006] [Indexed: 05/06/2023]
Abstract
In this paper we present a detailed analytical study of the phase diagram and of the structural properties of a field theoretic model with a short-range attraction and a competing long-range screened repulsion. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702 (2006). The model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions. We employ the self-consistent Hartree approximation and a replica approach, and we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales, and emphasize that the formation of microphase structures may play a prominent role in the process of colloidal gelation.
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Affiliation(s)
- Marco Tarzia
- Dipartimento di Scienze Fisiche and INFN sezione di Napoli, Università degli Studi di Napoli "Federico II," Complesso Universitario di Monte Sant'Angelo, via Cinthia, 80126 Napoli, Italy
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16
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Sharma M, Yashonath S. Breakdown of the Stokes−Einstein Relationship: Role of Interactions in the Size Dependence of Self-Diffusivity. J Phys Chem B 2006; 110:17207-11. [PMID: 16928019 DOI: 10.1021/jp064364a] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Einstein and others derived the reciprocal dependence of the self-diffusivity D on the solute radius r(u) for large solutes based on kinetic theory. We examine here (a) the range of r(u) over which Stokes-Einstein (SE) dependence is valid and (b) the precise dependence for small solutes outside of the SE regime. We show through molecular dynamics simulations that there are two distinct regimes for smaller solutes: (i) the interaction or Levitation effect (LE) regime for solutes of intermediate size and (ii) the D proportional, variant 1/r(u)(2) for still smaller solutes. We show that as the solute-solvent size ratio decreases, the breakdown in the Stokes-Einstein relationship leading to the LE regime has its origin in dispersion interaction between the solute and the solvent. These results explain reports of enhanced solute diffusion in solvents existing in the literature seen for small solutes for which no explanation exists.
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Affiliation(s)
- Manju Sharma
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012, India
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17
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Kumar SK, Szamel G, Douglas JF. Nature of the breakdown in the Stokes-Einstein relationship in a hard sphere fluid. J Chem Phys 2006; 124:214501. [PMID: 16774417 DOI: 10.1063/1.2192769] [Citation(s) in RCA: 116] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular dynamics simulations of high density hard sphere fluids clearly show a breakdown of the Stokes-Einstein equation (SE). This result has been conjectured to be due to the presence of mobile particles, i.e., ones which have the propensity to "hop" distances that are integer multiples of the interparticle distance. We conclusively show that the sedentary particles, i.e., ones complementary to the "hoppers," obey the SE relationship to a good approximation, even though the fluid as a whole violates the SE equation at high densities. These results support the notion that the unusual diffusive behavior of supercooled liquids is dominated by the hopping particles.
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Affiliation(s)
- Sanat K Kumar
- Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
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18
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Tarzia M, Coniglio A. Pattern formation and glassy phase in the phi4 theory with a screened electrostatic repulsion. PHYSICAL REVIEW LETTERS 2006; 96:075702. [PMID: 16606111 DOI: 10.1103/physrevlett.96.075702] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2005] [Indexed: 05/08/2023]
Abstract
We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar, and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.
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Affiliation(s)
- Marco Tarzia
- Dipartimento di Scienze Fisiche, INFN sezione di Napoli, Università degli Studi di Napoli Federico II, Complesso Universitario di Monte Sant' Angelo, via Cinthia, 80126 Napoli, Italy
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19
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Berthier L, Biroli G, Bouchaud JP, Cipelletti L, El Masri D, L'Hôte D, Ladieu F, Pierno M. Direct Experimental Evidence of a Growing Length Scale Accompanying the Glass Transition. Science 2005; 310:1797-800. [PMID: 16357256 DOI: 10.1126/science.1120714] [Citation(s) in RCA: 668] [Impact Index Per Article: 35.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Understanding glass formation is a challenge, because the existence of a true glass state, distinct from liquid and solid, remains elusive: Glasses are liquids that have become too viscous to flow. An old idea, as yet unproven experimentally, is that the dynamics becomes sluggish as the glass transition approaches, because increasingly larger regions of the material have to move simultaneously to allow flow. We introduce new multipoint dynamical susceptibilities to estimate quantitatively the size of these regions and provide direct experimental evidence that the glass formation of molecular liquids and colloidal suspensions is accompanied by growing dynamic correlation length scales.
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Affiliation(s)
- L Berthier
- Laboratoire des Colloïdes, Verres, et Nanomatériaux, UMR 5587, Université Montpellier II and CNRS, 34095 Montpellier, France.
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20
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Berthier L, Garrahan JP. Numerical Study of a Fragile Three-Dimensional Kinetically Constrained Model. J Phys Chem B 2005; 109:3578-85. [PMID: 16851396 DOI: 10.1021/jp045491e] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We numerically study the three-dimensional generalization of the kinetically constrained east model, the north-or-east-or-front (NEF) model. We characterize the equilibrium behavior of the NEF model in detail, measuring the temperature dependence of several quantities: alpha-relaxation time, distributions of relaxation times, dynamic susceptibility, dynamic correlation length, and four-point susceptibility. We show that the NEF model describes quantitatively experimental observations over an exceptionally wide range of time scales. We illustrate this by fitting experimental data obtained both in the mildly supercooled regime by optical Kerr effect and close to the glass transition by dielectric spectroscopy.
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Affiliation(s)
- Ludovic Berthier
- Laboratoire des Verres UMR 5587, Université Montpellier II and CNRS, 34095 Montpellier, France
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21
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Berthier L, Garrahan JP. Real space origin of temperature crossovers in supercooled liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:041201. [PMID: 14682930 DOI: 10.1103/physreve.68.041201] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2003] [Indexed: 05/24/2023]
Abstract
We show that the various crossovers between dynamical regimes observed in experiments and simulations of supercooled liquids can be explained in simple terms from the existence and statistical properties of dynamical heterogeneities. We confirm that dynamic heterogeneity is responsible for the slowing down of glass formers at temperatures well above the dynamic singularity Tc predicted by mode-coupling theory. Our results imply that activated processes govern the long-time dynamics even in the temperature regime where they are neglected by mode-coupling theory. We show that alternative interpretations based on topographic properties of the potential energy landscape are inefficient ways of describing simple physical features which are naturally accounted for within our approach. We show in particular that the reported links between mode coupling and landscape singularities do not exist.
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Affiliation(s)
- Ludovic Berthier
- Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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Garrahan JP, Chandler D. Coarse-grained microscopic model of glass formers. Proc Natl Acad Sci U S A 2003; 100:9710-4. [PMID: 12900500 PMCID: PMC187830 DOI: 10.1073/pnas.1233719100] [Citation(s) in RCA: 201] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We introduce a coarse-grained model for atomic glass formers. Its elements are physically motivated local microscopic dynamical rules parameterized by observables. Results of the model are established and used to interpret the measured behaviors of supercooled fluids approaching glass transitions. The model predicts the presence of a crossover from hierarchical super-Arrhenius dynamics at short length scales to diffusive Arrhenius dynamics at large length scales. This prediction distinguishes our model from other theories of glass formers and can be tested by experiment.
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Affiliation(s)
- Juan P Garrahan
- Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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Tanaka H. Possible resolution of the Kauzmann paradox in supercooled liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:011505. [PMID: 12935148 DOI: 10.1103/physreve.68.011505] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2003] [Indexed: 05/24/2023]
Abstract
Generally, the entropy of the supercooled liquid decreases more rapidly than that of the crystal. Thus, the former, if we extrapolate it smoothly below the glass-transition temperature T(g), becomes equal to the latter at the so-called Kauzmann temperature T(K). Further extrapolation below T(K) leads to the unphysical situation that the entropy of disordered liquid is lower than the ordered crystal, which results in the violation of the third law of thermodynamics. This is known as the "Kauzmann paradox" which has been the key problem of liquid-glass transition for a long time. Here we propose a simple resolution of the Kauzmann paradox by answering a fundamental question of how deeply we can supercool a liquid. We argue that the lower metastable limit T(LML), below which a liquid should crystallize before its structural relaxation, is located above the Kauzmann temperature T(K). Thus, the entropy crisis at T(K) is naturally avoided by crystallization. We suggest that it is dynamic heterogeneity that destabilizes a deeply supercooled "equilibrium" liquid state as well as a glassy state against crystallization. This may have a significant implication on the stability of a glassy state, which is of industrial importance in relation to the storage of glassy material.
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Affiliation(s)
- Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
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24
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Qi F, El Goresy T, Böhmer R, Döß A, Diezemann G, Hinze G, Sillescu H, Blochowicz T, Gainaru C, Rössler E, Zimmermann H. Nuclear magnetic resonance and dielectric spectroscopy of a simple supercooled liquid: 2-methyl tetrahydrofuran. J Chem Phys 2003. [DOI: 10.1063/1.1563599] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
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25
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XiaoHua Qiu and, Ediger MD. Length Scale of Dynamic Heterogeneity in Supercooled d-Sorbitol: Comparison to Model Predictions. J Phys Chem B 2002. [DOI: 10.1021/jp021888b] [Citation(s) in RCA: 114] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- XiaoHua Qiu and
- Department of Chemistry, 1101 University Avenue, University of WisconsinMadison, Madison, Wisconsin 53706
| | - M. D. Ediger
- Department of Chemistry, 1101 University Avenue, University of WisconsinMadison, Madison, Wisconsin 53706
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26
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Grousson M, Krakoviack V, Tarjus G, Viot P. Langevin dynamics of the Coulomb frustrated ferromagnet: A mode-coupling analysis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:026126. [PMID: 12241256 DOI: 10.1103/physreve.66.026126] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2002] [Indexed: 05/23/2023]
Abstract
We study the Langevin dynamics of the soft-spin, continuum version of the Coulomb-frustrated Ising ferromagnet. By using the dynamical mode-coupling approximation, supplemented by reasonable approximations for describing the equilibrium static correlation function, and the somewhat improved dynamical self-consistent screening approximation, we find that the system displays a transition from an ergodic to a nonergodic behavior. This transition is similar to that obtained in the idealized mode-coupling theory of glass-forming liquids and in the mean-field generalized spin glasses with one-step replica symmetry breaking. The significance of this result and the relation to the appearance of a complex free-energy landscape are also discussed.
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Affiliation(s)
- M Grousson
- Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France
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27
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Keyes T, Chowdhary J. Potential energy landscape and mechanisms of diffusion in liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:041106. [PMID: 12005805 DOI: 10.1103/physreve.65.041106] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2001] [Indexed: 05/23/2023]
Abstract
The mechanism of diffusion in supercooled liquids is investigated from the potential energy landscape point of view, with emphasis on the crossover from high- to low-T dynamics over the range T(A) > or =T > or =T(c). Molecular dynamics simulations with a time dependent mapping to the associated local minimum or inherent structure (IS) are performed on unit-density Lennard-Jones. Dynamical quantities introduced include r2(is)(t), the mean-square displacement (MSD) within a basin of attraction of an IS, R2(t), the MSD of the IS itself, and g(t), the distribution of IS waiting times. The configuration space is treated as a composite of the contributions of cooperative local regions, and a method is given to obtain the physically meaningful g(loc)(t) and mean waiting time tau(loc) from g(t). An understanding of the crossover is obtained in terms of r2(is)(t) and tau(loc). At intermediate T, r2(is)(t) possesses an interval of linear t dependence allowing calculation of an intrabasin diffusion constant D(is). Near T(c), where intrabasin diffusion is well established for t<tau(loc), diffusion is intrabasin dominated with D=D(is); D may be calculated within a basin. Below T(c), tau(loc) exceeds the time tau(pl) needed for the system to explore the basin, indicating the action of barriers at the border; tau(loc)=tau(pl) is a criterion for transition to activated hopping. Intrabasin diffusion provides a means of confinement not involving barriers and plays a key role in the dynamics above T(c). The distinction is discussed between motion among the IS (IS dynamics) below T(c) and saddle or border dynamics above T(c), where the system is always close to one of the saddle barriers connecting the basins and IS boundaries are closely spaced and easily crossed. A border index is introduced based upon the relation of R2(t) to the conventional MSD, and shown to vanish at T approximately T(c). It is proposed that intrabasin diffusion is a manifestation of saddle dynamics.
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Affiliation(s)
- T Keyes
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
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28
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Affiliation(s)
- Daniel Kivelson
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Gilles Tarjus
- Laboratoire de Physique Theorique des Liquides, Universite P. et M. Curie, 4 Place Jussieu, Paris 75005, France
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29
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Reinsberg SA, Qiu XH, Wilhelm M, Spiess HW, Ediger MD. Length scale of dynamic heterogeneity in supercooled glycerol near Tg. J Chem Phys 2001. [DOI: 10.1063/1.1369160] [Citation(s) in RCA: 161] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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30
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Alba-Simionesco C. Salient properties of glassforming liquids close to the glass transition. ACTA ACUST UNITED AC 2001. [DOI: 10.1016/s1296-2147(01)01165-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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31
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Demirjian BG, Dosseh G, Chauty A, Ferrer ML, Morineau D, Lawrence C, Takeda K, Kivelson D, Brown S. Metastable Solid Phase at the Crystalline-Amorphous Border: The Glacial Phase of Triphenyl Phosphite. J Phys Chem B 2001. [DOI: 10.1021/jp000765t] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Berj George Demirjian
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Gilberte Dosseh
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Aude Chauty
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Maria-Luisa Ferrer
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Denis Morineau
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Christopher Lawrence
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Kiyoshi Takeda
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Daniel Kivelson
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095
| | - Stuart Brown
- Department of Physics, University of California, Los Angeles, California 90095
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