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Franz S, Donati C, Parisi G, Glotzer SC
On dynamical correlations in supercooled liquids
PHILOSOPHICAL MAGAZINE B-PHYSICS OF CONDENSED MATTER STATISTICAL MECHANICS ELECTRONIC OPTICAL AND MAGNETIC PROPERTIES 79 (11-12): 1827-1831 NOV-DEC 1999
[x] We show how the growth of a dynamical correlation length and its associated susceptibility recently observed by the present authors and co-workers as T-c is approached can be understood in an appropriate theoretical framework. We discuss some predictions for these quantities in the region below T-c which have not yet been explored in numerical simulations.
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Allegrini P, Douglas JF, Glotzer SC
Dynamic entropy as a measure of caging and persistent particle motion in supercooled liquids
PHYSICAL REVIEW E 60 (5): 5714-5724 Part B, NOV 1999
[x]
View Abstract
The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature T-c. A number of methods exist for estimating the entropy of dynamical systems, and we utilize an approximation based on calculating the mean first-passage time (MFPT) for particle displacement because of its tractability and its accessibility in real and simulation measurements. The MFPT dynamic entropy S(epsilon) is defined as equal to the inverse of the average first-passage time for a particle to exit a sphere of radius epsilon. This measure of the degree of chaotic motion allows us to identify characteristic time and space scales and to quantify the increasingly correlated particle motion and intermittency occurring in supercooled liquids. In particular, we identify a "cage" size defining the scale at which the particles are transiently localized, and we observe persistent particle motion at intermediate length scales beyond the scale where caging occurs. Furthermore, we find that the dynamic entropy at the scale of one interparticle spacing extrapolates to zero as the mode-coupling temperature T-c is approached.
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Lee BP, Douglas JF, Glotzer SC
Filler-induced composition waves in phase-separating polymer blends
PHYSICAL REVIEW E 60 (5): 5812-5822 Part B, NOV 1999
[x]
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The influence of immobile tiller particles (spheres, fibers, platelets) on polymer-blend phase separation is investigated computationally using a generalization of the Cahn-Hilliard-Cook (CHC) model. Simulation shows that the selective affinity of one of the polymers for the filler surface leads to the development of concentration waves about the filler particles at sin early stage of phase separation in near critical composition blends. These "target" patterns are overtaken in late-stage phase separation by a growing "background" spinodal pattern characteristic of blends without filler particles. The Linearized CHC model is used to estimate the number of composition oscillations emanating from isolated filler particles. In far-off-critical composition blends, an "encapsulation layer" grows at the surface of the filler rather than a target pattern. The results of these simulations compare favorably with experiments on filled phase-separating ultrathin blend films in which the filler particles are immobilized on a solid substrate.
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Donati C, Glotzer SC, Poole PH, Kob W, Plimpton SJ
Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid
PHYSICAL REVIEW E 60 (3): 3107-3119 SEP 1999
[x]
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Using extensive molecular dynamics simulations of an equilibrium, glass-forming Lennard-Jones mixture, we characterize in detail the local atomic motions. We show that spatial correlations exist among particles undergoing extremely large ("mobile") or extremely small:("immobile") displacements over a suitably chosen time interval. The immobile particles form the cores of relatively compact clusters, while the mobile particles move cooperatively and form quasi-one-dimensional stringlike clusters. The strength and length scale of the correlations between mobile particles are found to grow strongly with decreasing temperature, and the mean cluster size appears to diverge near the mode-coupling critical; temperature. We show that these correlations in the particle displacements are related to equilibrium fluctuations in the local potential energy and local composition.
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Sastry S, Debenedetti PG, Stillinger FH, Schroder TB, Dyre JC, Glotzer SC
Potential energy landscape signatures of slow dynamics in glass forming liquids
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 270 (1-2): 301-308 AUG 1 1999
[x]
View Abstract
We study the properties of local potential energy minima (inherent structures') sampled by liquids at low temperatures as an approach to elucidating the mechanisms of the observed dynamical slowing down observed as the glass transition temperature is approached. This onset of slow dynamics is accompanied by the sampling of progressively deeper potential energy minima. Further, evidence is found in support of a qualitative change in the inherent structures sampled in a temperature range that includes the mode coupling critical temperature T-c, such that a separation of vibrational relaxation within inherent structure basins from that due to inter-basin transitions becomes valid at temperatures T < T-c, Average inherent structure energies do not show any qualitatively significant system size dependence.
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Lapena AM, Glotzer SC, Langer SA, Liu AJ
Effect of ordering on spinodal decomposition of liquid-crystal/polymer mixtures
PHYSICAL REVIEW E 60 (1): R29-R32 JUL 1999
[x]
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Partially phase-separated liquid-crystal/polymer dispersions display highly fibrillar domain morphologies that are dramatically different from the typical structures found in isotropic mixtures. To explain this, we numerically explore the coupling between phase ordering an phase-separation kinetics in model two-dimensional fluid mixtures phase separating into a nematic phase, rich in liquid crystal, coexisting with an isotropic phase, rich in polymer. We find that phase ordering can lead to fibrillar networks of the minority polymer-rich phase.
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Donati C, Glotzer SC, Poole PH
Growing spatial correlations of particle displacements in a simulated liquid on cooling toward the glass transition
PHYSICAL REVIEW LETTERS 82 (25): 5064-5067 JUN 21 1999
[x]
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We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show that for an equilibrium liquid this function is related to fluctuations in a bulk dynamical variable. We evaluate this function using computer simulations of an equilibrium glass-forming liquid, and show that long range spatial correlations of displacements emerge and grow on cooling toward the mode coupling critical temperature.
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Bennemann C, Donati C, Baschnagel J, Glotzer SC
Growing range of correlated motion in a polymer melt on cooling towards the glass transition
NATURE 399 (6733): 246-249 MAY 20 1999
[x]
View Abstract
Many liquids cooled to low temperatures form glasses (amorphous solids) instead of crystals. As the glass transition is approached, molecules become localized and relaxation times increase by many orders of magnitude(1). Many features of this 'slowing down' are reasonably well described(2) by the mode-coupling theory of supercooled liquids(3). The ideal form of this theory predicts a dynamical critical temperature T-c at which the molecules become permanently trapped in the 'cage' formed by their neighbours, and vitrification occurs. Although there is no sharp transition, because molecules do eventually escape their cage, its signature can still be observed in real and simulated liquids. Unlike conventional critical phenomena (such as the behaviour at the liquid-gas critical point), the mode-coupling transition is not accompanied by a diverging static correlation length. But simulation(4-10) and experiment(11,12) show that liquids are dynamically heterogeneous, suggesting the possibility of a relevant 'dynamical' length scale characterizing the glass transition. Here we use computer simulations to investigate a melt of short, unentangled polymer chains over a range of temperatures for which the mode-coupling theory remains valid. We find that although density fluctuations remain short-ranged, spatial correlations between monomer displacements become long-ranged as T-c is approached on cooling. In this way, we identify a growing dynamical correlation length, and a corresponding order parameter, associated with the glass transition. This finding suggests a possible connection between well established concepts in critical phenomena and the dynamics of glass-forming liquids.
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Glotzer SC, Donati C
Quantifying spatially heterogeneous dynamics in computer simulations of glass-forming liquids
JOURNAL OF PHYSICS-CONDENSED MATTER 11 (10A): A285-A295 MAR 15 1999
[x] We examine the phenomenon of dynamical heterogeneity in computer simulations of an equilibrium, glass-forming liquid. We describe several approaches for quantifying the spatial correlation of single-particle motion, and show that spatial correlations of particle displacements become increasingly long range as the temperature decreases toward the made-coupling critical temperature.