Mean-field theory, mode-coupling theory, and the onset temperature in supercooled liquids

Brumer, Yisroel; Reichman, David R.

doi:10.1103/physreve.69.041202

Cited by 93 publications

(80 citation statements)

References 39 publications

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“…Our results, together with some other recent studies [38,44,45,48,53,60,62,63,64,68], suggest that several essential features of the dynamics of supercooled liquids need to be recognized and we now list some of them.…”

Section: Discussionmentioning

confidence: 96%

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Real space origin of temperature crossovers in supercooled liquids

2003

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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 complicated and 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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Section: Discussionmentioning

confidence: 96%

“…In fact, the issue of the location of T c has been recently addressed in Ref. [64], where it was found that for a variety of systems, the temperature T c obtained from the actual MCT equations systematically coincides with the onset temperature T o discussed above.…”

Section: B Relaxation Timementioning

confidence: 99%

Real space origin of temperature crossovers in supercooled liquids

2003

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“…Our value of T * A corre-sponds well with that found from detailed mode coupling calculations 73 . As Reichmann and coworkers have pointed out 79 , structure based mode coupling calculations give a larger value of mode coupling temperature than do fits to simulation data using phenomenological mode coupling expressions. The latter phenomenological fits 73 yield a lower temperature T * M CT = 0.475.…”

Section: Displays T *mentioning

confidence: 94%

Intermolecular Forces and the Glass Transition

Hall

Wolynes

2007

J. Phys. Chem. B

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Random first order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first order transition theory, is used to treat individual glassy configurations, while the liquid phase is treated using common liquid state approximations.Free energies are calculated using liquid state perturbation theory. The transition temperature T * A , the temperature where the onset of activated behavior is predicted by mean field theory, the lower crossover temperature T * c where barrierless motions actually occur through fractal or stringy motions (corresponding to the phenomenological mode coupling transition temperature), and T * K , the Kauzmann temperature (corresponding to an extrapolated entropy crisis), are calculated in addition to T * g , the glass transition temperature that corresponds to laboratory cooling rates. Relationships between these quantities agree well with existing experimental and simulation data on van der Waals liquids. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for ∆C V and ∆C p that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the α-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.2

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“…Fig. 5 shows, as expected, that the dynamics slows down markedly when temperature is decreased below T o ≈ 1.0, which marks the onset of slow dynamics in this model [23,41]. We extract the mean relaxation time, τ (T ), via the usual relation P (τ ) = e −1 .…”

Section: A Global Dynamicsmentioning

confidence: 99%

Renormalization group study of a kinetically constrained model for strong glasses

2005

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We derive a dynamic field theory for a kinetically constrained model, based on the FredricksonAndersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d ≥ 2, the behaviour of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d = 1 its behaviour is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.

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Mean-field theory, mode-coupling theory, and the onset temperature in supercooled liquids

Cited by 93 publications

References 39 publications

Real space origin of temperature crossovers in supercooled liquids

Real space origin of temperature crossovers in supercooled liquids

Intermolecular Forces and the Glass Transition

Renormalization group study of a kinetically constrained model for strong glasses

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