Fitting of viscosity: Distinguishing the temperature dependences predicted by various models of supercooled liquids

Kivelson, Daniel; Tarjus, Gilles; Zhao, Xiaolin; Kivelson, Steven

doi:10.1103/physreve.53.751

Cited by 138 publications

(185 citation statements)

References 32 publications

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“…Analysis of the temperature dependence of E(T ) will allow us to make contact with previous work based on effective activation energies, 45 and to discuss the variation of fragility in a way more convenient for highlighting the role of the PES (Sec. IV).…”

Section: Effective Activation Energiesmentioning

confidence: 99%

“…(3) is not expected to hold exactly around T * . 45 In the inset of the upper plot of Fig. 3, the fragility parameter B is shown as a function of size ratio for AMLJ-λ mixtures.…”

Section: Effective Activation Energiesmentioning

confidence: 99%

“…(3), we proceed as suggested by Kivelson et al. 45 First we fit the high temperature portion of our data (T > T onset ) to an Arrhenius law τ ∞ exp [E ∞ /T ] and then we use τ ∞ and E ∞ as fixed parameters in global a fit of our simulation data to Eq. (3).…”

Section: Effective Activation Energiesmentioning

confidence: 99%

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Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface

Coslovich

Pastore

2007

The Journal of Chemical Physics

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We numerically investigated the connection between isobaric fragility and the properties of highorder stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes. Such an increase is sharper, the more fragile is the mixture. Correlations between fragility and other properties of high-order stationary points, including the vibrational density of states and the localization features of unstable modes, are also discussed.

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Section: Effective Activation Energiesmentioning

confidence: 99%

“…(3) is not expected to hold exactly around T * . 45 In the inset of the upper plot of Fig. 3, the fragility parameter B is shown as a function of size ratio for AMLJ-λ mixtures.…”

Section: Effective Activation Energiesmentioning

confidence: 99%

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Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface

Coslovich

Pastore

2007

The Journal of Chemical Physics

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“…Such results have been obtained by fitting viscosity data on a number of fragile glass-forming liquids to a formula with three constants. 39 We have used the same formula to fit our Q ͑T͒ result given in Fig. 15, thereby determining the values of the three constants ͑T ‫ء‬ , B, and E ϱ in Ref.…”

Section: Appendix B: Activation Barrier Determinationmentioning

confidence: 99%

Computing the viscosity of supercooled liquids

Kushima

Lin

et al. 2009

The Journal of Chemical Physics

136

184

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We describe an atomistic method for computing the viscosity of highly viscous liquids based on activated state kinetics. A basin-filling algorithm allowing the system to climb out of deep energy minima through a series of activation and relaxation is proposed and first benchmarked on the problem of adatom diffusion on a metal surface. It is then used to generate transition state pathway trajectories in the potential energy landscape of a binary Lennard-Jones system. Analysis of a sampled trajectory shows the system moves from one deep minimum to another by a process that involves high activation energy and the crossing of many local minima and saddle points. To use the trajectory data to compute the viscosity we derive a Markov Network model within the Green-Kubo formalism and show that it is capable of producing the temperature dependence in the low-viscosity regime described by molecular dynamics simulation, and in the high-viscosity regime (10(2)-10(12) Pa s) shown by experiments on fragile glass-forming liquids. We also derive a mean-field-like description involving a coarse-grained temperature-dependent activation barrier, and show it can account qualitatively for the fragile behavior. From the standpoint of molecular studies of transport phenomena this work provides access to long relaxation time processes beyond the reach of current molecular dynamics capabilities. In a companion paper we report a similar study of silica, a representative strong liquid. A comparison of the two systems gives insight into the fundamental difference between strong and fragile temperature variations. We describe an atomistic method for computing the viscosity of highly viscous liquids based on activated state kinetics. A basin-filling algorithm allowing the system to climb out of deep energy minima through a series of activation and relaxation is proposed and first benchmarked on the problem of adatom diffusion on a metal surface. It is then used to generate transition state pathway trajectories in the potential energy landscape of a binary Lennard-Jones system. Analysis of a sampled trajectory shows the system moves from one deep minimum to another by a process that involves high activation energy and the crossing of many local minima and saddle points. To use the trajectory data to compute the viscosity we derive a Markov Network model within the Green-Kubo formalism and show that it is capable of producing the temperature dependence in the low-viscosity regime described by molecular dynamics simulation, and in the high-viscosity regime ͑10 2 -10 12 Pa s͒ shown by experiments on fragile glass-forming liquids. We also derive a mean-field-like description involving a coarse-grained temperature-dependent activation barrier, and show it can account qualitatively for the fragile behavior. From the standpoint of molecular studies of transport phenomena this work provides access to long relaxation time processes beyond the reach of current molecular dynamics capabilities. In a companion paper we report a similar study of ...

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“…An open question, triggered by this marked change, is whether transport parameters reflect an underlying phase transition to a state in which quantities become infinite (a "dynamic divergence") (3). In the presence of conflicting opinions (4)(5)(6)(7)(8)(9), many models and theories have been developed that focus on the temperature dependence of transport parameters of liquids in their supercooled phase in particular, ηðTÞ. The corresponding behaviors are often characterized by a super-Arrhenius (SA) behavior, which differs from the wellknown Arrhenius equation (AE: ln η∕η 0 ¼ E∕k B T) by the presence of an upward curvature in the T dependence.…”

mentioning

confidence: 99%

Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature

Mallamace

Branca

Corsaro

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

210

233

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It is becoming common practice to partition glass-forming liquids into two classes based on the dependence of the shear viscosity η on temperature T . In an Arrhenius plot, ln η vs 1∕T , a strong liquid shows linear behavior whereas a fragile liquid exhibits an upward curvature [super-Arrhenius (SA) behavior], a situation customarily described by using the Vogel-Fulcher-Tammann law. Here we analyze existing data of the transport coefficients of 84 glassforming liquids. We show the data are consistent, on decreasing temperature, with the onset of a well-defined dynamical crossover η × , where η × has the same value, η × ≈ 10 3 Poise, for all 84 liquids. The crossover temperature, T × , located well above the calorimetric glass transition temperature T g , marks significant variations in the system thermodynamics, evidenced by the change of the SA-like T dependence above T × to Arrhenius behavior below T × . We also show that below T × the familiar Stokes-Einstein relation D∕T ∼ η −1 breaks down and is replaced by a fractional form D∕T ∼ η −ζ , with ζ ≈ 0.85. dynamical arrest | dynamic transition | supercooled liquids

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Fitting of viscosity: Distinguishing the temperature dependences predicted by various models of supercooled liquids

Cited by 138 publications

References 32 publications

Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface

Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface

Computing the viscosity of supercooled liquids

Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature

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