Relationship between thermodynamics and dynamics of supercooled liquids

Mittal, Jeetain; Errington, Jeffrey R.; Truskett, Thomas M.

doi:10.1063/1.2336197

Cited by 108 publications

(45 citation statements)

References 24 publications

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“…The excess entropy S 2 describes the contribution of two-point correlations to the total entropy of the system. It has been found that S 2 agrees very well with the total entropy in different systems including some models of water (43,44).…”

Section: Relation Of Tetrahedral Entropy To Translational Order Paramsupporting

confidence: 64%

A tetrahedral entropy for water

Kumar

Buldyrev

Stanley

2009

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

104

124

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We introduce the space-dependent correlation function C Q (r) and time-dependent autocorrelation function C Q (t) of the local tetrahedral order parameter Q ≡ Q(r, t). By using computer simulations of 512 waterlike particles interacting through the transferable interaction potential with five points (TIP5 potential), we investigate C Q (r) in a broad region of the phase diagram. We find that at low temperatures C Q (t) exhibits a two-step time-dependent decay similar to the self-intermediate scattering function and that the corresponding correlation time τ Q displays a dynamic cross-over from non-Arrhenius behavior for T > T W to Arrhenius behavior for T < T W , where T W denotes the Widom temperature where the correlation length has a maximum as T is decreased along a constant-pressure path. We define a tetrahedral entropy S Q associated with the local tetrahedral order of water molecules and find that it produces a major contribution to the specific heat maximum at the Widom line. Finally, we show that τ Q can be extracted from S Q by using an analog of the Adam-Gibbs relation.specific heat of water | orientational entropy of tetrahedral liquids | anomalies of liquid water | Widom line I t has long been appreciated that the local structure around a molecule of liquid water arising from the vertices formed by four nearest neighbors is approximately tetrahedral at ambient pressure and that the degree of tetrahedrality increases when water is cooled (1-5). An important advance occurred in the past 10 years when computer simulations allowed the quantification of the degree of tetrahedrality (6-10) by assigning to each molecule a local tetrahedral order parameter Q (11-16). At high temperatures, the probability distribution P(Q, T) is bimodal, with one peak corresponding to a high degree of tetrahedrality and the other to a less tetrahedral environment (Fig. 1). Upon decreasing temperature, the peak associated with a high degree of tetrahedrality grows, suggesting that the local structure of water becomes much more tetrahedral at lower temperatures (13,14,17). IntroductionWater has been hypothesized to belong to the class of polymorphic liquids, phase separating-at sufficiently low temperatures and high pressures-into two distinct liquid phases: a high density liquid (HDL) with smaller Q and a low density liquid (LDL) with larger Q (18). The coexistence line separating these two phases may terminate at a liquid-liquid (LL) critical point, above which (in the LL supercritical region) appears a line of correlation length maximum in the pressure-temperature plane. The locus of maximum correlation length in the one-phase region is called the Widom line T W ≡ T W (P) (19), near which different response functions, such as isobaric specific heat C P and isothermal compressibility K T , display maxima. Recent neutron-scattering experiments (20) and computer simulations (19) show that the dynamics of water gradually cross over from being non-Arrhenius for T > T W to Arrhenius for T < T W .Although dynamic heterogeneities h...

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Section: Relation Of Tetrahedral Entropy To Translational Order Paramsupporting

confidence: 64%

A tetrahedral entropy for water

Kumar

Buldyrev

Stanley

2009

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

104

124

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“…Interestingly, this was suggested by Bestul and Chang 96 in a paper preceding Adam-Gibbs by one year, which showed data consistent with a universal value of the excess entropy at the glass transition for several liquids. Much more recently, Truskett and co-workers 97 suggested that the excess entropy S ex controls the relaxation time in the spirit of Rosenfeld 76,77 scaling; this is also consistent with isomorph invariance. As a final example of a theory where entropy controls the relaxation time, consider the random first-order transition ͑RFOT͒ theory of Wolynes and co-worker ͑reviewed in Ref.…”

Section: Cause Of the Non-arrhenius Relaxation Time: The "Isomorph Fimentioning

confidence: 61%

Pressure-energy correlations in liquids. IV. “Isomorphs” in liquid phase diagrams

Gnan

Schrøder

Pedersen

et al. 2009

The Journal of Chemical Physics

343

847

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This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the phase diagram. A number of thermodynamic, static, and dynamic isomorph invariants are identified. These include the excess entropy, the isochoric specific heat, reduced-unit static and dynamic correlation functions, as well as reduced-unit transport coefficients. The dynamic invariants apply for both Newtonian and Brownian dynamics. It is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed. Selected isomorph predictions are validated by computer simulations of the Kob-Andersen binary Lennard-Jones mixture, which is a strongly correlating liquid. The final section of the paper relates the isomorph concept to phenomenological melting rules, Rosenfeld's excess entropy scaling, Young and Andersen's approximate scaling principle, and the two-order parameter maps of Debenedetti and co-workers. This section also shows how the existence of isomorphs implies an "isomorph filter" for theories for the non-Arrhenius temperature dependence of viscous liquids' relaxation time, and it explains isochronal superposition for strongly correlating viscous liquids.

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“…Deviations from this linear relation were already reported in supercooled liquids 38,65,66 , alkanes at high densities 37 and water 39,42 . In this work, we use a third order polynomial, where the second and third order terms account for deviations from the linear behaviour that we found when applying Eqs.…”

Section: Viscosity Based On Group Contributionsmentioning

confidence: 75%

Group Contribution Method for Viscosities Based on Entropy Scaling Using the Perturbed-Chain Polar Statistical Associating Fluid Theory

Lötgering-Lin

Groß

2015

Ind. Eng. Chem. Res.

128

201

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In this work we propose a new predictive entropy-scaling approach for Newtonian shear viscosities based on group contributions. The approach is based on Rosenfeld's original work [Y. Rosenfeld, Phys. Rev. A 1977, 15, 2545 -2549. The entropy scaling is formulated as third order polynomial in terms of the residual entropy as calculated from a group-contribution perturbed chain polar statistical associating fluid theory (PCP-SAFT) equation of state. In this study we analyze the course of entropy scaling parameters within homologous series and suggest suitable mixing rules for the parameters of functional groups. The viscosity of non-polar, of polar, and of selfassociating (hydrogen bonding) components are considered. In total 22 functional groups are parametrized to viscosity data of 110 pure substances, from 12 different chemical families. The mean absolute relative deviations (MADs) to experimental

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Relationship between thermodynamics and dynamics of supercooled liquids

Cited by 108 publications

References 24 publications

A tetrahedral entropy for water

A tetrahedral entropy for water

Pressure-energy correlations in liquids. IV. “Isomorphs” in liquid phase diagrams

Group Contribution Method for Viscosities Based on Entropy Scaling Using the Perturbed-Chain Polar Statistical Associating Fluid Theory

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