Lennard-Jones binary mixture: A thermodynamical approach to glass transition

Coluzzi, Barbara; Parisi, G.; Verrocchio, P.

doi:10.1063/1.480866

Cited by 87 publications

(131 citation statements)

References 43 publications

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“…Equation (29) has since been shown, however, to be an excellent approximation also for several models with attraction, including the KABLJ mixture. [53][54][55] This was regarded as a bit of a mystery, but can now be understood as a consequence of the fact that dynamics and heat capacity of strongly correlating liquids are well reproduced by a corresponding IPL system 54 -a consequence of the hidden scale invariance of strongly correlating liquids discussed briefly in the introduction (see Papers I-III). Figure 13 tests the Rosenfeld-Tarazona prediction for the systems investigated in Fig.…”

Section: B An Approximate Equation Of State For Generalized Lj Systemsmentioning

confidence: 99%

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

Schrøder

Gnan

Pedersen

et al. 2011

The Journal of Chemical Physics

114

115

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This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the N V T ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.

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Section: B An Approximate Equation Of State For Generalized Lj Systemsmentioning

confidence: 99%

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

Schrøder

Gnan

Pedersen

et al. 2011

The Journal of Chemical Physics

114

115

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“…On the basis of the free energy functional calculation for hard spheres, Rosenfeld and Tarazona 68 showed that the temperature dependence of the potential energy of liquids can be described by U(T) ∼ T 3/5 . In a number of simulations, 7,9,49,69,70 this theoretical prediction has been found to hold for sufficiently low T values. The potential energy for our system is also well represented by the form…”

Section: S(t)mentioning

confidence: 94%

Spatially Heterogeneous Dynamics and the Adam−Gibbs Relation in the Dzugutov Liquid

et al. 2005

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We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the RosenfeldTarazona T 3/5 law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S conf , a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S conf and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to S conf , and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S conf . We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late--relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TS conf , in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S conf may be a consequence of the fact that the clusters are composed of strings.

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“…By using this method it was possible to solve a large number of models where some of the ideas and tools (e.g., configurational entropy, entropy crisis, mode coupling equations) can be treated in an explicit and unified way (56). The method also allows analytic computations of properties of glasses at low temperature for hard and soft spheres, where the whole low-temperature phase diagram can be obtained by using simple integral equations such as generalized hypernetted chain (HNC) equations (57)(58)(59)(60)(61).…”

Section: Structural Fragile Glassesmentioning

confidence: 99%

Spin glasses and fragile glasses: Statics, dynamics, and complexity

Parisi

2006

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

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In this paper I will briefly review some theoretical results that have been obtained in recent years for spin glasses and fragile glasses. I will concentrate my attention on the predictions coming from the so called broken replica symmetry approach and on their experimental verifications. I will also mention the relevance or these results for other fields, and in general for complex systems.broken replica symmetry ͉ complex systems ͉ nonequilibrium ͉ taxonomy S pin glasses have been intensively studied in the last 30 years. They are very interesting for many reasons:Y Spin glasses are the simplest example of glassy systems. There is a highly nontrivial mean field approximation that can be used to derive some of the main properties of glassy systems, e.g., history-dependent response (1-3); this property, in the context of mean field approximation, is related to the existence of many equilibrium states. (Much ink has been used to discuss the precise mathematical meaning of this last sentence; for a careful discussion see refs. 4 and 5.) Y The study of spin glasses opens an important window for studying off-equilibrium behavior. Aging (6) and the related violations of the equilibrium fluctuation dissipation relations emerge in a natural way and they can be studied in a simple setting (7-10). Many of the ideas developed in this context can be used in other physical fields such as fragile glasses, colloids, granular materials and combinatorial optimization problems (and also for other complex systems). Y The theoretical concepts and the tools developed in the study of spin glasses are based on two logically equivalent, but very different methods: the algebraic broken replica symmetry method and the probabilistic cavity approach. They have a wide domain of applications. Some of the properties that appear in the mean field approximation, such as ultrametricity, are unexpected and counterintuitive. Y Spin glasses also provide a testing ground for a more mathematically inclined probabilistic approach: the rigorous proof of the correctness of the solution of the mean field model came out after 20 years of efforts where new ideas [e.g., stochastic stability (11-13)], and new variational principles (14, 15) were at the basis of a recent rigorous proof (16).In this paper I will present a short review of some of the results that have been obtained by using this approach. General ResultsThe simplest spin glass Hamiltonian is of the form:where the Js are quenched (i.e., time independent) random variables located on the links connecting two points of the lattice and the s are Ising variables (i.e., Ϯ1). The total number of points is denoted with N and it goes to infinity in the thermodynamic limit. We can consider four models of increasing complexity:Y The Sherrington-Kirkpatrick (SK) model (17) As far as the free energy is concerned, one can prove the following rigorous results:The SK model is thus a good starting point for studying also the finite-dimensional case with short-range interaction, which is the most realistic and d...

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Lennard-Jones binary mixture: A thermodynamical approach to glass transition

Cited by 87 publications

References 43 publications

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

Spatially Heterogeneous Dynamics and the Adam−Gibbs Relation in the Dzugutov Liquid

Spin glasses and fragile glasses: Statics, dynamics, and complexity

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