Glass transitions in one-, two-, three-, and four-dimensional binary Lennard-Jones systems

Brüning, Ralf; St-Onge, Denis A.; Patterson, Steve; Kob, Walter

doi:10.1088/0953-8984/21/3/035117

Cited by 91 publications

(108 citation statements)

References 72 publications

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“…However, in two dimensions [ Fig: 2(c)], we see deviations from the AG relation for low temperatures and small system sizes. It has been reported recently that the 2D KA model is prone to orientational ordering [27], which we confirm (data not shown). It is therefore not clear to what extent these observed deviations are significant.…”

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confidence: 91%

Adam-Gibbs Relation for Glass-Forming Liquids in Two, Three, and Four Dimensions

et al. 2012

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The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in 2, 3, and 4 spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in 3 and 4 dimensions. But in 2 dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.A central theme in the study of glass forming liquids is a satisfactory understanding of the behaviour of relaxation times as the glass transition is approached, showing temperature dependence typically stronger than the Arrhenius law:, which is of central importance in glass forming liquids, explains the behaviour of the relaxation time i.e. dynamics in terms of the configurational entropy i.e. thermodynamics. It also forms the basis of more sophisticated theories of glass transition connecting dynamics to thermodynamics e.g. the random first order transition theory (RFOT) [5][6][7][8][9]. In these theories the spatial dimensionality (D) appears explicitly in the relationship between dynamics and thermodynamics. However, the large number of experimental and numerical studies wherein the AG relation has been tested [10][11][12][13][14][15][16][17] have all been in 3 dimensions. The present study aims to critically examine whether the AG relation is valid in different spatial dimensions or gets generalized in a D dependent way.The AG relation is based on the picture that relaxation in glass forming liquids occurs through the collective rearrangement of "cooperatively rearranging regions" (CRR). The CRRs define a minimum size of groups of rearranging particles (atoms, molecules etc. depending on the nature of the glass former) such that smaller groups of particles are incapable of rearrangement independently of their surroundings. Adam and Gibbs argued that the configurational entropy (the entropy associated with the multiplicity of distinct arrangements of particles, obtained by subtracting a "vibrational" component from the total entropy) per particle S c (T ) of a liquid varies inversely as the size of the CRR, z(T ), since the configurational entropy per CRR, S * , is roughly independent of temperature: S c (T ) = S * z(T ) . The further assumption that the free energy barrier for a rearrangement is proportional to the size of the CRR (∆G = zδµ, δµ = chemical potential barrier per particle) results in the Adam-Gibbs relation:The above relation is obtained independent of reference to the spatial dimensionality of the system and is hence expected to be same in all spatial dimensions. A rationalization of the AG relation, based on more detailed considerations of possible activated relaxation mechanisms, is offer...

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confidence: 91%

Adam-Gibbs Relation for Glass-Forming Liquids in Two, Three, and Four Dimensions

et al. 2012

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“…We will denote the Kob-Andersen Model in 3-dimensions as 3d KA and the slightly modified version of it for 2-dimensions as 2d mKA [30]. The pure repulsive models will be referred to as 3d R10 and 2d R10 for 3-dimensions and 2-dimensions respectively.…”

Section: Models and Methodsmentioning

confidence: 99%

Finite-size scaling for the glass transition: The role of a static length scale

Karmakar

Procaccia

2012

Phys. Rev. E

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Over the last decade computer simulations have had an increasing role in shedding light on difficult statistical physical phenomena and in particular on the ubiquitous problem of the glass transition. Here in a wide variety of materials the viscosity of a super-cooled liquid increases by many orders of magnitude upon decreasing the temperature over a modest range. A natural concern in these computer simulation is the very small size of the simulated systems compared to experimental ones, raising the issue of how to assess the thermodynamic limit. Here we offer a theory for the glass transition based on finite size scaling, a method that was found very useful in the context of critical phenomena and other interesting problems. As is known, the construction of such a theory rests crucially on the existence of a growing static length scale upon decreasing the temperature. We demonstrate that the static length scale that was discovered in Ref.[3] fits the bill extremely well, allowing us to provide a finite size scaling theory for the α relaxation time of the glass transition, including predictions for the thermodynamic limit based on simulations in small systems.

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“…Perhaps due to this costliness, only very recently have simulations of higher dimensional liquids and glassy systems been reported. For example, Bruning et al (15) have looked at thermodynamic phenomena in glassy systems of dimensionality ranging from d ϭ 2 to d ϭ 4. Van Meel et al (16) have compared nucleation phenomena in 3 and 4 dimensions.…”

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confidence: 99%

Spatial dimension and the dynamics of supercooled liquids

Eaves

Reichman

2009

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

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Inspired by recent theories that apply ideas from critical phenomena to the glass transition, we have simulated an atomistic model of a supercooled liquid in three and four spatial dimensions. At the appropriate temperatures and density, dynamic density correlation functions in three and four spatial dimensions correspond nearly exactly. Dynamic heterogeneity, quantified through the breakdown of the Stokes-Einstein relationship, is weaker in four dimensions than in three. We discuss this in the context of recent theories for dynamical heterogeneity. Because dimensionality is a crucially important variable, our work adds a stringent test for emerging theories of glassy dynamics.dynamical heterogeneity ͉ glass transition W hen a liquid is cooled rapidly below its melting point (T m ), it may form a glass instead of a crystal (1, 2). As the temperature decreases by small fractions of T m , relaxation times increase by orders of magnitude before becoming so large that it becomes impossible to keep the liquid in metastable equilibrium as cooling proceeds. Unlike the case of standard thermodynamic transitions, there are no simple structural changes that accompany this dramatic dynamical arrest (3). Indeed, the atomic structure of a glass is strikingly similar to that of the dense liquid. The approach to vitrification and the nature of the glassy state are topics of immense intellectual challenge to theorists and experimentalists alike. Because glassy dynamics have been observed in diverse fields ranging from materials science to biology, a comprehensive understanding of the glass transition will have broad and perhaps important practical consequences.Progress toward a complete theory of the glass transition is hindered by the fact that fundamentally different pictures can often explain the same phenomena. Experimental temperature and time dependent data are usually not sufficient to rule out qualitatively different theoretical approaches or scenarios. In the past decade, researchers have considered new observables that reveal the underlying physics more clearly. Dynamic heterogeneity, where the relaxation time scales of particles separated by only a few molecular diameters can differ by orders of magnitude, has now been established as a robust feature of the glass transition (4-8). The quantitative features of dynamic heterogeneity, such as scaling exponents that connect growing dynamical length scales to growing times scales, may eventually provide the key information that singles out a particular picture or theory of the glass transition as correct and complete (7,9,10).Computer simulations can test competing predictions of rival theories. In disordered magnetic systems, termed ''spin glasses,'' different pictures make different predictions for how various quantities depend on dimensionality (11-14). Clearly, dimensionality is a variable of limited range in experiments but conceptually unlimited in computer simulations. The only limitation on the study of high dimensional systems on the computer is one of computatio...

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Glass transitions in one-, two-, three-, and four-dimensional binary Lennard-Jones systems

Cited by 91 publications

References 72 publications

Adam-Gibbs Relation for Glass-Forming Liquids in Two, Three, and Four Dimensions

Adam-Gibbs Relation for Glass-Forming Liquids in Two, Three, and Four Dimensions

Finite-size scaling for the glass transition: The role of a static length scale

Spatial dimension and the dynamics of supercooled liquids

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