Spatial dimension and the dynamics of supercooled liquids

Abstract

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...

Communications: Comparison of activation barriers for the Johari–Goldstein and alpha relaxations and its implications

“…This possibility is consistent with the observation of Wales and associates that the connectivity of the metabasins decreases on cooling, to which they attribute the super-Arrhenius behavior of fragile liquids. 8,11 Any molecular interpretation of the JG relaxation must surely take into account the recent discovery of dynamic heterogeneity in supercooled liquids, described in a review by Ediger 25 and in some recent theoretical papers, [26][27][28][29] none of which however mentions this relaxation. This is understandable given the general impression that the JG is an intrabasin transition and thus not obviously relevant to the dynamic heterogeneity, which is concerned with the alpha relaxation and with the related diffusion coefficient.…”

Slow dynamics of the high density Gaussian core model

“…The best way to verify the mean-field scenario would be to take the mean-field limit by either going to higher dimensions or making the system's interactions longerranged. Recently, simulations for four dimensional systems have been performed [10,16]. Results therein hint that the dynamic heterogeneities are suppressed compared with three dimensional systems and agreement with MCT moderately improves [10].…”

Isomorph invariance of the structure and dynamics of classical crystals

“…For many years the LJ potential has been the standard pair potential for theoretical studies of liquids [17][18][19] . It is also the most widely computer-simulated potential, because it has become a standard building block in molecular models and models of complex systems like biomembranes and large biomolecules 20,21 .…”