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Excitations Are Localized and Relaxation Is Hierarchical in Glass-Forming Liquids

Aaron S. Keys

Lester O. Hedges

Juan P. Garrahan

Sharon C. Glotzer

David Chandler*

  • Department of Chemistry, University of California, Berkeley, California 94720, USA, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA, and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA

  • Department of Chemistry, University of California, Berkeley, California 94720, USA, and Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

  • School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom

  • Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA, and Department of Materials Science Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA

  • Department of Chemistry, University of California, Berkeley, California 94720, USA

  • *Corresponding author. chandler@berkeley.edu
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Phys. Rev. X 1, 021013 – Published 30 November, 2011Erratum Phys. Rev. X 1, 029901 (2011)

DOI: https://doi.org/10.1103/PhysRevX.1.021013

Abstract

For several atomistic models of glass formers, at conditions below their glassy-dynamics–onset temperatures, To, we use importance sampling of trajectory space to study the structure, statistics, and dynamics of excitations responsible for structural relaxation. Excitations are detected in terms of persistent particle displacements of length a. At supercooled conditions, for a of the order of or smaller than a particle diameter, we find that excitations are associated with correlated particle motions that are sparse and localized, occupying a volume with an average radius that is temperature-independent and no larger than a few particle diameters. We show that the statistics and dynamics of these excitations are facilitated and hierarchical. Excitation-energy scales grow logarithmically with a. Excitations at one point in space facilitate the birth and death of excitations at neighboring locations, and space-time excitation structures are microcosms of heterogeneous dynamics at larger scales. This nature of dynamics becomes increasingly dominant as temperature T is lowered. We show that slowing of dynamics upon decreasing temperature below To is the result of a decreasing concentration of excitations and concomitantly growing length scales for dynamical correlations that develop in a hierarchical manner, and further that the structural-relaxation time τ follows the parabolic law, log(τ/τo)=J2(1/T−1/To)2, for T<To, where J, τo and To can be predicted quantitatively from dynamics at short time scales. Particle motion is facilitated and directional, and we show that this becomes more apparent with decreasing T. We show that stringlike motion is a natural consequence of facilitated, hierarchical dynamics.

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6 December, 2011

23 December, 2011

Erratum

Publisher’s Note: Excitations are localized and relaxation is hierarchical in glass-forming liquids [Phys. Rev. X 1, 021013 (2011)]

Aaron S. Keys, Lester O. Hedges, Juan P. Garrahan, Sharon C. Glotzer, and and David Chandler
Phys. Rev. X 1, 029901 (2011)

Popular Summary

Supercooling a viscous liquid fast enough leads to the formation of a glass, a material that is mechanically rigid, like crystalline solids, but structurally amorphous, similar to liquids. Our understanding of the molecular processes underlying the glass formation has remained uncertain. Manifestations of the complexity and cooperativity of these processes include stretched exponential decay of time-correlation functions and precipitous slowing of dynamics upon cooling, with relaxation times growing faster than exponentials of reciprocal temperature. Theoretical treatments of the glass structure and dynamics fall into two classes. In one, originating from Adam and Gibbs’s work in 1965, a supercooled liquid is pictured as a mosaic of nearly rigid domains that cannot move or change shape or size without moving all the atoms within the same domain; relaxation follows from collective reorganization of atoms within these so-called “cooperative rearranging regions.” In the other, dating back to Glarum’s work in 1960, the material contains a gas of point-like excitations or local soft spots comprising only a few atoms or molecules; relaxation follows from hierarchical dynamics in which these defects facilitate the creation and destruction of neighboring excitations. In the former case, dynamics slows because mosaic domains grow, while in the latter, dynamics slows because excitation separations grow. There is support for both perspectives, and possibly the two can be related, but the most basic underlying features—the cooperative regions in the former and localized excitations in the latter—have yet to be demonstrated. Here, we show that the latter emerges from Newtonian dynamics.

We do so by considering the molecular dynamics of several different atomistic models for glass-forming liquids in both two and three dimensions. For each, we ask the question: How does an atom move between distinct neighboring positions separated by a length a? We are able to answer this question by augmenting standard but extensive numerical simulation with methods of importance sampling of trajectory space. Our findings show that, in glass-forming liquids, microscopic dynamics on one microscopic scale is a microcosm of dynamics on larger scales, much as imagined in the 1980s by P. W. Anderson and co-workers. The specific nature of the hierarchy we elucidate allows us to establish a universal class of models that accurately predict the behaviors of glass-forming liquids.

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Outline

Information

Phys. Rev. X 1, 021013– Published 30 November, 2011
  • Received 19 July 2011
  • Corrected 6 December 2011
  • Publisher error corrected 23 December 2011
Article part of CHORUS
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