Does a Growing Static Length Scale Control the Glass Transition?

Abstract

Several theories of the glass transition propose that the structural relaxation time τα is controlled by a growing static length scale ξ that is determined by the free energy landscape but not by the local dynamical rules governing its exploration. We argue, based on recent simulations using particle-radius-swap dynamics, that only a modest factor in the increase in τα on approach to the glass transition may stem from the growth of a static length, with a vastly larger contribution attributable instead to a slowdown of local dynamics. This reinforces arguments that we base on the observed strong coupling of particle diffusion and density fluctuations in real glasses.PACS numbers: 64.70. Pf, When a liquid is cooled sufficiently rapidly to avoid crystallization, its viscosity η increases. In general, η ≃ Gτ α , where G is the (plateau) shear modulus and τ α characterizes the relaxation time of density fluctuations. As the temperature T is lowered, G evolves mildly but τ α increases by about 15 order of magnitude [1] until, at the transition temperature T G , it becomes too large to measure experimentally. The liquid then becomes a glass, and falls out of equilibrium. Near the glass transition, the diffusion of a tagged particle also becomes very slow. The characteristic time τ D over which a particle diffuses its own radius increases, albeit not as much as τ α . The decoupling of these two quantities (referred to as the Stokes-Einstein breakdown) is significant, but comparatively mild: the ratio S = τ α /τ D is increased by only a few orders of magnitude at T G [2,3].The dependence of τ α on T is used to classify glassy liquids [4]. Writing τ α = τ 0 exp(E/k B T ) where τ 0 is a vibrational time scale (in the picosecond range) and E some activation energy, one finds that E is constant in some liquids, called strong, but increases up to a factor 5 under cooling in other liquids, called fragile. Fragility is best shown in the 'Angell plot' of log(τ α ) vs. T G /T [4], which is linear for strong liquids but highly curved for fragile ones. Quantitatively, fragility is defined as There are competing explanations of the increase in the activation energy E in fragile liquids, which occurs with no obvious change of static structure [5]. Several theories, including the Adam-Gibbs scenario [6], Random First Order Theory (RFOT) [7][8][9], and those involving locally favored structures [10,11], posit that the increase in E stems from the growth of a purely static length scale ξ, characterizing some 'hidden order' in the many-body free-energy landscape that is not captured by traditional probes of static structure such as pair correlations.In particular, in modern interpretations of RFOT [7,8], ξ is a 'point-to-set' correlation length set by the minimum scale on which alternative packings are available to a patch of fluid whose environment is held frozen. Shorter scale motions do cross local barriers, but cannot discover a new pattern for the density which keeps returning to its initial state. In this view, regardless of how r...

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