(746c) [Invited Talk] Quantifying Dynamic Heterogeneity of Glasses: Percolation Perspective

Authors: 
Kofke, D. A., University at Buffalo, The State University of New York
Moustafa, S. G., University at Buffalo, The State University of New York
Schultz, A. J., University at Buffalo, The State University of New York
Douglas, J. F., National Institute of Standards and Technology
Starr, F. W., Wesleyan University
In the dilute limit, transport properties of hard particles are given by the Boltzmann kinetic theory and their values depend explicitly on the thermodynamic properties (e.g., compressibility factor Z in the Enskog model). However, the behavior is physically different for condensed liquids (e.g., in contrast to gases, the viscosity decreases with temperature for dense systems). The essential difference is the emergence of transient caging of particles at high densities. This effect causes most atoms to stay in their cages for relatively long time (immobile), while the rest (mobile) “escape” earlier, eventually yielding non-Gaussian displacement distribution (i.e., dynamic heterogeneity) with increasing density.

At higher densities, the dynamics of some liquids (e.g., fragile) are known to slow dramatically as the system approaches a jammed state of structurally arrested molecules. At such a glassy state, the internal timescale (relaxation between two equilibrium states) becomes much larger than the observation timescale, such that the system behaves effectively as rigid (viscosity ~1E13 poise). This exceptional slowdown is manifested in a non-Arrhenius trend in diffusion and viscosity, which is believed (via both theory and experiment) to be caused by the dynamic heterogeneity phenomena. Although the dynamics of glassy systems have been long-studied, a generalized model that can work for both continuous and discontinuous potentials is still needed.

In this work, we propose a tentative phenomenological model in which viscosity (collective quantity) is directly connected to the evolution of immobile regions through single-particle metrics. This model is based on the fact that viscosity is a measure of momentum “diffusion”; in other words, how stress transports from one side of the box to the other through a medium of percolated (connected) immobile particles. Therefore, the time at which immobile particles lose percolation (percolation time) is expected to be connected to viscosity. Percolation time is still a measure of collective phenomena (percolation); therefore, the second task is to represent it in terms of simpler, single-particle, metrics (e.g., relaxation time of immobile fraction and/or clusters, and the mechanism by which this proceeds, e.g., string-like motion or something else).

In order to quantitatively show the generality of this model to describe the slow dynamics we used molecular dynamics simulation with both discontinuous (binary hard spheres; BHS) and continuous (binary Lennard-Jones; BLJ) models. For BHS, the percolation model was able to accurately reproduce the non-Arrhenius behavior of the viscosity from an onset volume fraction of approximation symbol ~0.5 to a maximum value of approximation symbol ~0.593. For LJ we used the KA and WCA models at constant densities (1.25 and 1.2, respectively), and preliminary results suggest that the temperature dependence of viscosity might also be described in the context of a percolation framework.

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