Connections of activated hopping processes with the breakdown of the Stokes-Einstein relation and with aspects of dynamical heterogeneities

Abstract

We develop a new extended version of the mode-coupling theory (MCT) for glass transition, which incorporates activated hopping processes via the dynamical theory originally formulated to describe diffusion-jump processes in crystals. The dynamical-theory approach adapted here to glass-forming liquids treats hopping as arising from vibrational fluctuations in quasi-arrested state where particles are trapped inside their cages, and the hopping rate is formulated in terms of the Debye-Waller factors characterizing the structure of the quasi-arrested state. The resulting expression for the hopping rate takes an activated form, and the barrier height for the hopping is ``self-generated'' in the sense that it is present only in those states where the dynamics exhibits a well defined plateau. It is discussed how such a hopping rate can be incorporated into MCT so that the sharp nonergodic transition predicted by the idealized version of the theory is replaced by a rapid but smooth crossover. We then show that the developed theory accounts for the breakdown of the Stokes-Einstein relation observed in a variety of fragile glass formers. It is also demonstrated that characteristic features of dynamical heterogeneities revealed by recent computer simulations are reproduced by the theory. More specifically, a substantial increase of the non-Gaussian parameter, double-peak structure in the probability distribution of particle displacements, and the presence of a growing dynamic length scale are predicted by the extended MCT developed here, which the idealized version of the theory failed to reproduce. These results of the theory are demonstrated for a model of the Lennard-Jones system, and are compared with related computer-simulation results and experimental data.

13 pages, 5 figures

References in corpus (3)

• Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids
• Higher-order glass-transition singularities in systems with short-ranged attractive potentials
• Role of structural relaxations and vibrational excitations in the high-frequency dynamics of liquids and glasses

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• Connecting real glasses to mean-field models
• The emergence of cooperativity accompanying vitrification: Insights from density fluctuation dynamics
• Theory of Kinetically-Constrained-Models Dynamics
• Microscopic Theory of a Fluctuation-Induced Dynamical Crossover in Supercooled Liquids