Excitations are localized and relaxation is hierarchical in glass-forming liquids (1107.3628v5)

Abstract: For several atomistic models of glass formers, at conditions below their glassy dynamics onset temperatures, ${T_\mathrm{o}}$, 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 $T_\mathrm{o}$ is the result of a decreasing concentration of excitations and concomitant growing hierarchical length scales, and further that the structural relaxation time $\tau$ follows the parabolic law, $\log(\tau / \tau_\mathrm{o}) = J^2(1/T - 1/T_\mathrm{o})^2$, for $T<T_\mathrm{o}$, where $J$, $\tau_\mathrm{o}$ and $T_\mathrm{o}$ can be predicted quantitatively from dynamics at short time scales. Particle motion is facilitated and directional, and we show this becomes more apparent with decreasing $T$. We show that stringlike motion is a natural consequence of facilitated, hierarchical dynamics.

• The paper demonstrates that excitations in glass-forming liquids below the onset temperature To are sparse, spatially localized, and drive a hierarchical relaxation process.
• Through importance sampling, the study shows excitations occupy a small, temperature-independent volume, and their diminishing concentration below To leads to slowing dynamics.
• The research introduces a parabolic temperature dependence for structural relaxation time, offering a robust predictive framework supported by hierarchical dynamical models (KCMs).

An Analysis of Localization and Hierarchical Dynamics in Glass-Forming Liquids

The paper in question presents a comprehensive paper of the dynamics of glass-forming liquids, focusing on the concept of excitations, or localized particle motions, and elucidating their role in the relaxation processes of these systems. Through the utilization of various atomistic models, the authors employ importance sampling of trajectory space to characterize the spatial and statistical properties of excitations at temperatures below the onset of glassy dynamics, denoted as $T_\mathrm{o}$.

The paper robustly demonstrates that excitations at supercooled conditions, measured through particle displacements, are both sparse and spatially localized. These excitations result from correlated particle motions that occupy a temperature-independent volume no larger than a few particle diameters. The authors argue that the slowing of dynamics as the system is supercooled below $T_\mathrm{o}$ is due to a diminishing concentration of these excitations and the concomitant growth of hierarchical length scales. Notably, the research finds that the structural relaxation time $\tau$ follows a parabolic temperature dependence: $$\log(\tau / \tau_\mathrm{o}) = J^2(1/T - 1/T_\mathrm{o})^2$$, where parameters such as $J$, $\tau_\mathrm{o}$, and $T_\mathrm{o}$ can be quantitatively predicted from the dynamics observed at short timescales.

Theoretical implications of these findings highlight the robust predictive capability of the parabolic law introduced, which consolidates disparate data across a variety of glass-forming systems. The logarithmic scaling of excitation energy with displacement length further supports the notion of hierarchical dynamical models, such as kinetically constrained models (KCMs), which describe excitation processes as local events stimulating dynamics in neighboring regions, leading to larger-scale excitations. This reinforces the presumption that the dynamic behavior of localized excitations is a critical facet of glassy dynamics, potentially contradicting competing theories like the Adam-Gibbs theory, which relates dynamics to growing cooperative regions.

From a practical standpoint, this paper provides invaluable insights for the understanding of the fundamental mechanisms underlying glass formation and relaxation. Through dynamic facilitation, where particle motion and excitation birth/death processes propagate hierarchically, the authors address the rich tapestry of supercooled liquid behavior without invoking traditional cooperative rearranging regions. Such findings may have considerable implications for the synthesis and stabilization of glassy materials across various applications in materials science and condensed matter physics.

In summary, this research constitutes a pivotal step in glass physics, providing quantitative tools and a theoretical framework for predicting the glass transition phenomenology. Future developments might include more detailed exploration of excitation interactions and the extension of these methods to broader classes of materials and conditions, potentially extending to higher-dimensional models and quantum glassy dynamics as well.