Excitations are localized and relaxation is hierarchical in glass-forming liquids

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.

15 pages, 6 figures, + links to movies; To appear in Phys. Rev. X

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