Irreversible reorganization in a supercooled liquid originates from localized soft modes

Abstract

The transition of a fluid to a rigid glass upon cooling is a common route of transformation from liquid to solid that embodies the most poorly understood features of both phases 1,2,3 . From the liquid perspective, the puzzle is to understand stress relaxation in the disordered state. From the perspective of solids, the challenge is to extend our description of structure and its mechanical consequences to materials without long range order. Using computer simulations, we show that the localized low frequency normal modes of a configuration in a supercooled liquid are causally correlated to the irreversible structural reorganization of the particles within that configuration. We also demonstrate that the spatial distribution of these soft local modes can persist in spite of significant particle reorganization. The consequence of these two results is that it is now feasible to construct a theory of relaxation length scales in glass-forming liquids without recourse to dynamics and to explicitly relate molecular properties to their collective relaxation.A crucial concept 4-9 for the transition between liquid and glass is that the dramatic increase in viscosity of a supercooled liquid as it approaches vitrification is caused by the growth of localized domains of particles that must rearrange for the liquid to flow. Locating a causal link between local structure and such dynamical heterogeneities has proven elusive 10,11 .Recently, a fruitful computational approach to isolating the structural origin of dynamical heterogeneity has been put forward in the dual notions of an "isoconfigurational ensemble" and "propensity for motion" 12. The iso-configurational ensemble refers to the ensemble of trajectories that are run from an identical configuration of particles with random initial momenta sampled from the equilibrium Boltzmann distribution. Propensity refers to the mean squared displacement of individual particles when averaged over the ensemble at a given time scale. The heterogeneous character and increased clustering exhibited in the spatial propensity maps established that the spatial distribution of these dynamic heterogeneities can be explicitly attributed to structural features, as yet unidentified.Our goal is to understand that aspect of dynamic heterogeneity directly associated with structural relaxation. To this end we are interested in motions that a) involve local reorganisation of particle configurations (here measured in terms of changes in nearest neighbour pairings 13 ) and b) are irreversible over some observation time 14 and, hence, contribute to relaxation. To investigate this we consider a two dimensional binary

The jamming scenario—an introduction and outlook

“…1.8(b) shows that for sphere packings, the low-frequency quasilocalized modes have the lowest energy barriers and that the energy barriers decreases systematically with frequency and participation ratio. This result, together with previous observations [54][55][56], should have important consequences for the dynamics and instabilities that occur as the temperature is raised from zero, the system is compressed, or a shear stress is applied. One would expect these modes to shift downwards to zero frequency under the last two circumstances [57] and to give rise to highly heterogeneous deformations in the sample.…”

“…1.18. Experiments in granular materials [142] and numerical observations of normal modes of the energy of inherent structures [56,143,144] reach similar conclusions. The normal modes of the free energy considered here are expected to correlate with the dynamics much better than those of the energy, and must be considered in particular when the interaction potential is strongly non-linear.…”

“…1.6.1). This view has been explored in model glasses [56], which have also shown that the structural rearrangements occurring at finite temperatures were along low-frequency normal modes, which in that case were quasi-localized. Fig.…”

“…However, the failure often occurs in the form of rather localized rearrangement events rather than via a longrange catastrophic collapse [56,58,59]. Since the system goes unstable when the frequency of a mode reaches zero, it is possible to identify a rearrangement with the lowest-frequency mode just before the rearrangement [113].…”

“…The corresponding excitations, the anomalous modes, allow one to understand several seemingly disparate anomalies in glasses and granular materials in a coherent fashion. The picture advanced in this review suggests that (1) the length scale l * corresponding to the crossover characterizes force propagation in granular packings [26,27], (2) the frequency scale of the crossover corresponds to that of the boson peak in glasses [11,17,24,126], (3) the low-energy diffusivity of the modes above the crossover is responsible for the mild linear increase of the thermal conductivity with temperature above the plateau in glasses [34,39,40], (4) at least for colloidal glasses, the microscopic structure is marginally stable toward anomalous modes [55,140], (5) the modes appear to govern structural rearrangements in liquids at least in the viscosity range that can be probed numerically [54][55][56]and (6) the structure of the modes corresponds to that of structural arrangements in amorphous solids under mechanical load [44,148]. At the linear level those excitations and their consequences are now becoming rather well-understood theoretically for sphere packings, with the notable exception of (i) the observed quasi-localization of the lowest-frequency anomalous modes [44,45] and (ii) the apparently fractal statistics of force propagation below the cut-off length ℓ * above which continuum elasticity applies.…”