Exploring the complex free-energy landscape of the simplest glass by rheology

Abstract

For amorphous solids, it has been intensely debated whether the traditional view on solids, in terms of the ground state and harmonic low energy excitations on top of it, such as phonons, is still valid. Recent theoretical developments of amorphous solids revealed the possibility of unexpectedly complex free-energy landscapes where the simple harmonic picture breaks down. Here we demonstrate that standard rheological techniques can be used as powerful tools to examine nontrivial consequences of such complex free-energy landscapes. By extensive numerical simulations on a hard sphere glass under quasistatic shear at finite temperatures, we show that above the so-called Gardner transition density, the elasticity breaks down, the stress relaxation exhibits slow, and ageing dynamics and the apparent shear modulus becomes protocol-dependent. Being designed to be reproducible in laboratories, our approach may trigger explorations of the complex free-energy landscapes of a large variety of amorphous materials.

Mean-field stability map of hard-sphere glasses

“…Remarkably, the phase diagrams shown in Fig. 1 are qualitatively similar to those obtained in numerical simulations of three-dimensional systems [38,39], for which we also note that for increasing preparation density ϕ g , the values of the yield strain γ Y and the yield stress increase as well. The main qualitative difference is the shape of the shear jamming and shear yielding curves in the vicinity of the critical point where they merge, which might be explained by RSB effects.…”

“…Furthermore, the theory has been extended to hard sphere with a short range attraction [33], to investigate a peculiar two-step yielding transition that characterizes colloidal systems [34]. These predictions, obtained in the mean-field d → ∞ limit, have been partially confirmed by extensive numerical simulations in d = 3 [35][36][37][38][39] and experiments on a granular material in d = 2 [40].…”

Gardner physics in amorphous solids and beyond

“…In particular, around jamming it is found that µ(∆ EA ) ∼ P κ while µ(∆ < ∆ EA ) ∼ P µ(∆ EA ), hence a dramatic softening should be observed if the system is allowed to leave the glass state in which it was prepared. This theoretical prediction for d → ∞ systems has been verified numerically 111,125…”

Hierarchical Landscape of Hard Disk Glasses

“…On the other hand, it is unlikely that a Gardner phase can exist in dimensions as low as d = 2, where jamming criticality remains similar to the one in d = ∞ [15,16,18,21], suggesting that the Gardner transition, in itself, is not needed for a theory to capture the jamming criticality. Resolving this paradox is important, as mean-field theory can be used to tackle a large number of physical questions from a fully microscopic perspective, such as thermodynamic properties [4,19,[22][23][24], the structure of phase space, the evolution of vibrational dynamics [25,26], or the rheology of hard sphere glasses [27][28][29]. In addition, it is also important to understand under which conditions a complex free energy landscape may become physically relevant, in order to make novel predictions for experimental work dealing with the glassy dynamics of granular, colloidal, and molecular systems.…”