Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions

Abstract

Recent literature indicates that attractive interactions between particles of a dense liquid play a secondary role in determining its bulk mechanical properties. Here we show that, in contrast with their apparent unimportance to the bulk mechanics of dense liquids, attractive interactions can have a major effect on macro-and microscopic elastic properties of glassy solids. We study several broadlyapplicable dimensionless measures of stability and mechanical disorder in simple computer glasses, in which the relative strength of attractive interactions -referred to as particle 'stickiness' -can be readily tuned. We show that increasing particle stickiness can result in the decrease of various quantifiers of mechanical disorder, both on macro-and microscopic scales, with a pair of intriguing exceptions to this rule. Interestingly, in some cases strong attractions can lead to a reduction of the number density of soft, quasilocalized modes, by up to an order of magnitude, and to a substantial decrease in their core size, similar to the effects of thermal annealing on elasticity observed in recent works. Contrary to the behavior of canonical glass models, we provide compelling evidence indicating that the stabilization mechanism in our sticky-sphere glasses stems predominantly from the self-organized depletion of interactions featuring large, negative stiffnesses. Finally, we establish a fundamental link between macroscopic and microscopic quantifiers of mechanical disorder, which we motivate via scaling arguments. Future research directions are discussed.

Mechanical disorder of sticky-sphere glasses. II. Thermo-mechanical inannealability

“…In this work we employ a 50:50 binary mixture of 'large' and 'small' particles of equal mass m in three dimensions (3D) at fixed volume V . Pairs of particles interact via the Piecewise-Sticky-Spheres (PSS) pairwise potential, introduced first in [36], and also studied extensively in the first paper [35] of this series. The equilibrium supercooled liquid dynamics of this model was very recently studied in [42].…”

“…The equilibrium supercooled liquid dynamics of this model was very recently studied in [42]. The PSS model was chosen for this study since in [35] it featured the strongest variation of elastic properties as a function of its key control parameter, which is described next.…”

“…where ε is a microscopic energy scale, x min , x c are the (dimensionless) locations of the minimum of the LJ potential and modified cutoff, respectively, and the length parameters λ ij are expressed in terms of the 'smallsmall' interaction length λ small small , with λ large small = 1.18λ small small and λ large large = 1.4λ small small . The coefficients a, b, {c 2 } can be found in [35]; they are chosen such that the attractive and repulsive parts of the potential and two derivatives are continuous at x min and at x c . The pairwise potential ϕ PSS is plotted in Fig.…”

“…In the previous paper [35] of this series, we prepared glassy samples by instantaneously quenching high temperature equilibrium liquid states; the equilibrium parent temperatures were chosen to be at least a factor of 4 higher than the computer glass transition temperature T g , defined here as the temperature at which the structural relaxation time ∼ 10 4 τ , with τ representing a characteristic vibrational time scale. As we shall see below, and as previously observed [19,[43][44][45], elastic properties and various dimensionless quantifiers of mechanical disorder exhibit a plateau above some crossover temperature, denoted in what follows as T co .…”

“…This is precisely the question we address in the present work, which is the second out of a series of reports aimed at tracing out the effects of strong, attractive interactions between the constituent particles of a glass, on that glass's mechanical disorder. In the first paper [35], we aimed at avoiding thermal annealing effects on elasticity, in order to cleanly single-out the role of strong attractive interactions in determining glasses' elastic properties, mechanical disorder and stability. In order to compare between different computer glass models on the same footing, we followed Refs.…”