Unjamming in models with analytic pairwise potentials

Abstract

Canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cutoff in the interaction range. The sharp cutoff renders the potential nonanalytic but makes it possible to describe many properties of the solid in terms of the coordination number z, which has an unambiguous definition in these cases. Pairwise potentials without a sharp cutoff in the interaction range have not been studied in this context, but should in fact be considered to understand the relevance of the unjamming phenomenology in systems where such a cutoff is not present. In this work we explore two systems with such interactions: an inverse power law and an exponentially decaying pairwise potential, with the control parameters being the exponent (of the inverse power law) for the former and the number density for the latter. Both systems are shown to exhibit the characteristic features of the unjamming transition, among which are the vanishing of the shear-to-bulk modulus ratio and the emergence of an excess of low-frequency vibrational modes. We establish a relation between the pressure-to-bulk modulus ratio and the distance to unjamming in each of our model systems. This allows us to predict the dependence of other key observables on the distance to unjamming. Our results provide the means for a quantitative estimation of the proximity of generic glass-forming models to the unjamming transition in the absence of a clear-cut definition of the coordination number and highlight the general irrelevance of nonaffine contributions to the bulk modulus.

Mechanical properties of simple computer glasses

“…2), as a function of the exponent β of the inverse-power-law interactions. The shear-to-bulk moduli ratio G/K echos this nonmonotonicity: G/K decreases dramatically as β is made small, in addition to its expected decrease at large β -the limit at which the IPL model experiences an unjamming transition [28]. We have shown that the small-β decrease is due to the increasingly dominant role of the pressure in determining the shear modulus, in parallel to the decreasing role of the nonaffine, relaxation term.…”

Universal Nonphononic Density of States in 2D, 3D, and 4D Glasses

“…In a broad class of glass-forming models, referred to in what follows as 'generic' glass-forming models [29], the unjamming phenomenology is often irrelevant, as these systems dwell far away from the critical unjamming point [30]. Notwithstanding, generic model glasses still feature soft non-phononic excitations; examples of such excitations are presented in Fig.…”

Absence of Marginal Stability in a Structural Glass

“…However, molecular and metallic glasses are usually modeled by longer-ranged, continuous pair interactions for which no jamming transition takes place [1,2]. In this context, much less is known about the role of marginal stability [30], and the existence of a Gardner phase has not been established. Therefore, it is not known whether marginal stability can be used to understand the low-temperature anomalies in generic structural glasses.To address this important question, we combined theoretical and numerical analysis of the low-temperature vibrational properties of a standard model for atomic glasses.…”