Response of jammed packings to thermal fluctuations

Abstract

We focus on the response of mechanically stable (MS) packings of frictionless, bidisperse disks to thermal fluctuations, with the aim of quantifying how nonlinearities affect system properties at finite temperature. In contrast, numerous prior studies characterized the structural and mechanical properties of MS packings of frictionless spherical particles at zero temperature. Packings of disks with purely repulsive contact interactions possess two main types of nonlinearities, one from the form of the interaction potential (e.g. either linear or Hertzian spring interactions) and one from the breaking (or forming) of interparticle contacts. To identify the temperature regime at which the contact-breaking nonlinearities begin to contribute, we first calculated the minimum temperatures T cb required to break a single contact in the MS packing for both single and multiple eigenmode perturbations of the T = 0 MS packing. We find that the temperature required to break a single contact for equal velocity-amplitude perturbations involving all eigenmodes approaches the minimum value obtained for a perturbation in the direction connecting disk pairs with the smallest overlap. We then studied deviations in the constant volume specific heat CV and deviations of the average disk positions ∆r from their T = 0 values in the temperature regime T cb < T < Tr, where Tr is the temperature beyond which the system samples the basin of a new MS packing. We find that the deviation in the specific heat per particle ∆C with increasing system size. To characterize the relative strength of contact-breaking versus form nonlinearities, we measured the ratio of the average position deviations ∆r ss /∆r ds for single-and double-sided linear and nonlinear spring interactions. We find that ∆r ss /∆r ds > 100 for linear spring interactions is independent of system size. This result emphasizes that contact-breaking nonlinearities are dominant over form nonlinearities in the low temperature range T cb < T < Tr for model jammed systems.

Pressure Dependent Shear Response of Jammed Packings of Frictionless Spherical Particles

“…Studies [16] have suggested that β originates from the near-contacts represented in the divergent first peak of the radial distribution function [17] near jamming onset. However, interparticle contacts both form and break as the system is compressed above jamming onset [8]. Second, our recent studies [18] have shown that the shear modulus of individual jammed packings typically decreases with increasing p along geometrical families [19] that maintain the same contact network.…”

“…When systems are below jamming onset φ < φ J , they possess too few interparticle contacts to constrain all degrees of freedom in the system, N c < N iso c [7], and they display fluid-like properties with zero static shear modulus. In systems composed of N spherical particles with purely repulsive interactions, no static friction, and periodic boundary conditions, N iso c = dN − d + 1 [8], where d is the spatial dimension, N = N − N r , and N r is the number of rattler particles that do not belong to the force-bearing contact network [9]. A number of groups have carried out computational studies to understand the structural and mechanical properties of jammed particulate solids with φ > φ J [10][11][12][13][14].…”

Nature of excitations and defects in structural glasses

“…The minimal number of contacts required for stability is the isostatic number, which is exactly reached at the jamming transition. In the vicinity of the transition, the solid is marginally stable 2,25 : a small perturbation can remove a few contacts and destabilize the entire solid 26,27 . This geometrical feature gives rise to low-frequency collective excitations that are extremely different from phonons 21,28,29 .…”

Field Theory for Amorphous Solids

“…Recent observations of stress correlations support such unification. In simulations both of granular materials [7,8] and deeply supercooled liquids [9][10][11], the spatial shear-stress correlator has quadrapolar anisotropy and a power-law decay ∝ 1/r d in d dimensions. Similar observations have been made for strain correlations in experiment, both for colloids [12,13] and granular materials [14].…”