Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity

TL;DR

This review explores the jamming transition in disordered particle systems, focusing on the geometric, mechanical, and scaling properties near the critical point, including effects of friction and particle shape.

Contribution

It provides a comprehensive analysis of the jamming transition, emphasizing the role of contact number, isostaticity, and the breakdown of affine assumptions in soft particle packings.

Findings

Jamming systems are marginally stable and isostatic at the transition.

Many properties scale with the distance to the jamming point.

Friction and particle shape influence contact number and proximity to jamming.

Abstract

Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can jam into a rigid, disordered state where they withstand finite shear stresses before yielding. Here we review the current understanding of the transition to jamming and the nature of the jammed state for disordered packings of particles that act through repulsive contact interactions and are at zero temperature and zero shear stress. We first discuss the breakdown of affine assumptions that underlies the rich mechanics near jamming. We then extensively discuss jamming of frictionless soft spheres. At the jamming point, these systems are marginally stable (isostatic) in the sense of constraint counting, and many geometric and mechanical properties scale with distance to this jamming point. Finally we discuss current explorations of jamming of frictional and non-spherical (ellipsoidal) particles. Both friction and asphericity tune the contact number at jamming away from the isostatic limit, but in opposite directions. This allows one to disentangle distance to jamming and distance to isostaticity. The picture that emerges is that most quantities are governed by the contact number and scale with distance to isostaticity, while the contact number itself scales with distance to jamming.