The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions

TL;DR

This study explores how deformable particle shape and bending energy influence the vibrational and mechanical properties of jammed packings in three dimensions, revealing significant effects on low-frequency modes and shear modulus scaling.

Contribution

It introduces a detailed model of 3D deformable particles with shape degrees of freedom and analyzes their impact on jamming properties, highlighting the role of shape and bending energy.

Findings

Deformable particles without bending energy exhibit low-frequency quartic modes.

Packings with non-zero bending energy are isostatic with no quartic modes.

Shear modulus scales with pressure as P^0.75 for zero bending energy and P^0.5 for non-zero bending energy.

Abstract

We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus $\langle G \rangle$ scales with pressure $P$ as $\langle G \rangle \sim P^{\beta}$, with $\beta \approx 0.75$ for jammed packings of deformable particles with zero bending energy. In contrast, $\beta \approx 0.5$ for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.