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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 〈 G 〉 scales with pressure P as 〈 G 〉 ∼ P β , with β ≈ 0.75 for jammed packings of deformable particles with zero bending energy. In contrast, β ≈ 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.
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The role of deformability in determining the structural and mechanical properties of bubbles and emulsions
We perform computational studies of jammed particle packings in two dimensions undergoing isotropic compression using the well-characterized soft particle (SP) model and deformable particle (DP) model that we developed for bubbles and emulsions. In the SP model, circular particles are allowed to overlap, generating purely repulsive forces. In the DP model, particles minimize their perimeter, while deforming at the fixed area to avoid overlap during compression. We compare the structural and mechanical properties of jammed packings generated using the SP and DP models as a function of the packing fraction ρ, instead of the reduced number density φ. We show that near jamming onset the excess contact number Δz=z-z J and shear modulus G scale as Δρ 0.5 in the large system limit for both models, where Δρ=ρ-ρ J and z J ≈4 and ρ J ≈0.842 are the values at jamming onset. Δz and G for the SP and DP models begin to differ for ρ≥0.88. In this regime, Δz∼G can be described by a sum of two power-laws in Δρ, i.e. Δz∼G∼C 0 Δρ 0.5 +C 1 Δρ 1.0 to lowest order. We show that the ratio C 1 /C 0 is much larger for the DP model compared to that for the SP model. We also characterize the void space in jammed packings as a function of ρ. We find that the DP model can describe the formation of Plateau borders as ρ→1.0. We further show that the results for z and the shape factor A versus ρ for the DP model agree with recent experimental studies of foams and emulsions.
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- PAR ID:
- 10099328
- Date Published:
- Journal Name:
- Soft Matter
- ISSN:
- 1744-683X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/C9SM00775J
