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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. 

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. 

Abstract Flexible, compliant permeation barrier layers are critically needed in the optics/optoelectronics industry to protect deformable, polymer‐based optical elements, such as those found in variable focus lenses. To address these needs, a transparent and deformable polymeric permeation barrier coating consisting of poly(1H,1H,6H,6H‐perfluorohexyl diacrylate) (pPFHDA) is prepared by initiated chemical vapor deposition. pPFHDA is a highly crosslinked fluoropolymer, which is deposited onto temperature‐sensitive elastomeric membranes at ambient temperature with high uniformity and conformality. This is believed to be the first demonstration of vapor deposition of the PFHDA monomer. Coatings with thicknesses nominally ranging from 200 to 750 nm are prepared and shown to be impermeable to high‐index optical fluid (polyphenyl thioether) over 2 months at 70 °C, which translates to more than 4 year lifespan at room temperature, even after being subjected to 0.26% biaxial strain. Moreover, due to its amorphous nature, the pPFHDA is transparent from wavelengths of 300–1690 nm and also thermally stable to temperatures of 300 °C. These properties should make pPFHDA coating a particularly compelling candidate for flexible optical/optoelectronic devices requiring transparent and compliant barrier layers.