Rearrangements during slow compression of a jammed two-dimensional emulsion.

As amorphous materials get jammed, both geometric and dynamic heterogeneity are observed. We investigate the correlation between the local geometric heterogeneity and local rearrangements in a slowly compressed bidisperse quasi-two-dimensional emulsion system. The compression is driven by evaporation of the continuous phase and causes the area packing fraction to increase from 0.88 to 0.99. We quantify the structural heterogeneity of the system using the radical Voronoi tessellation following the method of Rieser et al. [Phys. Rev. Lett. 116, 088001 (2016)]0031-900710.1103/PhysRevLett.116.088001. We define two structural quantities characterizing local structure, the first of which considers nearest neighbors and the second of which includes information from second-nearest neighbors. We find that droplets in heterogeneous local regions are more likely to have local rearrangements. These rearrangements are generally T1 events where two droplets converge toward a void, and two droplets move away from the void to make room for the converging droplets. Thus, the presence of the voids tends to orient the T1 events. The presence of a correlation between the structural quantities and the rearrangement dynamics remains qualitatively unchanged over the entire range of packing fractions observed.

Compression and fracture of ordered and disordered droplet rafts.

We simulate a two-dimensional array of droplets being compressed between two walls. The droplets are adhesive due to an attractive depletion force. As one wall moves toward the other, the droplet array is compressed and eventually induced to rearrange. The rearrangement occurs via a fracture, where depletion bonds are quickly broken between a subset of droplets. For monodisperse, hexagonally ordered droplet arrays, this fracture is preceded by a maximum force exerted on the walls, which drops rapidly after the fracture occurs. In small droplet arrays a fracture is a single well-defined event, but for larger droplet arrays, competing fractures can be observed. These are fractures nucleated nearly simultaneously in different locations. Finally, we also study the compression of bidisperse droplet arrays. The addition of a second droplet size further disrupts fracture events, showing differences between ideal crystalline arrays, crystalline arrays with a small number of defects, and fully amorphous arrays. These results are in good agreement with previously published experiments.

Bounded distributions place limits on skewness and larger moments.

Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness D3 is bounded from below by a function of the coefficient of variation (CoV) δ as D3 > δ - 1/δ. The results are extended to any distribution that is bounded with minimum value xmin and/or bounded with maximum value xmax. We build on the results to provide bounds for kurtosis D4, and conjecture analogous bounds exists for higher statistical moments.

Effects of polydispersity on the plastic behaviors of dense two-dimensional granular systems under shear.

We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied amorphous systems with low polydispersity. In particular, an analysis of the nonaffine motion of particles reveals qualitative differences between large and small particles: The smaller particles have dramatically more nonaffine motion, which is induced by the presence of the large particles. We characterize how the nonaffine motion changes from the low- to high-polydispersity regimes. We further demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes. A macroscopic consequence of the nonaffine motion is a decrease in the energy dissipation rate for highly polydisperse samples, which is due both to a geometric consequence of the changing jamming conditions for higher polydispersity and to the changing character of nonaffine motion.

Leveraging 3D Bioprinting and Photon-Counting Computed Tomography to Enable Noninvasive Quantitative Tracking of Multifunctional Tissue Engineered Constructs.

3D bioprinting is revolutionizing the fields of personalized and precision medicine by enabling the manufacturing of bioartificial implants that recapitulate the structural and functional characteristics of native tissues. However, the lack of quantitative and noninvasive techniques to longitudinally track the function of implants has hampered clinical applications of bioprinted scaffolds. In this study, multimaterial 3D bioprinting, engineered nanoparticles (NPs), and spectral photon-counting computed tomography (PCCT) technologies are integrated for the aim of developing a new precision medicine approach to custom-engineer scaffolds with traceability. Multiple CT-visible hydrogel-based bioinks, containing distinct molecular (iodine and gadolinium) and NP (iodine-loaded liposome, gold, methacrylated gold (AuMA), and Gd2 O3 ) contrast agents, are used to bioprint scaffolds with varying geometries at adequate fidelity levels. In vitro release studies, together with printing fidelity, mechanical, and biocompatibility tests identified AuMA and Gd2 O3 NPs as optimal reagents to track bioprinted constructs. Spectral PCCT imaging of scaffolds in vitro and subcutaneous implants in mice enabled noninvasive material discrimination and contrast agent quantification. Together, these results establish a novel theranostic platform with high precision, tunability, throughput, and reproducibility and open new prospects for a broad range of applications in the field of precision and personalized regenerative medicine.

Isomorphs in sheared binary Lennard-Jones glass: Transient response.

We have studied shear deformation of binary Lennard-Jones glasses to investigate the extent to which the transient part of the stress strain curves is invariant when the thermodynamic state point is varied along an isomorph. Shear deformations were carried out on glass samples of varying stability, determined by cooling rate, and at varying strain rates, at state points deep in the glass. Density changes up to and exceeding a factor of two were made. We investigated several different methods for generating isomorphs but none of the previously developed methods could generate sufficiently precise isomorphs given the large density changes and nonequilibrium situation. Instead, the temperatures for these higher densities were chosen to give state points isomorphic to the starting state point by requiring the steady-state flow stress for isomorphic state points to be invariant in reduced units. In contrast to the steady-state flow stress, we find that the peak stress on the stress strain curve is not invariant. The peak stress decreases by a few percent for each ten percent increase in density, although the differences decrease with increasing density. Analysis of strain profiles and nonaffine motion during the transient phase suggests that the root of the changes in peak stress is a varying tendency to form shear bands, with the largest tendency occurring at the lowest densities. We suggest that this reflects the effective steepness of the potential; a higher effective steepness gives a greater tendency to form shear bands.

Hopper flows of deformable particles.

Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width w: Q ∼ (w/σavg - k)ß, where σavg is the average particle diameter, kσavg is an offset where Q ∼ 0, the power-law scaling exponent ß = d - 1/2, and d is the spatial dimension. Recent studies of hopper flows of deformable particles in different background fluids suggest that the particle stiffness and dissipation mechanism can also strongly affect the power-law scaling exponent ß. We carry out computational studies of hopper flows of deformable particles with both kinetic friction and background fluid dissipation in two and three dimensions. We show that the exponent ß varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, λ = ζ/µ. ß = d - 1/2 in the λ → 0 limit and d - 3/2 in the λ → ∞ limit, with a midpoint λc that depends on the hopper opening angle θw. We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent ß. The offset k increases with particle stiffness until k ∼ kmax in the hard-particle limit, where kmax ∼ 3.5 is larger for λ → ∞ compared to that for λ → 0. Finally, we show that the simulations of hopper flows of deformable particles in the λ → ∞ limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.

Clogging and avalanches in quasi-two-dimensional emulsion hopper flow.

We experimentally and computationally study the flow of a quasi-two-dimensional emulsion through a constricting hopper shape. Our area fractions are above jamming such that the droplets are always in contact with one another and are in many cases highly deformed. At the lowest flow rates, the droplets often clog and thus exit the hopper via intermittent avalanches. At the highest flow rates, the droplets exit continuously. The transition between these two types of behaviors is a fairly smooth function of the mean strain rate. The avalanches are characterized by a power-law distribution of the time interval between droplets exiting the hopper, with long intervals between the avalanches. Our computational studies reproduce the experimental observations by adding a flexible compliance to the system (in other words, a finite stiffness of the sample chamber). The compliance results in continuous flow at high flow rates, and allows the system to clog at low flow rates leading to avalanches. The computational results suggest that the interplay of the flow rate and compliance controls the presence or absence of the avalanches.

Soft particle clogging in two-dimensional hoppers.

We study the outflow of soft particles through quasi-two-dimensional hoppers with both experiments and simulations. The experiments utilize spheres made with hydrogel, silicone rubber, and glass. The hopper chamber has an adjustable exit width and tilt angle (the latter to control the magnitude of gravitational forcing). Our simulation mimics the experiments using purely two-dimensional soft particles with viscous interactions but no friction. Results from both simulations and experiments demonstrate that clogging is easier for reduced gravitational force or stiffer particles. For particles with low or no friction, the average number of particles in a clogging arch depends only on the ratio between hopper exit width and the mean particle diameter. In contrast, for the silicone rubber particles with larger frictional interactions, arches have more particles than the low friction cases. Additionally, an analysis of the number of particles left in the hopper when clogging occurs provides evidence for a hydrostatic pressure effect that is relevant for the clogging of soft particles, but less so for the harder (glass) or frictional (silicone rubber) particles.

Direct observation of crystal nucleation and growth in a quasi-two-dimensional nonvibrating granular system.

We study a quasi-two-dimensional macroscopic system of magnetic spherical particles settled on a shallow concave dish under a temporally oscillating magnetic field. The system reaches a stationary state where the energy losses from collisions and friction with the concave dish surface are compensated by the continuous energy input coming from the oscillating magnetic field. Random particle motions show some similarities with the motions of atoms and molecules in a glass or a crystal-forming fluid. Because of the curvature of the surface, particles experience an additional force toward the center of the concave dish. When decreasing the magnetic field, the effective temperature is decreased and diffusive particle motion slows. For slow cooling rates we observe crystallization, where the particles organize into a hexagonal lattice. We study the birth of the crystalline nucleus and the subsequent growth of the crystal. Our observations support nonclassical theories of crystal formation. Initially a dense amorphous aggregate of particles forms, and then in a second stage this aggregate rearranges internally to form the crystalline nucleus. As the aggregate grows, the crystal grows in its interior. After a certain size, all the aggregated particles are part of the crystal and after that crystal growth follows the classical theory for crystal growth.

Supramolecular DNA Photonic Hydrogels for On-Demand Control of Coloration with High Spatial and Temporal Resolution.

Hydrogels embedded with periodic arrays of nanoparticles display a striking photonic crystal coloration that may be useful for applications such as camouflage, anticounterfeiting, and chemical sensing. Dynamically generating color patterns requires control of nanoparticle organization within a polymer network on-demand, which is challenging. We solve this problem by creating a DNA hydrogel system that shows a 50 000-fold decrease in modulus upon heating by ∼10 °C. Magnetic nanoparticles entrapped within these DNA gels generate a structural color only when the gel is heated and a magnetic field is applied. A spatially controlled photonic crystal coloration was achieved by photopatterning with a near-infrared illumination. Color was "erased" by illuminating or heating the gel in the absence of an external magnetic field. The on-demand assembly technology demonstrated here may be beneficial for the development of a new generation of smart materials with potential applications in erasable lithography, encryption, and sensing.

Neglecting polydispersity degrades propensity measurements in supercooled liquids.

We conduct molecular dynamics simulations of a bidisperse Kob-Andersen (KA) glass former, modified to add in additional polydispersity. The original KA system is known to exhibit dynamical heterogeneity. Prior work defined propensity, the mean motion of a particle averaged over simulations reconstructing the initial positions of all particles but with randomized velocities. The existence of propensity shows that structure and dynamics are connected. In this paper, we study systems which mimic problems that would be encountered in measuring propensity in a colloidal glass former, where particles are polydisperse (they have slight size variations). We mimic polydispersity by altering the bidisperse KA system into a quartet consisting of particles both slightly larger and slightly smaller than the parent particles in the original bidisperse system. We then introduce errors into the reconstruction of the initial positions that mimic mistakes one might make in a colloidal experiment. The mistakes degrade the propensity measurement, in some cases nearly completely; one no longer has an iso-configurational ensemble in any useful sense. Our results show that a polydisperse sample is suitable for propensity measurements provided one avoids reconstruction mistakes.

Rheology finds distinct glass and jamming transitions in emulsions.

We study the rheology of monodisperse and bidisperse emulsions with various droplet sizes (1-2 µm diameter). Above a critical volume fraction φc, these systems exhibit solid-like behavior and a yield stress can be detected. Previous experiments suggest that for small thermal particles, rheology will see a glass transition at φc = φg ≈ 0.58; for large athermal systems, rheology will see a jamming transition at φc = φJ ≈ 0.64. However, simulations point out that at the crossover of thermal and athermal regimes, the glass and jamming transitions may both be observed in the same sample. Here we conduct an experiment by shearing four oil-in-water emulsions with a rheometer. We observe both a glass and a jamming transition for our smaller diameter droplets, and only a jamming transition for our larger diameter droplets. The bidisperse sample behaves similarly to the small droplet sample, with two transitions observed. Our rheology data are well-fit by both the Herschel-Bulkley model and the three component model. Based on the fitting parameters, our raw rheological data would not collapse onto a master curve. Our results show that liquid-solid transitions in dispersions are not universal, but depend on particle size.

Mechanical properties of 2D aggregates of oil droplets as model mono-crystals.

We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. The elastic properties of ideal mono-crystal samples are fully captured by a simple analytical model consisting of an assembly of individual capillary springs. The yielding properties of the crystal are captured with a minimal bond breaking model.

Brownian motion of ellipsoidal particles on a granular magnetic bath.

We study the Brownian motion of ellipsoidal particles lying on an agitated granular bath composed of magnetic particles. We quantify the mobility of different floating ellipsoidal particles using the mean-square displacement and the mean-square angular displacement, and relate the diffusion coefficients to the bath particle motion. In terms of the particle major radius R, we find the translational diffusion coefficient scales roughly as 1/R^{2} and the rotational diffusion coefficient scales as roughly 1/R^{4}; this is consistent with the assumption that diffusion arises from random kicks of the bath particles underneath the floating particle. By varying the magnetic forcing, the bath particles' diffusivity changes by a factor of ten; over this range, the translational and rotational diffusion of the floating particles change by a factor of 50. However, the ratio of the two diffusion constants for the floating particles is forcing-independent. Unusual aspects of the floating particle motion include non-Gaussian statistics for their displacements.

Embedded 3D Bioprinting of Gelatin Methacryloyl-Based Constructs with Highly Tunable Structural Fidelity.

Three-dimensional (3D) bioprinting of hydrogel-based constructs at adequate consistency and reproducibility can be obtained through a compromise between the hydrogel's inherent instability and printing fidelity. There is an increasing demand to develop bioprinting modalities that enable high-fidelity fabrication of 3D hydrogel structures that closely correspond to the envisioned design. In this work, we performed a systematic, in-depth characterization and optimization of embedded 3D bioprinting to create 3D gelatin-methacryloyl (gelMA) structures with highly controlled fidelity using Carbopol as suspension bath. The role of various embedded printing process parameters in bioprinting fidelity was investigated using a combination of experimental and theoretical approaches. We examined the effect of rheological properties of gelMA and Carbopol at varying concentrations, as well as printing conditions on the volumetric flow rate of gelMA bioink. Printing speed was examined and optimized to successfully print gelMA into the support bath at varying Carbopol concentrations. Printing fidelity was characterized in terms of printed strand diameter, uniformity, angle, and area. The optimal Carbopol solution that retained filament shape at highest fidelity was determined. The efficacy of developed bioprinting approach was then demonstrated by fabricating 3D hydrogel constructs with varying geometries and visualized using an advanced synchrotron-based imaging technique. We also investigated the influence of the Carbopol medium on cross-linking and the resulting stiffness of gelMA constructs. Finally, in vitro cytotoxicity of the developed bioprinting approach was assessed by printing human umbilical vein endothelial cells encapsulated in the gelMA bioink. These results demonstrate the significance of the close interplay between bioink-support bath rheology and printing parameters and help to establish an optimized workflow for creating 3D hydrogel structures with high fidelity and cytocompatibility via embedded bioprinting techniques. This robust platform could further expand the application of bioprinted soft tissue constructs in a wide variety of biomedical applications.

Visualizing free-energy landscapes for four hard disks.

We present a simple model system with four hard disks moving in a circular region for which free-energy landscapes can be directly calculated and visualized in two and three dimensions. We construct several energy landscapes for our system, and we explore the strengths and limitations of each in terms of understanding system dynamics, in particular the relationship between state transitions and free-energy barriers. We also demonstrate the importance of distinguishing between system dynamics in real space and those in landscape coordinates, and we show that care must be taken to appropriately combine dynamics with barrier properties to understand the transition rates. This simple model provides an intuitive way to understand free-energy landscapes, and it illustrates the benefits that free-energy landscapes can have over potential energy landscapes.

Isomorph invariance of dynamics of sheared glassy systems.

We study hidden scale invariance in the glassy phase of the Kob-Andersen binary Lennard-Jones system. After cooling below the glass transition, we generate a so-called isomorph from the fluctuations of potential energy and virial in the NVT ensemble: a set of density, temperature pairs for which structure and dynamics are identical when expressed in appropriate reduced units. To access dynamical features, we shear the system using the SLLOD algorithm coupled with Lees-Edwards boundary conditions and study the statistics of stress fluctuations and the particle displacements transverse to the shearing direction. We find good collapse of the statistical data, showing that isomorph theory works well in this regime. The analysis of stress fluctuations, in particular the distribution of stress changes over a given strain interval, allows us to identify a clear signature of avalanche behavior in the form of an exponential tail on the negative side. This feature is also isomorph invariant. The implications of isomorphs for theories of plasticity are discussed briefly.

Model-free 3D localization with precision estimates for brightfield-imaged particles.

Volumetric imaging and 3D particle tracking are becoming increasingly common and have a variety of microscopy applications including in situ fluorescent imaging, in-vitro single-molecule characterization, and analysis of colloidal systems. While recent interest has generated discussion of optimal schemes for localizing diffraction-limited fluorescent puncta, there have been relatively few published routines for tracking particles imaged with bright-field illumination. To address this, we outline a simple, look-up-table based 3D tracking strategy, which can be adapted to most commercially available wide-field microscopes, and present two image processing algorithms that together yield high-precision localization and return estimates of statistical accuracy. Under bright-field illumination, a particle's depth can be determined based on the size and shape of its diffractive pattern due to Mie scattering. Contrary to typical "super-resolution" fluorescence tracking routines, which typically fit a diffraction-limited spot to a model point-spread-function, the lateral (XY) tracking routine relies on symmetry to locate a particle without prior knowledge of the form of the particle. At low noise levels (signal:noise > 1000), the symmetry routine estimates particle positions with accuracy better than 0.01 pixel. Depth localization is accomplished by matching images of particles to those in a pre-recorded look-up-table. The routine presented here optimally interpolates between LUT entries with better than 0.05 step accuracy. Both routines are tolerant of high levels of image noise, yielding sub-pixel/step accuracy with signal-to-noise ratios as small as 1, and, by design, return confidence intervals indicating the expected accuracy of each calculated position. The included implementations operate extremely quickly and are amenable to real-time analysis at frame rates exceeding several hundred frames per second.

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 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 - zJ and shear modulus G scale as Δρ0.5 in the large system limit for both models, where Δρ = ρ - ρJ and zJ ≈ 4 and ρJ ≈ 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 ∼ C0Δρ0.5 + C1Δρ1.0 to lowest order. We show that the ratio C1/C0 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. 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.