Experimental study of random-close-packed colloidal particles

Dense random packing of disks with a power-law size distribution in thermodynamic limit

The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases infinitely, while the mean density of the disk centers and the range of the size distribution are kept constant. We investigate the structure factor dependence on momentum transfer across various number of disks and extrapolate these findings to the thermodynamic limit. The fractal power-law decay of the structure factor is recovered in reciprocal space within the fractal range, which corresponds to the range of the size distribution in real space. The fractal exponent coincides with the exponent of the power-law size distribution as was shown previously by the authors of the work of Cherny et al. [J. Chem. Phys. 158(4), 044114 (2023)]. The dependence of the structure factor on density is examined. As is found, the power-law exponent remains unchanged but the fractal range shrinks when the packing fraction decreases. Additionally, the finite-size effects are studied at extremely low momenta of the order of the inverse system size. We show that the structure factor is parabolic in this region and calculate the prefactor analytically. The obtained results reveal fractal-like properties of the packing and can be used to analyze small-angle scattering from such systems.

A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem

It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the densest packing. Here, our combined experimental and simulation study provides a physical realization of the finite sphere packing problem by studying arrangements of colloids in a flaccid lipid vesicle. We map out a state diagram displaying linear, planar, and cluster conformations of spheres, as well as bistable states which alternate between cluster-plate and plate-linear conformations due to membrane fluctuations. Finally, by systematically analyzing truncated polyhedral packings, we identify clusters of 56 ≤ N ≤ 70 number of spheres, excluding N = 57 and 63, that pack more efficiently than linear arrangements.

Fractal dimensions of jammed packings with power-law particle size distributions in two and three dimensions

Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent -β. The static structure factor exhibits diverging power-law behavior for small wave numbers, allowing us to identify a structural fractal dimension d_{f}. In three dimensions, d_{f}≈2.0 for 2.5≤β≤3.8, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find 1.0≲d_{f}≲1.34 for 2.1≤β≤2.9. Furthermore, we show that the fractal behavior persists when rattler particles are removed, indicating that the long-wavelength structural properties of the packings are controlled by the large particle backbone conferring mechanical rigidity to the system. A numerical scheme for computing structure factors for triclinic unit cells is presented and employed to analyze the jammed packings.

Finite-size effects in the static structure factor S(k) and S(0) for a two-dimensional Yukawa liquid

Finite-size effects in the static structure factor S(k) are analyzed for an amorphous substance. As the number of particles is reduced, S(0) increases greatly, up to an order of magnitude. Meanwhile, there is a decrease in the height of the first peak S_{peak}. These finite-size effects are modeled accurately by the Binder formula for S(0) and our empirical formula for S_{peak}. Procedures are suggested to correct for finite-size effects in S(k) data and in the hyperuniformity index H≡S(0)/S_{peak}. These principles generally apply to S(k) obtained from particle positions in noncrystalline substances. The amorphous substance we simulate is a two-dimensional liquid, with a soft Yukawa interaction modeling a dusty plasma experiment.

Intermediate-range order governs dynamics in dense colloidal liquids

The conventional wisdom is that liquids are completely disordered and lack nontrivial structure beyond nearest-neighbor distances. Recent observations have upended this view and demonstrated that the microstructure in liquids is surprisingly rich and plays a critical role in numerous physical, biological, and industrial processes. However, approaches to uncover this structure are either system-specific or yield results that are not physically intuitive. Here, through single-particle resolved three-dimensional confocal microscope imaging and the use of a recently introduced four-point correlation function, we show that bidisperse colloidal liquids have a highly nontrivial structure comprising alternating layers with icosahedral and dodecahedral order, which extends well beyond nearest-neighbor distances and grows with supercooling. By quantifying the dynamics of the system on the particle level, we establish that it is this intermediate-range order, and not the short-range order, which has a one-to-one correlation with dynamical heterogeneities, a property directly related to the relaxation dynamics of glassy liquids. Our experimental findings provide a direct and much sought-after link between the structure and dynamics of liquids and pave the way for probing the consequences of this intermediate-range order in other liquid state processes.

Cross over to collective rearrangements near the dry-wet transition in two-dimensional foams

Liquid foams respond plastically to external perturbations over some critical magnitude. This rearrangement process is directly related to the mechanical properties of the foams, playing a significant role in determining foam lifetime, deformability, elasticity, and fluidity. In this paper, we experimentally investigate the rearrangement dynamics of foams near a dry-wet transition. When a foam transforms from a dry state to a wet state, it is found that considering collective events, separated T1 events propagate in dry foams, while T1 events occur simultaneously in wet foams. This cross over to collective rearrangements is closely related to the change in local bubble arrangements and mobility. Furthermore, it is also found that a probability of collective rearrangement events occurring follows a Poisson distribution, suggesting that there is little correlation between discrete collective rearrangement events. These results constitute progress in understanding the dynamical properties of soft jammed systems, relevant for biological and material sciences as well as food science.

Mixing properties of bi-disperse ellipsoid assemblies: mean-field behaviour in a granular matter experiment

The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical relationship for mixture distributions to explain the observations of an extensive X-ray computed tomography study of granular ellipsoidal packings. We study a size-bi-disperse mixture of two types of ellipsoids of revolutions that have the same aspect ratio of α ≈ 0.57 and differ in size, by about 10% in linear dimension, and compare these to mono-disperse systems of ellipsoids with the same aspect ratio. Jammed configurations with a range of packing densities are achieved by employing different tapping protocols. We numerically interrogate the final packing configurations by analyses of the local packing fraction distributions calculated from the Voronoi diagrams. Our main finding is that the bi-disperse ellipsoidal packings studied here can be interpreted as a mixture of two uncorrelated mono-disperse packings, insensitive to the compaction protocol. Our results are consolidated by showing that the local packing fraction shows no correlation beyond their first shell of neighbours in the binary mixtures. We propose a model of uncorrelated binary mixture distribution that describes the observed experimental data with high accuracy. This analysis framework will enable future studies to test whether the observed mean-field behaviour is specific to the particular granular system or the specific parameter values studied here or if it is observed more broadly in other bi-disperse non-spherical particle systems.

Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids

Especially small values of the static structure factor S(k) at long wavelengths, i.e., small k, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of S(k) data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of S(k) at small k is typically in a range 0.02-0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that S(k) at small k generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of S(0), so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

Random Close Packing as a Dynamical Phase Transition

Sphere packing is an ancient problem. The densest packing is known to be a face-centered cubic (FCC) crystal, with space-filling fraction ϕ_{FCC}=π/sqrt[18]≈0.74. The densest "random packing," random close packing (RCP), is yet ill defined, although many experiments and simulations agree on a value ϕ_{RCP}≈0.64. We introduce a simple absorbing-state model, biased random organization (BRO), which exhibits a Manna class dynamical phase transition between absorbing and active states that has as its densest critical point ϕ_{c_{max}}≈0.64≈ϕ_{RCP} and, like other Manna class models, is hyperuniform at criticality. The configurations we obtain from BRO appear to be structurally identical to RCP configurations from other protocols. This leads us to conjecture that the highest-density absorbing state for an isotropic biased random organization model produces an ensemble of configurations that characterizes the state conventionally known as RCP.

Dynamic evolution of hyperuniformity in a driven dissipative colloidal system

Hyperuniformity is evolving to become a unifying concept that can help classify and characterize equilibrium and nonequilibrium states of matter. Therefore, understanding the extent of hyperuniformity in dissipative systems is critical. Here, we study the dynamic evolution of hyperuniformity in a driven dissipative colloidal system. We experimentally show and numerically verify that the hyperuniformity of a colloidal crystal is robust against various lattice imperfections and environmental perturbations. This robustness even manifests during crystal disassembly as the system switches between strong (class I), logarithmic (class II), weak (class III), and non-hyperuniform states. To aid analyses, we developed a comprehensive computational toolbox, enabling real-time characterization of hyperuniformity in real- and reciprocal-spaces together with the evolution of several order metric features, and measurements showing the effect of external perturbations on the spatiotemporal distribution of the particles. Our findings provide a new framework to understand the basic principles that drive a dissipative system to a hyperuniform state.

Mechanism of transient stagnant formation in convection of binary mixtures

Two-dimensional convection rolls are usually stable near the critical Rayleigh number in single component fluids. However, in binary mixtures, it has been reported that the roll patterns become unstable over time and that stagnant domains are transiently formed. The formation of transient stagnant domains (TSD) occurs in systems where one component is more viscous than the other. Meanwhile, the mechanism of the TSD formation has been unclear yet. Here, we use experiments using well-mixed silicone oils and colloidal suspensions to show that the formation of transient stagnant regions is chiefly related to the concentration dependence of the kinematic viscosity rather than spatially averaged properties. Furthermore, we find that the concentration dependence of density is also related to the formation of stagnant regions. The coupling between density, viscosity and concentration fluctuations may play an important role for thermal convection in multi-component mixtures.

Size distribution dependence of collective relaxation dynamics in a two-dimensional wet foam

Foams can be ubiquitously observed in nature and in industrial products. Despite the relevance of their properties to deformation, fluidity, and collapse, all of which are essential for applications, there are few experimental studies of collective relaxation dynamics in a wet foam. Here, we directly observe how the relaxation dynamics changes with increasing liquid fraction in both monodisperse and polydisperse two-dimensional foams. As we increase the liquid fraction, we quantitatively characterize the slowing-down of the relaxation, and the increase of the correlation length. We also find two different relaxation modes which depend on the size distribution of the bubbles. It suggests that the bubbles which are simply near to each other play an important role in large rearrangements, not just those in direct contact. Finally, we confirm the generality of our experimental findings by a numerical simulation for the relaxation process of wet foams.

A procedure to join the force and volume ensemble statistical descriptions of granular media

Granular media consist of a large number of discrete particles interacting mostly through contact forces that, being dissipative, jeopardizes a classical statistical equilibrium approach based on energy. Instead, two independent equilibrium statistical descriptions have been proposed: the Volume Ensemble and the Force Network Ensemble. Hereby, we propose a procedure to join them into a single description, using Discrete Element simulations of a granular medium of monodisperse spheres in the limit state of isotropic compression as testing ground. By classifying grains according to the number of faces of the Voronoï cells around them, our analysis establishes an empirical relationship between that number of faces and the number of contacts on the grain. In addition, a linear relationship between the number of faces of each Voronoï cell and the number of elementary cells proposed by T. Aste and T. Di Matteo in 2007 is found. From those two relations, an expression for the total entropy (volumes plus forces) is written in terms of the contact number, an entropy that, when maximized, gives an equation of state connecting angoricity (the temperature-like variable for the force network ensemble) and compactivity (the temperature-like variable for the volume ensemble). So, the procedure establishes a microscopic connection between geometry and mechanics and, constitutes a further step towards building a complete statistical theory for granular media in equilibrium.

X-ray nanotomography of dry colloidal packings

Random packings are crucial in understanding arrangement and geometry of particles. Random packings of dry small particles may be subject to adhesion or friction, as expected theoretically and numerically. We explore experimentally random packings of dry colloids with X-ray nanotomography that directly provides three-dimensional structural and geometric information of dry colloidal packings. We find that dry colloidal packings, as characterized by contact number and packing density, are quite consistent with adhesive loose packings that significantly deviate from random loose packings for hard spheres. This study may offer direct evidence for adhesive loose packings comprising dry small particles, as proven by X-ray nanotomography.

Structure and dynamics in suspensions of soft core-shell colloids in the fluid regime

We report on a detailed experimental study of the structure and short-time dynamics in fluid-regime suspensions of soft core-shell spherical particles with different molecular weights of the chains forming the soft outer shell, and therefore different degrees of particle softness, using 3D dynamic light scattering (3D-DLS). Owing to the particle softness, the liquid-crystal coexistence regime is found to be broader than that of hard-sphere (HS) suspensions. Static light scattering in the dilute regime yields form factors that can be described using a spherical core-shell model and second virial coefficients A₂ > 0 indicative of purely repulsive interactions. The particle-particle interactions are longer ranged for all considered systems except those of the smaller molecular weight chain grafted particles which show a HS-like behavior. 3D-DLS experiments in the concentrated regime up to the liquid-crystal transition provide the short-time diffusion function, D(q), in a broad range of scattering wavenumbers, q, from which the structural (cage) and short-time self-diffusion coefficients D(q_m) and D_S = D(q ≫ q_m), respectively, are deduced as functions of the effective particle volume fraction, ϕ = c/c^*, where c^* is the overlap concentration, calculated using the hydrodynamic particle radius, R_H. The size of the nearest-neighbor cage of particles is characterized by 2π/q_m, with D(q) and the static structure factor S(q) attaining at q_m the smallest and largest values, respectively. Experimental data of D(q_m) and D_S are contrasted with analytic theoretical predictions based on a simplifying hydrodynamic radius model where the internal hydrodynamic structure of the core-shell particles is mapped on a single hydrodynamic radius parameter γ = R_H/R_eff, for constant direct interactions characterized by an (effective) hard-core radius R_eff. The particle softness is reflected, in particular, in the corresponding shape of the static structure factor, while the mean solvent (Darcy) permeability of the particles related to γ is reflected in the dynamic properties only. For grafted particles with longer polymer chains, D(q_m) and D_S are indicative of larger permeability values while particles with shorter chains are practically nonpermeable. The particle softness is also evident in the effective random close packing fraction estimated from the extrapolated zero-value limit of the cage diffusion coefficient D(q_m).

Entropy-driven docosahedral short-range order in simple liquids and glasses

The energetically favored icosahedral structure has been seen as the central figure for describing the local structure of simple liquids and glasses. Although regular icosahedral structures are rarely found, it is accepted that distorted icosahedral structures occur in simple liquids and glasses. However, which local structure dominates and why it is more frequent than the others remain unanswered questions. In this study, by using a recently developed structure descriptor, we show that docosahedral structures are the most favored not only in models of simple liquids and glasses but also in an experimental colloid glass. We also show that the the predominance of docosahedral structures is entropy-driven. Our findings represent a significant milestone towards comprehending mysterious phenomena such as supercooling, glass transition, and crystallization, where local structures play a key role.

Two Diverging Length Scales in the Structure of Jammed Packings

At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, ξ_{Z}, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, ξ_{f}, is associated with contact-number fluctuations in subsystems of different sizes. On scales below ξ_{f}, the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of ξ_{Z} and ξ_{f} are different and appear to be different in two and three dimensions.

On the design of random metasurface based devices

Metasurfaces are generally designed by placing scatterers in periodic or pseudo-periodic grids. We propose and discuss design rules for functional metasurfaces with randomly placed anisotropic elements that randomly sample a well-defined phase function. By analyzing the focusing performance of random metasurface lenses as a function of their density and the density of the phase-maps used to design them, we find that the performance of 1D metasurfaces is mostly governed by their density while 2D metasurfaces strongly depend on both the density and the near-field coupling configuration of the surface. The proposed approach is used to design all-polarization random metalenses at near infrared frequencies. Challenges, as well as opportunities of random metasurfaces compared to periodic ones are discussed. Our results pave the way to new approaches in the design of nanophotonic structures and devices from lenses to solar energy concentrators.

Favored local structures in amorphous colloidal packings measured by microbeam X-ray diffraction

Local structure and symmetry are keys to understanding how a material is formed and the properties it subsequently exhibits. This applies to both crystals and amorphous and glassy materials. In the case of amorphous materials, strong links between processing and history, structure and properties have yet to be made because measuring amorphous structure remains a significant challenge. Here, we demonstrate a method to quantify proportions of the bond-orientational order of nearest neighbor clusters [Steinhardt, et al. (1983) Phys Rev B 28:784-805] in colloidal packings by statistically analyzing the angular correlations in an ensemble of scanning transmission microbeam small-angle X-ray scattering (μSAXS) patterns. We show that local order can be modulated by tuning the potential between monodisperse, spherical colloidal silica particles using salt and surfactant additives and that more pronounced order is obtained by centrifugation than sedimentation. The order in the centrifuged glasses reflects the ground state order in the dispersion at lower packing fractions. This diffraction-based method can be applied to amorphous systems across decades in length scale to connect structure to behavior in disordered systems with a range of particle interactions.

Characterizing pixel and point patterns with a hyperuniformity disorder length

We introduce the concept of a "hyperuniformity disorder length" h that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of particles within a distance h from the boundary of the window. We first compute special expectations and bounds in d dimensions, and then illustrate the range of behavior of h versus window size L by analyzing several different types of simulated two-dimensional pixel patterns-where particle positions are stored as a binary digital image in which pixels have value zero if empty and one if they contain a particle. The first are random binomial patterns, where pixels are randomly flipped from zero to one with probability equal to area fraction. These have long-ranged density fluctuations, and simulations confirm the exact result h=L/2. Next we consider vacancy patterns, where a fraction f of particles on a lattice are randomly removed. These also display long-range density fluctuations, but with h=(L/2)(f/d) for small f, and h=L/2 for f→1. And finally, for a hyperuniform system with no long-range density fluctuations, we consider "Einstein patterns," where each particle is independently displaced from a lattice site by a Gaussian-distributed amount. For these, at large L,h approaches a constant equal to about half the root-mean-square displacement in each dimension. Then we turn to gray-scale pixel patterns that represent simulated arrangements of polydisperse particles, where the volume of a particle is encoded in the value of its central pixel. And we discuss the continuum limit of point patterns, where pixel size vanishes. In general, we thus propose to quantify particle configurations not just by the scaling of the density fluctuation spectrum but rather by the real-space spectrum of h(L) versus L. We call this approach "hyperuniformity disorder length spectroscopy".

Size-Dependent Localization in Polydisperse Colloidal Glasses

We have investigated concentrated suspensions of polydisperse hard spheres and have determined the dynamics and sizes of individual particles using confocal microscopy. With increasing concentration, the dynamics of the small and large particles start to differ. The large particles exhibit slower dynamics and stronger localization. Moreover, as the particle size increases, the local volume fraction ϕ_{loc} also increases. In the glass state, the localization length significantly decreases beyond ϕ_{loc}≈0.67. This suggests a link between local crowding and dynamical heterogeneities. However dynamical arrest of subpopulations seems not directly linked to a large value of ϕ_{loc}, indicating the importance of collective effects.

Dynamical transition in a jammed state of a quasi-two-dimensional foam

The states of foam are empirically classified into dry foam and wet foam by the volume fraction of the liquid. Recently, a transition between the dry foam state and the wet foam state has been found by characterizing the bubble shapes [Furuta et al., Sci. Rep. 6, 37506 (2016)2045-232210.1038/srep37506]. In the literature, it is indirectly ascertained that the transition from the dry to the wet form is related to the onset of the rearrangement of the bubbles, namely, the liquid fraction at which the bubbles become able to move to replace their positions. The bubble shape is a static property, and the rearrangement of the bubbles is a dynamic property. Thus, we investigate the relation between the bubble shape transition and the rearrangement event occurring in a collapsing process of the bubbles in a quasi-two-dimensional foam system. The current setup brings a good advantage to observe the above transitions, since the liquid fraction of the foam continuously changes in the system. It is revealed that the rearrangement of the bubbles takes place at the dry-wet transition point where the characteristics of the bubble shape change.

Large-scale structure of randomly jammed spheres

We numerically analyze the density field of three-dimensional randomly jammed packings of monodisperse soft frictionless spherical particles, paying special attention to fluctuations occurring at large length scales. We study in detail the two-point static structure factor at low wave vectors in Fourier space. We also analyze the nature of the density field in real space by studying the large-distance behavior of the two-point pair correlation function, of density fluctuations in subsystems of increasing sizes, and of the direct correlation function. We show that such real space analysis can be greatly improved by introducing a coarse-grained density field to disentangle genuine large-scale correlations from purely local effects. Our results confirm that both Fourier and real space signatures of vanishing density fluctuations at large scale are absent, indicating that randomly jammed packings are not hyperuniform. In addition, we establish that the pair correlation function displays a surprisingly complex structure at large distances, which is however not compatible with the long-range negative correlation of hyperuniform systems but fully compatible with an analytic form for the structure factor. This implies that the direct correlation function is short ranged, as we also demonstrate directly. Our results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior.

Close relationship between a dry-wet transition and a bubble rearrangement in two-dimensional foam

Liquid foams are classified into a dry foam and a wet foam, empirically judging from the liquid fraction or the shape of the gas bubbles. It is known that physical properties such as elasticity and diffusion are different between the dry foam and the wet foam. Nevertheless, definitions of those states have been vague and the dry-wet transition of foams has not been clarified yet. Here we show that the dry-wet transition is closely related to rearrangement of the gas bubbles, by simultaneously analysing the shape change of the bubbles and that of the entire foam in two dimensional foam. In addition, we also find a new state in quite low liquid fraction, which is named “superdry foam”. Whereas the shape change of the bubbles strongly depends on the change of the liquid fraction in the superdry foam, the shape of the bubbles does not change with changing the liquid fraction in the dry foam. Our results elucidate the relationship between the transitions and the macroscopic mechanical properties.

Experimental study of the relationship between local particle-size distributions and local ordering in random close packing

We experimentally study the structural properties of a sediment of size distributed colloids. By determining each particle size using a size estimation algorithm, we are able to investigate the relationship between local environment and local ordering. Our results show that ordered environments of particles tend to generate where the local particle-size distribution is within 5%. In addition, we show that particles whose size is close to the average size have 12 coordinate neighbors, which matches the coordination number of the fcc and hcp crystals. On the other hand, bcc structures are observed around larger particles. Our results represent experiments to show a size dependence of the specific ordering in colloidal systems.

Search for hyperuniformity in mechanically stable packings of frictionless disks above jamming

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction ϕ(J). For configurations with a fixed isotropic global stress tensor, we investigate the fluctuations of the local packing fraction ϕ(r) to test whether such configurations display the hyperuniformity that has been claimed to exist exactly at ϕ(J). For our configurations, generated by a rapid quench protocol, we find that hyperuniformity persists only out to a finite length scale and that this length scale appears to remain finite as the system stress decreases towards zero, i.e., towards the jamming transition. Our result suggests that the presence of hyperuniformity at jamming may be sensitive to the specific protocol used to construct the jammed configurations.

Emergent Hyperuniformity in Periodically Driven Emulsions

We report the self-organization of microfluidic emulsions into anomalously homogeneous structures. Upon periodic driving confined emulsions undergo a first-order transition from a reversible to an irreversible dynamics. We evidence that this dynamical transition is accompanied by structural changes at all scales yielding macroscopic yet finite hyperuniform structures. Numerical simulations are performed to single out the very ingredients responsible for the suppression of density fluctuations. We show that, as opposed to equilibrium systems, the long-range nature of the hydrodynamic interactions are not required for the formation of hyperuniform patterns, thereby suggesting a robust relation between reversibility and hyperuniformity which should hold in a broad class of periodically driven materials.

Rheology and dynamics of colloidal superballs

Recent advances in colloidal synthesis make it possible to generate a wide array of precisely controlled, non-spherical particles. This provides a unique opportunity to probe the role that particle shape plays in the dynamics of colloidal suspensions, particularly at higher volume fractions, where particle interactions are important. We examine the role of particle shape by characterizing both the bulk rheology and micro-scale diffusion in a suspension of pseudo-cubic silica superballs. Working with these well-characterized shaped colloids, we can disentangle shape effects in the hydrodynamics of isolated particles from shape-mediated particle interactions. We find that the hydrodynamic properties of isolated superballs are marginally different from comparably sized hard spheres. However, shape-mediated interactions modify the suspension microstructure, leading to significant differences in the self-diffusion of the superballs. While this excluded volume interaction can be captured with a rescaling of the superball volume fraction, we observe qualitative differences in the shear thickening behavior of moderately concentrated superball suspensions that defy simple rescaling onto hard sphere results. This study helps to define the unknowns associated with the effects of shape on the rheology and dynamics of colloidal solutions.

Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids

Jamming is a geometric phase transition occurring in dense particle systems in the absence of temperature. We use computer simulations to analyze the effect of thermal fluctuations on several signatures of the transition. We show that scaling laws for bulk and shear moduli only become relevant when thermal fluctuations are extremely small, and propose their relative ratio as a quantitative signature of jamming criticality. Despite the nonequilibrium nature of the transition, we find that thermally induced fluctuations and mechanical responses obey equilibrium fluctuation-dissipation relations near jamming, provided the appropriate fluctuating component of the particle displacements is analyzed. This shows that mechanical moduli can be directly measured from particle positions in mechanically unperturbed packings, and suggests that the definition of a "nonequilibrium index" is unnecessary for amorphous materials. We find that fluctuations of particle displacements are spatially correlated, and define a transverse and a longitudinal correlation length scale which both diverge as the jamming transition is approached. We analyze the frozen component of density fluctuations and find that it displays signatures of nearly hyperuniform behavior at large length scales. This demonstrates that hyperuniformity in jammed packings is unrelated to a vanishing compressibility and explains why it appears remarkably robust against temperature and density variations. Differently from jamming criticality, obstacles preventing the observation of hyperuniformity in colloidal systems do not originate from thermal fluctuations.

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

Structural characterization of submerged granular packings

We consider the impact of the effective gravitational acceleration on microstructural properties of granular packings through experimental studies of spherical granular materials saturated within fluids of varying density. We characterize the local organization of spheres in terms of contact connectivity, distribution of the Delaunay free volumes, and the shape factor (parameter of nonsphericity) of the Voronoï polygons. The shape factor gives a clear physical picture of the competition between less and more ordered domains of particles in experimentally obtained packings. As the effective gravity increases, the probability distribution of the shape factor becomes narrower and more localized around the lowest values of the shape factor corresponding to regular hexagon. It is found that curves of the pore distributions are asymmetric with a long tail on the right-hand side, which progressively reduces while the effective gravity gets stronger for lower densities of interstitial fluid. We show that the distribution of local areas (Voronoï cells) broadens with decreasing value of the effective gravity due to the formation of lose structures such as large pores and chainlike structures (arches or bridges). Our results should be particularly helpful in testing the newly developed simulation techniques involving liquid-related forces associated with immersed granular particles.

Characterization of maximally random jammed sphere packings: Voronoi correlation functions

We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.090604], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in the MRJ packings, a preliminary Voronoi topology analysis indicates the presence of strongly distorted icosahedra.

Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem

Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are "hyperuniform" (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns "multihyperuniform" because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multihyperuniformity. These findings suggest that a disordered hyperuniform pattern may represent the most uniform sampling arrangement attainable in the avian system, given intrinsic packing constraints within the photoreceptor epithelium. In addition, they show how fundamental physical constraints can change the course of a biological optimization process. Our results suggest that multihyperuniform disordered structures have implications for the design of materials with novel physical properties and therefore may represent a fruitful area for future research.

Phonon dispersion and elastic moduli of two-dimensional disordered colloidal packings of soft particles with frictional interactions

Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits in situ variation of particle packing fraction. Bulk, B, and shear, G, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio G/B with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft particles. In addition, G and B individually agree with numerical predictions for frictional particles. This remarkable level of agreement enabled us to extract an energy scale for the interparticle interaction from the individual elastic constants and to derive an approximate estimate for the interparticle friction coefficient.

Dense colloidal fluids form denser amorphous sediments

We relate, by simple analytical centrifugation experiments, the density of colloidal fluids with the nature of their randomly packed solid sediments. We demonstrate that the most dilute fluids of colloidal hard spheres form loosely packed sediments, where the volume fraction of the particles approaches in frictional systems the random loose packing limit, ϕRLP = 0.55. The dense fluids of the same spheres form denser sediments, approaching the so-called random close packing limit, ϕRCP = 0.64. Our experiments, where particle sedimentation in a centrifuge is sufficiently rapid to avoid crystallization, demonstrate that the density of the sediments varies monotonically with the volume fraction of the initial suspension. We reproduce our experimental data by simple computer simulations, where structural reorganizations are prohibited, such that the rate of sedimentation is irrelevant. This suggests that in colloidal systems, where viscous forces dominate, the structure of randomly close-packed and randomly loose-packed sediments is determined by the well-known structure of the initial fluids of simple hard spheres, provided that the crystallization is fully suppressed.

Observation and characterization of the vestige of the jamming transition in a thermal three-dimensional system

We study the dependence on the packing fraction of the pair-correlation function g(r) and particle mobility in a dense three-dimensional packing of soft colloids made of poly N-isopropyl acrylamide (pNIPAM), a thermosensitive gel. We find that g(r) for our samples is qualitatively like that of a liquid at all packing fractions. There is a peak in g(1), the height of the first peak of g(r), as a function of the packing fraction. This peak is identified as a vestige, which remains at finite temperature, of the divergence found at the jamming transition in simulations of soft frictionless spheres at zero temperature. As the density is increased, the particle dynamics slow down and near the packing fraction where there is a peak in g(1) the particles become arrested on the time scale of the experiment.

The physics of the colloidal glass transition

As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.

Measurement of wide frequency range structural microvibrations with a pocket digital camera and sub-pixel techniques

Analysis of vibrations and displacements is a hot topic in structural engineering. Although there is a wide variety of methods for vibration analysis, direct measurement of displacements in the mid and high frequency range is not well solved and accurate devices tend to be very expensive. Low-cost systems can be achieved by applying adequate image processing algorithms. In this paper, we propose the use of a commercial pocket digital camera, which is able to register more than 420 frames per second (fps) at low resolution, for accurate measuring of small vibrations and displacements. The method is based on tracking elliptical targets with sub-pixel accuracy. Our proposal is demonstrated at a 10 m distance with a spatial resolution of 0.15 mm. A practical application over a simple structure is given, and the main parameters of an attenuated movement of a steel column after an impulsive impact are determined with a spatial accuracy of 4 µm.

Substrate viscosity enhances correlation in epithelial sheet movement

The movement of the epithelium plays vital roles in the development and renewal of complex tissues, from the separation of tissues in the early embryo, to turnover in the homeostasis of the gastrointestinal mucosa. Yet, despite its importance, a clear interpretation of the mechanism for collective motion in epithelial sheets remains elusive. This interpretation is prohibited by the lack of understanding of the relationship between motion and cell-cell contact, and their mediation by the mechanical properties of the underlying substrate. To better mimic physiological substrates that have inherent viscosity, we probe this relationship using polydimethylsiloxane, a substrate whose mechanical properties can be tuned from predominantly elastic to viscous by altering its cross-linking content. We therefore characterize the comparative spatiotemporal correlations in cell velocity during the movement of an epithelial monolayer as a function of the viscoelasticity of the substrate. Our results show that high correlation in cell velocity is achieved when the substrate G''(ω) is ~0.4 × G'(ω). This correlation is driven by a balance between cell-cell contact and the adhesion and contraction of the extracellular matrix. For G'(ω) > G'(ω), this balance shifts, and contraction of the tissue drives the substrate to flow, further elevating the correlation in movement.

Incompressibility of polydisperse random-close-packed colloidal particles

We use confocal microscopy to study the compressibility of a random-close-packed sample of colloidal particles. To do this, we introduce an algorithm to estimate the size of each particle. Taking into account their sizes, we compute the compressibility of the sample as a function of wave vector q, and find that this compressibility vanishes linearly as q→0, showing that the packing structure is incompressible. The particle sizes must be considered to calculate the compressibility properly. These results also suggest that the experimental packing is hyperuniform.

Confined glassy dynamics at grain boundaries in colloidal crystals

Grain boundary (GB) microstructure and dynamics dictate the macroscopic properties of polycrystalline materials. Although GBs have been investigated extensively in conventional materials, it is only recently that molecular dynamics simulations have shown that GBs exhibit features similar to those of glass-forming liquids. However, current simulation techniques to probe GBs are limited to temperatures and driving forces much higher than those typically encountered in atomic experiments. Further, the short spatial and temporal scales in atomic systems preclude direct experimental access to GB dynamics. Here, we have used confocal microscopy to investigate the dynamics of high misorientation angle GBs in a three-dimensional colloidal polycrystal, with single-particle resolution, in the zero-driving force limit. We show quantitatively that glassy behavior is inherent to GBs as exemplified by the slowing down of particle dynamics due to transient cages formed by their nearest neighbors, non-Gaussian probability distribution of particle displacements and string-like cooperative rearrangements of particles. Remarkably, geometric confinement of the GB region by adjacent crystallites decreases with the misorientation angle and results in an increase in the size of cooperatively rearranging regions and hence the fragility of the glassy GBs.