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

A new look at effective interactions between microgel particles

Thermoresponsive microgels find widespread use as colloidal model systems, because their temperature-dependent size allows facile tuning of their volume fraction in situ. However, an interaction potential unifying their behavior across the entire phase diagram is sorely lacking. Here we investigate microgel suspensions in the fluid regime at different volume fractions and temperatures, and in the presence of another population of small microgels, combining confocal microscopy experiments and numerical simulations. We find that effective interactions between microgels are clearly temperature dependent. In addition, microgel mixtures possess an enhanced stability compared to hard colloid mixtures - a property not predicted by a simple Hertzian model. Based on numerical calculations we propose a multi-Hertzian model, which reproduces the experimental behavior for all studied conditions. Our findings highlight that effective interactions between microgels are much more complex than usually assumed, displaying a crucial dependence on temperature and on the internal core-corona architecture of the particles.

Apparent strength versus universality in glasses of soft compressible colloids

Microgel colloids, solvent swollen hydrogel particles of microscopic size, are in osmotic equilibrium with their surroundings. This has a profound effect on the behaviour of dense solutions of these polymeric colloids, most notably their ability to swell and deswell depending on the osmotic pressure of the system as a whole. Here we develop a minimal simulation model to treat this intrinsic volume regulation in order to explore the effects this has on the properties of dense solutions close to a liquid-solid transition. We demonstrate how the softness dependent volume regulation of particles gives rise to an apparent change in the fragility of the colloidal glass transition, which can be scaled out through the use of an adjusted volume fraction that accounts for changes in particle size. Moreover, we show how the same model can be used to explain the selective deswelling of soft microgels in a crystalline matrix of harder particles leading to robust crystals free of defects. Our results not only highlight the non-trivial effects of osmotic regulation in governing the apparent physics of microgel suspensions, but also provides a platform to efficiently account for particle deswelling in simulations.

Glass transition of soft colloids

We explore the glassy dynamics of soft colloids using microgels and charged particles interacting by steric and screened Coulomb interactions, respectively. In the supercooled regime, the structural relaxation time τ_{α} of both systems grows steeply with volume fraction, reminiscent of the behavior of colloidal hard spheres. Computer simulations confirm that the growth of τ_{α} on approaching the glass transition is independent of particle softness. By contrast, softness becomes relevant at very large packing fractions when the system falls out of equilibrium. In this nonequilibrium regime, τ_{α} depends surprisingly weakly on packing fraction, and time correlation functions exhibit a compressed exponential decay consistent with stress-driven relaxation. The transition to this novel regime coincides with the onset of an anomalous decrease in local order with increasing density typical of ultrasoft systems. We propose that these peculiar dynamics results from the combination of the nonequilibrium aging dynamics expected in the glassy state and the tendency of colloids interacting through soft potentials to refluidize at high packing fractions.

Isostaticity and the solidification of semiflexible polymer melts

Using molecular dynamics simulations of a tangent-soft-sphere bead-spring polymer model, we examine the degree to which semiflexible polymer melts solidify at isostaticity. Flexible and stiff chains crystallize when they are isostatic as defined by appropriate degree-of-freedom-counting arguments. Semiflexible chains also solidify when isostatic if a generalized isostaticity criterion that accounts for the slow freezing out of configurational freedom as chain stiffness increases is employed. The configurational freedom associated with bond angles (θ) can be associated with the characteristic ratio C_∞ = (1 + 〈cos(θ)〉)/(1 - 〈cos(θ)〉). We find that the dependence of the average coordination number at solidification [Z(T_s)] on chains' characteristic ratio C_∞ has the same functional form [Z ≃ a - b ln(C_∞)] as the dependence of the average coordination number at jamming [Z(ϕ_J)] on C_∞ in athermal systems, suggesting that jamming-related phenomena play a significant role in thermal polymer solidification.

Casimir effect between pinned particles in two-dimensional jammed systems

The Casimir effect arises when long-ranged fluctuations are geometrically confined between two surfaces, leading to a macroscopic force. Traditionally, these forces have been observed in quantum systems and near critical points in classical systems. Here we show the existence of Casimir-like forces between two pinned particles immersed in two-dimensional systems near the jamming transition. We observe two components to the total force: a short-ranged, depletion force and a long-ranged, repulsive Casimir-like force. The Casimir-like force dominates as the jamming transition is approached, and when the pinned particles are much larger than the ambient jammed particles. We show that this repulsive force arises due to a clustering of particles with strong contact forces around the perimeter of the pinned particles. As the separation between the pinned particles decreases, a region of high-pressure develops between them, leading to a net repulsive force.

Single-pixel interior filling function approach for detecting and correcting errors in particle tracking

We present a general method for detecting and correcting biases in the outputs of particle-tracking experiments. Our approach is based on the histogram of estimated positions within pixels, which we term the single-pixel interior filling function (SPIFF). We use the deviation of the SPIFF from a uniform distribution to test the veracity of tracking analyses from different algorithms. Unbiased SPIFFs correspond to uniform pixel filling, whereas biased ones exhibit pixel locking, in which the estimated particle positions concentrate toward the centers of pixels. Although pixel locking is a well-known phenomenon, we go beyond existing methods to show how the SPIFF can be used to correct errors. The key is that the SPIFF aggregates statistical information from many single-particle images and localizations that are gathered over time or across an ensemble, and this information augments the single-particle data. We explicitly consider two cases that give rise to significant errors in estimated particle locations: undersampling the point spread function due to small emitter size and intensity overlap of proximal objects. In these situations, we show how errors in positions can be corrected essentially completely with little added computational cost. Additional situations and applications to experimental data are explored in SI Appendix In the presence of experimental-like shot noise, the precision of the SPIFF-based correction achieves (and can even exceed) the unbiased Cramér-Rao lower bound. We expect the SPIFF approach to be useful in a wide range of localization applications, including single-molecule imaging and particle tracking, in fields ranging from biology to materials science to astronomy.

Random three-dimensional jammed packings of elastic shells acting as force sensors

In a jammed solid of granular particles, the applied stress is in-homogeneously distributed within the packing. A full experimental characterization requires measurement of all the interparticle forces, but so far such measurements are limited to a few systems in two and even fewer in three dimensions. Particles with the topology of (elastic) shells are good local force sensors as relatively large deformations of the shells result from relatively small forces. We recently introduced such fluorescent shells as a model granular system in which force distributions can be determined in three dimensions using confocal microscopy and quantitative image analysis. An interesting aspect about these shells that differentiates them from other soft deformable particles is their buckling behavior at higher compression. This leads to deformations that do not conserve the inner volume of the particle. Here we use this system to accurately measure the contact forces in a three-dimensional packing of shells subjected to a static anisotropic compression and to shear. At small deformations forces are linear, however, for a buckled contact, the restoring force is related to the amount of deformation by a square root law, as follows from the theory of elasticity of shells. Near the unjamming-jamming transition (point J), we found the probability distribution of the interparticle forces P(f) to decay nearly exponentially at large forces, with little evidence of long-range force chains in the packings. As the packing density is increased, the tail of the distribution was found to crossover to a Gaussian, in line with other experimental and simulation studies. Under a small shear strain, up to 0.216, applied at an extremely low shear rate, we observed a shear-induced anisotropy in both the pair correlation function and contact force network; however, no appreciable change was seen in the number of contacts per particle.

Active cage model of glassy dynamics

We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture some characteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a crossover between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage and the ratio of the hopping length to the cage size.

Jammed elastic shells - a 3D experimental soft frictionless granular system

We present a new experimental system of monodisperse, soft, frictionless, fluorescent labeled elastic shells for the characterization of structure, universal scaling laws and force networks in 3D jammed matter. The elastic shells in a jammed packing are deformed in such a way that at each contact one of the shells buckles with a dimple and the other remain spherical, closely resembling overlapping spheres. Using confocal microscopy, we obtained 3D stacks of images of shells at different volume fractions which were subsequently processed in ImageJ software to find their coordinates. The determination of 3D coordinates involved three steps: locating the edges of shells in all 2D slices, analyzing their shape and subsequently finding their 2D coordinates, and finally determining their 3D centers by grouping the corresponding 2D coordinates. From this analysis routine we obtained particle coordinates with sub-pixel accuracy. In a contact pair we also identified the shell that underwent buckling forming a dimple by analyzing the intensity profile of a line that connects the centers of particle pairs. The amorphous structure of the packing was analyzed as a function of distance to the jamming threshold by investigating the radial distribution function, bond order parameters, contact numbers and the number of dimples per particle (buckling number), which is a unique property of this system. We find that the power law scaling of the contact number with excess volume fraction deviated from theoretical and computer simulation predictions. In addition, the buckling number also showed a similar scaling as that of the contact number with distance to the jamming transition.

Structure of marginally jammed polydisperse packings of frictionless spheres

We model the packing structure of a marginally jammed bulk ensemble of polydisperse spheres. To this end we expand on the granocentric model [Clusel et al., Nature (London) 460, 611 (2009)], explicitly taking into account rattlers. This leads to a relationship between the characteristic parameters of the packing, such as the mean number of neighbors and the fraction of rattlers, and the radial distribution function g(r). We find excellent agreement between the model predictions for g(r) and packing simulations, as well as experiments on jammed emulsion droplets. The observed quantitative agreement opens the path towards a full structural characterization of jammed particle systems for imaging and scattering experiments.

Aspects of jamming in two-dimensional athermal frictionless systems

In this work we provide an overview of jamming transitions in two dimensional systems focusing on the limit of frictionless particle interactions in the absence of thermal fluctuations. We first discuss jamming in systems with short range repulsive interactions, where the onset of jamming occurs at a critical packing density and where certain quantities show a divergence indicative of critical behavior. We describe how aspects of the dynamics change as the jamming density is approached and how these dynamics can be explored using externally driven probes. Different particle shapes can produce jamming densities much lower than those observed for disk-shaped particles, and we show how jamming exhibits fragility for some shapes while for other shapes this is absent. Next we describe the effects of long range interactions and jamming behavior in systems such as charged colloids, vortices in type-II superconductors, and dislocations. We consider the effect of adding obstacles to frictionless jamming systems and discuss connections between this type of jamming and systems that exhibit depinning transitions. Finally, we discuss open questions such as whether the jamming transition in all these different systems can be described by the same or a small subset of universal behaviors, as well as future directions for studies of jamming transitions in two dimensional systems, such as jamming in self-driven or active matter systems.

Physics in ordered and disordered colloidal matter composed of poly(N-isopropylacrylamide) microgel particles

This review collects and describes experiments that employ colloidal suspensions to probe physics in ordered and disordered solids and related complex fluids. The unifying feature of this body of work is its clever usage of poly(N-isopropylacrylamide) (PNIPAM) microgel particles. These temperature-sensitive colloidal particles provide experimenters with a 'knob' for in situ control of particle size, particle interaction and particle packing fraction that, in turn, influence the structural and dynamical behavior of the complex fluids and solids. A brief summary of PNIPAM particle synthesis and properties is given, followed by a synopsis of current activity in the field. The latter discussion describes a variety of soft matter investigations including those that explore formation and melting of crystals and clusters, and those that probe structure, rearrangement and rheology of disordered (jammed/glassy) and partially ordered matter. The review, therefore, provides a snapshot of a broad range of physics phenomenology which benefits from the unique properties of responsive microgel particles.

How the ideal jamming point illuminates the world of granular media

The zero temperature properties of frictionless soft spheres near the jamming point have been extensively studied both numerically and theoretically; these studies provide a reliable base for the interpretation of experiments. However, recent work by Ikeda et al. showed that, in a parameter space of the temperature and packing fraction, experiments to date on colloids have been rather far from the theoretical scaling regime. An important question is then whether theoretical results concerning point-J are applicable to any physical/experimental system, including granular media, which we consider here. On the surface, such a-thermal, frictional systems might appear even further from the idealized case of thermal soft spheres. In this work we address this question via experiments on shaken granular materials near jamming. We have systematically investigated such systems over a number of years using hard metallic grains. The important feature of the present work is the use of much softer grains, cut from photoelastic materials, making it possible to determine forces at the grain scale, the details of the contact networks and the motion of individual grains. Using this new type of particle, we first show that the contact network exhibits remarkable dynamics. We find strong heterogeneities, which are maximum at the packing fraction ϕ*, distinct from and smaller than the packing fraction ϕ(†), where the average number of contacts per particle, z, starts to increase. In the limit of zero mechanical excitation, these two packing fractions converge at point J. We also determine dynamics on time scales ranging from a small fraction of the shaking cycle to thousands of cycles. We can then map the observed system behavior onto results from simulations of ideal thermal soft spheres. Our results indicate that the ideal jamming point indeed illuminates the world of granular media.