Unified study of glass and jamming rheology in soft particle systems

Cooperativity and segregation in confined flows of soft binary glasses

When a suspension containing particles of different sizes flows through a confined geometry a size gradient can be established, with large particles accumulating in the channel center. Such size separation driven by hydrodynamic interactions is expected to facilitate membrane filtration and may lead to the design of novel and innovative separation techniques. For this, a wide range of particle concentrations has to be investigated, in order to clarify whether shear-induced migration can be utilized at concentrations close to or above the colloidal glass transition, where particle motion is severely hindered and hydrodynamic interactions are screened. We explore this scenario by studying the flow of binary mixtures of soft colloidal microgels, well above their liquid-solid transition, through narrow microchannels. We find that, even though the flow becomes strongly heterogeneous, in both space and time, characterized by a large cooperativity length, size segregation still occurs. This suggests that even above the glass transition shear-induced diffusion could still be used as a fractionation mechanism, which is of great relevance for process intensification purposes.

Numerical detection of the Gardner transition in a mean-field glass former

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.

Universal rescaling of flow curves for yield-stress fluids close to jamming

The experimental flow curves of four different yield-stress fluids with different interparticle interactions are studied near the jamming concentration. By appropriate scaling with the distance to jamming all rheology data can be collapsed onto master curves below and above jamming that meet in the shear-thinning regime and satisfy the Herschel-Bulkley and Cross equations, respectively. In spite of differing interactions in the different systems, master curves characterized by universal scaling exponents are found for the four systems. A two-state microscopic theory of heterogeneous dynamics is presented to rationalize the observed transition from Herschel-Bulkley to Cross behavior and to connect the rheological exponents to microscopic exponents for the divergence of the length and time scales of the heterogeneous dynamics. The experimental data and the microscopic theory are compared with much of the available literature data for yield-stress systems.

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.

Mean-field microrheology of a very soft colloidal suspension: Inertia induces shear thickening

Colloidal suspensions have a rich rheology and can exhibit shear thinning as well as shear thickening. Numerical simulations recently suggested that shear-thickening may be attributed to the inertia of the colloids, besides the hydrodynamic interactions between them. Here, we consider the ideal limit of a dense bath of soft colloids following an underdamped Langevin dynamics. We use a mean-field equation for the colloidal density to get an analytical expression of the drag force felt by a probe pulled at constant velocity through the suspension. Our results show that inertia can indeed induce shear thickening by allowing density waves to propagate through the suspension.

Nonlinear rheology of glass-forming colloidal dispersions: transient stress-strain relations from anisotropic mode coupling theory and thermosensitive microgels

Transient stress-strain relations close to the colloidal glass transition are obtained within the integration through transients framework generalizing mode coupling theory to flow driven systems. Results from large-scale numerical calculations are quantitatively compared to experiments on thermosensitive microgels, which reveals that theory captures the magnitudes of stresses semi-quantitatively even in the nonlinear regime, but overestimates the characteristic strain where plastic events set in. The former conclusion can also be drawn from flow curves, while the latter conclusion is supported by a comparison to single particle motion measured by confocal microscopy. The qualitative picture, as previously obtained from simplifications of the theory in schematic models, is recovered by the quantitative solutions of the theory for Brownian hard spheres.

Bulk and interfacial stresses in suspensions of soft and hard colloids

We explore the influence of particle softness and internal structure on both the bulk and interfacial rheological properties of colloidal suspensions. We probe bulk stresses by conventional rheology, by measuring the flow curves, shear stress versus strain rate, for suspensions of soft, deformable microgel particles and suspensions of near hard-sphere-like silica particles. A similar behaviour is seen for both kinds of particles in suspensions at concentrations up to the random close packing volume fraction, in agreement with recent theoretical predictions for sub-micron colloids. Transient interfacial stresses are measured by analyzing the patterns formed by the interface between the suspensions and their solvent, due to a generalized Saffman-Taylor hydrodynamic instability. At odds with the bulk behaviour, we find that microgels and hard particle suspensions exhibit vastly different interfacial stress properties. We propose that this surprising behaviour results mainly from the difference in particle internal structure (polymeric network for microgels versus compact solid for the silica particles), rather than softness alone.

Disordered solids without well-defined transverse phonons: the nature of hard-sphere glasses

We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by calculating the dynamical structure factors. The Ioffe-Regel limit (frequency) is reached when the phonon wavelength is comparable to the mean free path, beyond which phonons are no longer well defined. At zero temperature, the transverse Ioffe-Regel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamminglike transition and glass transition, respectively. As a consequence, glasses between the glass transition and the jamminglike transition, which are hard-sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.

Devising a protocol-related statistical mechanics framework for granular materials

Devising a statistical mechanics framework for jammed granular materials is a challenging task as those systems do not share some important properties required to characterize them with statistical thermodynamics tools. In a recent paper [Asenjo et al. Phys. Rev. Lett. 112, 098002 (2014)], a new definition of a granular entropy, which puts the protocol used to generate the packings at its roots, has been proposed. Following up these results, it is shown that the protocol used in Asenjo et al. can be recast as a canonical ensemble with a particular value of the temperature. Signature of gaussianity for large system sizes strongly suggests an asymptotic equivalence with a corresponding microcanonical ensemble where jammed states with certain basin volumes are sampled uniformly. We argue that this microcanonical ensemble is not Edwards's microcanonical ensemble and generalize this argument to other protocols.

Diverging viscosity and soft granular rheology in non-Brownian suspensions

We use large scale computer simulations and finite-size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size and carefully study the asymptotic limits of large system sizes and infinitely hard particle repulsion. We first focus on the asymptotic behavior of the shear viscosity in the hard particle limit. By measuring the viscosity increase over about 5 orders of magnitude, we are able to confirm its asymptotic power law divergence close to the jamming transition. However, a precise determination of the critical density and critical exponent is difficult due to the "multiscaling" behavior of the viscosity. Additionally, finite-size scaling analysis suggests that this divergence is accompanied by a growing correlation length scale, which also diverges algebraically. Finally, we study the effect of particle softness and propose a natural extension of the standard granular rheology, which we test against our simulation data. Close to the jamming transition, this "soft granular rheology" offers a detailed description of the nonlinear rheology of soft particles, which differs from earlier empirical scaling forms.

Avalanche contribution to shear modulus of granular materials

Shear modulus of frictionless granular materials near the jamming transition under oscillatory shear is numerically investigated. It is found that the shear modulus G satisfies a scaling law to interpolate between G∼(ϕ-ϕJ)(1/2) and G∼γ0(-1/2)(ϕ-ϕJ) for a linear spring model of the elastic interaction between contacting grains, where ϕ, ϕJ, and γ0 are, respectively, the volume fraction of grains, the fraction at the jamming point, and the amplitude of the oscillatory shear. The linear relation between the shear modulus and ϕ-ϕJ can be understood by slip avalanches.

Crossover between entropic and interfacial elasticity and osmotic pressure in uniform disordered emulsions

We develop a simple predictive model of the osmotic pressure Π and linear shear elastic modulus G of uniform disordered emulsions that includes energetic contributions from entropy and interfacial deformation. This model yields a smooth crossover between an entropically dominated G ∼ kBT/a(3) for droplet volume fractions ϕ below a jamming threshold for spheres, ϕc, and an interfacially dominated G ∼ σ/a for ϕ above ϕc, where a and σ are the undeformed radius and interfacial tension, respectively, of a droplet and T is the temperature. We show that this model reduces to the known ϕ-dependent jamming behavior G(ϕ) ∼ (σ/a)ϕ(ϕ - ϕc) as T → 0 for ϕ > ϕc of disordered uniform emulsions, and it also produces the known divergence for disordered hard spheres G(ϕ) ∼ (kBT/a(3))ϕ/(ϕc - ϕ) for ϕ < ϕc when σ → ∞. We compare predictions of this model to data for disordered uniform microscale emulsion droplets, corrected for electrostatic repulsions. The smooth crossover captures the observed trends in G and Π below ϕc better than existing analytic models of disordered emulsions, which do not make predictions below ϕc. Moreover, the model predicts that entropic contributions to the shear modulus can become more significant for nanoemulsions as compared to microscale emulsions.

Shear modulus of glasses: results from the full replica-symmetry-breaking solution

We compute the shear modulus of amorphous hard and soft spheres, using the exact solution in infinite spatial dimensions that has been developed recently. We characterize the behavior of this observable in the whole phase diagram, and in particular around the glass and jamming transitions. Our results are consistent with other theoretical approaches, which are unified within this general picture, and they are also consistent with numerical and experimental results. Furthermore, we discuss some properties of the out-of-equilibrium dynamics after a deep quench close to the jamming transition, and we show that a combined measure of the shear modulus and of the mean square displacement allows one to probe experimentally the complex structure of phase space predicted by the full replica-symmetry-breaking solution.

The jamming elasticity of emulsions stabilized by ionic surfactants

Oil-in-water emulsions composed of colloidal-scale droplets are often stabilized using ionic surfactants that provide a repulsive interaction between neighboring droplet interfaces, thereby inhibiting coalescence. If the droplet volume fraction is raised rapidly by applying an osmotic pressure, the droplets remain disordered, undergo an ergodic-nonergodic transition, and jam. If the applied osmotic pressure approaches the Laplace pressure of the droplets, then the jammed droplets also deform. Because solid friction and entanglements cannot play a role, as they might with solid particulate or microgel dispersions, the shear mechanical response of monodisperse emulsions can provide critical insight into the interplay of entropic, electrostatic, and interfacial forces. Here, we introduce a model that can be used to predict the plateau storage modulus and yield stress of a uniform charge-stabilized emulsion accurately if the droplet radius, interfacial tension, surface potential, Debye screening length, and droplet volume fraction are known.

Equilibrium and non-equilibrium cluster phases in colloids with competing interactions

The phase behavior of colloids that interact via competing interactions - short-range attraction and long-range repulsion - is studied by computer simulation. In particular, for a fixed strength and range of repulsion, the effect of the strength of an attractive interaction (ε) on the phase behavior is investigated at various colloid densities (ρ). A thermodynamically stable equilibrium colloidal cluster phase, consisting of compact crystalline clusters, is found below the fluid-solid coexistence line in the ε-ρ parameter space. The mean cluster size is found to linearly increase with the colloid density. At large ε and low densities, and at small ε and high densities, a non-equilibrium cluster phase, consisting of elongated Bernal spiral-like clusters, is observed. Although gelation can be induced either by increasing ε at constant density or vice versa, the gelation mechanism is different in either route. While in the ρ route gelation occurs via a glass transition of compact clusters, gelation in the ε route is characterized by percolation of elongated clusters. This study both provides the location of equilibrium and non-equilibrium cluster phases with respect to the fluid-solid coexistence, and reveals the dependencies of the gelation mechanism on the preparation route.

Impact of attractive interactions on the rheology of dense athermal particles

Using numerical simulations, the rheological response of an athermal assembly of soft particles with tunable attractive interactions is studied in the vicinity of jamming. At small attractions, a fragile solid develops and a finite yield stress is measured. Moreover, the measured flow curves have unstable regimes, which lead to persistent shear banding. These features are rationalized by establishing a link between the rheology and the interparticle connectivity, which also provides a minimal model to describe the flow curves.

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.

Rheology of soft colloids across the onset of rigidity: scaling behavior, thermal, and non-thermal responses

We study the rheological behavior of colloidal suspensions composed of soft sub-micron-size hydrogel particles across the liquid-solid transition. The measured stress and strain-rate data, when normalized by thermal stress and time scales, suggest our systems reside in a regime wherein thermal effects are important. In a different vein, critical point scaling predictions for the jamming transition, typical in athermal systems, are tested. Near dynamic arrest, the suspensions exhibit scaling exponents similar to those reported in Nordstrom et al., Phys. Rev. Lett., 2010, 105, 175701. The observation suggests that our system exhibits a glass transition near the onset of rigidity, but it also exhibits a jamming-like scaling further from the transition point. These observations are thought-provoking in light of recent theoretical and simulation findings, which show that suspension rheology across the full range of microgel particle experiments can exhibit both thermal and athermal mechanisms.

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.

Fractal free energy landscapes in structural glasses

Glasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marginal stability on approaching jamming. Critical exponents for the basin width, the weak force distribution and the spatial spread of quasi-contacts near jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control what features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here.

High-velocity drag friction in granular media near the jamming point

Drag friction that acts on a disk in a two-dimensional granular medium is studied at high packing fractions. We concentrate on a high-velocity region, in which the dynamic component of the force, obtained as an average of a strongly fluctuating force, clearly scales with velocity squared. We find that the total force composed of dynamic and static components, as well as its fluctuation, diverges with practically the same exponent as the packing fraction approaches the jamming point. To explain the critical behavior, we propose a simple theory equipped with a diverging length scale, which agrees well with the data and elucidates physical pictures for the divergence.

Finite size analysis of zero-temperature jamming transition under applied shear stress by minimizing a thermodynamic-like potential

By finding local minima of a thermodynamic-like potential, we generate jammed packings of frictionless spheres under constant shear stress σ and obtain the yield stress σy by sampling the potential energy landscape. For three-dimensional systems with harmonic repulsion, σy satisfies the finite size scaling with the limiting scaling relation σy∼ϕ-ϕc,∞, where ϕc,∞ is the critical volume fraction of the jamming transition at σ=0 in the thermodynamic limit. The finite size scaling implies a length ξ∼(ϕ-ϕc,∞)-ν with ν=0.81±0.05, which turns out to be a robust and universal length scale exhibited as well in the finite size scaling of multiple quantities measured without shear and independent of particle interaction. Moreover, comparison between our new approach and quasistatic shear reveals that quasistatic shear tends to explore low-energy states.

Freezing and phase separation of self-propelled disks

We study numerically a model of soft polydisperse and non-aligning self-propelled particles interacting through elastic repulsion, which was recently shown to exhibit active phase separation in two dimensions in the absence of any attractive interaction or breaking of the orientational symmetry. We construct a phase diagram in terms of activity and packing fraction and identify three distinct regimes: a homogeneous liquid with anomalous cluster size distribution, a phase-separated state both at high and at low density, and a frozen phase. We provide a physical interpretation of the various regimes and develop scaling arguments for the boundaries separating them.

Theories of glass formation and the glass transition

This key-issues review is a plea for a new focus on simpler and more realistic models of glass-forming fluids. It seems to me that we have too often been led astray by sophisticated mathematical models that beautifully capture some of the most intriguing features of glassy behavior, but are too unrealistic to provide bases for predictive theories. As illustrations of what I mean, the first part of this article is devoted to brief summaries of imaginative, sensible, but disparate and often contradictory ideas for solving glass problems. Almost all of these ideas remain alive today, with their own enthusiastic advocates. I then describe numerical simulations, mostly by H Tanaka and coworkers, in which it appears that very simple, polydisperse systems of hard disks and spheres develop long range, Ising-like, bond-orientational order as they approach glass transitions. Finally, I summarize my recent proposal that topologically ordered clusters of particles, in disordered environments, tend to become aligned with each other as if they were two-state systems, and thus produce the observed Ising-like behavior. Neither Tanaka's results nor my proposed interpretation of them fit comfortably within any of the currently popular glass theories.

Stability of polymer glasses vitrified under stress

How stress or strain imparts mobility to glasses is a scientific issue linking ideas of jamming and the glass transition across colloids, granular materials, polymers, and molecular glasses. Here, we address for the first time how stress applied during vitrification, formation of the glassy state by a temperature quench, affects the subsequent stability of the glassy state, even after the stress has been removed. Using entangled polymers that are easily manipulated mechanically above the glass transition temperature, we find that the resulting polymer glasses become less stable, exhibiting a higher physical aging rate, when stress is applied while rapidly cooling the polymer films. The data show an initial plateau value at low stress, before transitioning rapidly to a higher aging rate at larger stress. These results are suggestive of the glassy system being left trapped in a less stable, higher energy state with faster physical aging rate when stressed above some minimum value during vitrification.

Glass-like dynamics in the cell and in cellular collectives

Prominent fluctuations, heterogeneity, and cooperativity dominate the dynamics of the cytoskeleton as well as the dynamics of the cellular collective. Such systems are out of equilibrium, disordered, and remain poorly understood. To explain these findings, we consider a unifying mechanistic rubric that imagines these systems as comprising phases of soft condensed matter in proximity to a glass or jamming transition, with associated transitions between solid-like versus liquid-like phases. At the scale of the cytoskeleton, data suggest that intermittent dynamics, kinetic arrest, and dynamic heterogeneity represent mesoscale features of glassy protein-protein interactions that link underlying biochemical events to integrative cellular behaviors such as crawling, contraction, and remodeling. At the scale of the multicellular collective, jamming has the potential to unify diverse biological factors that previously had been considered mostly as acting separately and independently. Although a quantitative relationship between intra- and intercellular dynamics is still lacking, glassy dynamics and jamming offer insights linking the mechanobiology of cell to human physiology and pathophysiology.

Linear and nonlinear rheology of dense emulsions across the glass and the jamming regimes

We discuss the linear and nonlinear rheology of concentrated microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from a liquid to a highly compressed yet disordered solid.

Connecting the random organization transition and jamming within a unifying model system

While the random organization transition describes the change from reversible to irreversible dynamics in a nonequilibrium system, the athermal jamming transition at zero shear rate occurs when particles can no longer avoid overlaps. Despite the obvious differences between these two transitions, we show that they both occur within the same model packing problem. In this unifying model system the particles are first randomly distributed and then displaced in each step if they overlap. For random displacements we obtain a random organization transition, while jamming occurs in the case of deterministic shifts. We also analyze the critical behavior of random organization. Our results show that random organization and jamming are opposite limits of random sphere packings, and we expect that various equilibrium and nonequilibrium transitions can be formulated as related intermediate packing problems.

Yield stress in amorphous solids: a mode-coupling-theory analysis

The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly nonlinear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyze several classes of disordered solids, using simple models of hard-sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard-sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the caging dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and nonlinear rheology of amorphous materials.

Perspective: The glass transition

We provide here a brief perspective on the glass transition field. It is an assessment, written from the point of view of theory, of where the field is and where it seems to be heading. We first give an overview of the main phenomenological characteristics, or "stylised facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner. We describe recent developments, with a particular focus on real space properties, including dynamical heterogeneity and facilitation, the search for underlying spatial or structural correlations, and the relation between the thermal glass transition and athermal jamming. We then discuss briefly how competing theories of the glass transition have adapted and evolved to account for such real space issues. We consider in detail two conceptual and methodological approaches put forward recently, that aim to access the fundamental critical phenomenon underlying the glass transition, be it thermodynamic or dynamic in origin, by means of biasing of ensembles, of configurations in the thermodynamic case, or of trajectories in the dynamic case. We end with a short outlook.

Origin of rigidity in dry granular solids

Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a nonuniform density pattern. In this work, we focus on the emergence of shear rigidity in a class of solids where this paradigm is challenged. Dry granular materials have no energetically or entropically preferred density modulations. We show that, in contrast to traditional solids, the emergence of shear rigidity in these granular solids is a collective process, which is controlled solely by boundary forces, the constraints of force and torque balance, and the positivity of the contact forces. We develop a theoretical framework based on these constraints, which connects rigidity to broken translational symmetry in the space of forces, not positions of grains. We apply our theory to experimentally generated shear-jammed states and show that these states are indeed characterized by a persistent, non-uniform density modulation in force space, which emerges at the shear-jamming transition.

Rheology across the zero-temperature jamming transition

Many soft-matter systems show a transition between fluidlike and mechanically solidlike states when the volume fraction of the material, e.g., particles, drops, or bubbles is increased. Using an emulsion as a model system with a precisely controllable volume fraction, we show that the entire mechanical behavior in the vicinity of the jamming point can be understood if the mechanical transition is assumed to be analogous to a phase transition. We find power-law scalings in the distance to the jamming point, in which the parameters and exponents connect the behavior above and below jamming. We propose a simple two-state model with heterogeneous dynamics to describe the transition between jammed and mobile states. The model reproduces the steady-state and creep rheology and relates the power-law exponents to diverging microscopic time scales.

Athermal jamming versus thermalized glassiness in sheared frictionless particles

Numerical simulations of soft-core frictionless disks in two dimensions are carried out to study the behavior of a simple liquid as a function of temperature T, packing fraction φ, and uniform applied shear strain rate γ[over ·]. Inferring the hard-core limit from our soft-core results, we find that it depends on the two parameters φ and T/γ[over ·]. Here T/γ[over ·]→0 defines the athermal limit in which a shear-driven jamming transition occurs at a well defined φ(J) and T/γ[over ·]→∞ defines the thermalized limit where an equilibrium glass transition may take place at φ(G). This conclusion argues that athermal jamming and equilibrium glassy behavior are not controlled by the same critical point. Preliminary results suggest φ(G)<φ(J).

Multiple reentrant glass transitions of soft spheres at high densities: monotonicity of the curves of constant relaxation time in jamming phase diagrams depending on temperature over pressure and pressure

By using molecular-dynamics simulations, we determine the jamming phase diagrams at high densities for a bidisperse mixture of soft spheres that interact according to repulsive power-law pair potentials. We observe that the relaxation time varies nonmonotonically as a function of density at constant temperature. Therefore, the jamming phase diagrams contain multiple reentrant glass transitions if temperature and density are used as control parameters. However, if we consider a new formulation of the jamming phase diagrams where temperature over pressure and pressure are employed as control parameters, no nonmonotonic behavior is observed.

Spontaneous crystallization in athermal polymer packings

We review recent results from extensive simulations of the crystallization of athermal polymer packings. It is shown that above a certain packing density, and for sufficiently long simulations, all random assemblies of freely-jointed chains of tangent hard spheres of uniform size show a spontaneous transition into a crystalline phase. These polymer crystals adopt predominantly random hexagonal close packed morphologies. An analysis of the local environment around monomers based on the shape and size of the Voronoi polyhedra clearly shows that Voronoi cells become more spherical and more symmetric as the system transits to the ordered state. The change in the local environment leads to an increase in the monomer translational contribution to the entropy of the system, which acts as the driving force for the phase transition. A comparison of the crystallization of hard-sphere polymers and monomers highlights similarities and differences resulting from the constraints imposed by chain connectivity.

Jamming transition and inherent structures of hard spheres and disks

Recent studies show that volume fractions φ(J) at the jamming transition of frictionless hard spheres and disks are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate the dependence of φ(J) on the initial configurations of the parent fluid equilibrated at a volume fraction φ(eq), before compressing to generate a jammed packing. We find that φ(J) remains constant when φ(eq) is small but sharply increases as φ(eq) exceeds the dynamic transition point which the mode-coupling theory predicts. We carefully analyze configurational properties of both jammed packings and parent fluids and find that, while all jammed packings remain isostatic, the increase of φ(J) is accompanied with subtle but distinct changes of local orders, a static length scale, and an exponent of the finite-size scaling. These results are consistent with the scenario of the random first-order transition theory of the glass transition.

Transition from the viscous to inertial regime in dense suspensions

Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behavior at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This setup is conceptually identical to recent experiments of Boyer, Guazzelli, and Pouliquen [Phys. Rev. Lett. 107, 188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces, respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.

Shear flow of non-Brownian suspensions close to jamming

The dynamical mechanisms controlling the rheology of dense suspensions close to jamming are investigated numerically, using simplified models for the relevant dissipative forces. We show that the velocity fluctuations control the dissipation rate and therefore the effective viscosity of the suspension. These fluctuations are similar in quasi-static simulations and for finite strain rate calculations with various damping schemes. We conclude that the statistical properties of grain trajectories-in particular the critical exponent of velocity fluctuations with respect to volume fraction φ-only weakly depend on the dissipation mechanism. Rather they are determined by steric effects, which are the main driving forces in the quasistatic simulations. The critical exponent of the suspension viscosity with respect to φ can then be deduced, and is consistent with experimental data.

Critical scaling of a jammed system after a quench of temperature

Critical behavior of soft repulsive particles after quench of temperature near the jamming transition is numerically investigated. It is found that the plateau of the mean-square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.

Amorphous to amorphous transition in particle rafts

Space-filling assemblies of athermal hydrophobic particles floating at an air-water interface, called particle rafts, are shown to undergo an unusual phase transition between two amorphous states, i.e., a low density "less-rigid" state and a high density "more-rigid" state, as a function of particulate number density (Φ). The former is shown to be a capillary bridged solid and the latter is shown to be a frictionally coupled one. Simultaneous studies involving direct imaging as well as measuring its mechanical response to longitudinal and shear stresses show that the transition is marked by a subtle structural anomaly and a weakening of the shear response. The structural anomaly is identified from the variation of the mean coordination number, mean area of the Voronoi cells, and spatial profile of the displacement field with Φ. The weakened shear response is related to local plastic instabilities caused by the depinning of the contact line of the underlying fluid on the rough surfaces of the particles.