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

Effect of Embedded g-C3N4 Nanosheets on the Hydration and Thermal Response Behavior of Cross-Linked Thermoresponsive Copolymer Films

The effect of embedded graphitic carbon nitride (g-C3N4) nanosheets on hydration and thermal response behavior of cross-linked thermoresponsive poly(di(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) methyl ether methacrylate), abbreviated as P(MA-co-MA300), thin films is probed by white light interferometry. Compared with that of the cross-linked pure P(MA-co-MA300) films, the surface roughness of the cross-linked hybrid films is slightly increased, which is caused by the minor aggregation of g-C3N4 nanosheets during the spin-coating process. After exposure to a water vapor atmosphere, both cross-linked pure and hybrid films can absorb water and swell. However, the introduction of g-C3N4 not only induces a larger hydration extent but also triggers a nonlinear transition behavior upon heating. This prominent difference might be related to the residual hydrophilic groups (-NH2 and N-H) on the surface of g-C3N4 nanosheets, which enhance the interaction and absorption capability for water molecules in the hybrid films. Upon further increasing the amount of embedded g-C3N4 nanosheets in films, more hydrogen bonds are formed and a larger hydration extent of films is observed. To break all of the hydrogen bonds in films, a higher transition temperature (TT) is required. The observed hydration and transition behaviors of hybrid films can be used to design hydrogel-based films for hydrogen evolution or wastewater treatment.

Confinement controls the creep rate in soft granular packings

Flow in soft materials encompasses a wide range of viscous, plastic and elastic phenomena which provide challenges to modelling at the microscopic level. To create a controlled flow, we perform falling ball viscometry tests on packings of soft, frictionless hydrogel spheres. Systematic creep flow is found when a controlled driving stress is applied to a sinking sphere embedded in a packing. Here, we take the novel approach of applying an additional global confinement stress to the packing using an external load. This has enabled us to identify two distinct creep regimes. When confinement stress is small, the creep rate is independent of the load imposed. For larger confinement stresses, we find that the creep rate is set by the mechanical load acting on the packing. In the latter regime, the creep rate depends exponentially on the imposed stress. We can combine the two regimes via a rescaling onto a master curve, capturing the creep rate over five orders of magnitude. Our results indicate that bulk creep phenomena in these soft materials can be subtly controlled using an external mechanical force.

Creep Control in Soft Particle Packings

Granular packings display a wealth of mechanical features that are of widespread significance. One of these features is creep: the slow deformation under applied stress. Creep is common for many other amorphous materials such as many metals and polymers. The slow motion of creep is challenging to understand, probe, and control. We probe the creep properties of packings of soft spheres with a sinking ball viscometer. We find that in our granular packings, creep persists up to large strains and has a power law form, with diffusive dynamics. The creep amplitude is exponentially dependent on both applied stress and the concentration of hydrogel, suggesting that a competition between driving and confinement determines the dynamics. Our results provide insights into the mechanical properties of soft solids and the scaling laws provide a clear benchmark for new theory that explains creep, and provide the tantalizing prospect that creep can be controlled by a boundary stress.

Glass-liquid and glass-gel transitions of soft-shell particles

We study the structure and dynamics of colloidal particles with a spherical hard core and a thermo-responsive soft shell over the whole phase diagram by means of small-angle x-ray scattering and x-ray photon correlation spectroscopy. By changing the effective volume fraction by temperature and particle concentration, liquid, repulsive glass. and attractive gel phases are observed. The dynamics slow down with increasing volume fraction in the liquid phase and reflect a Vogel-Fulcher-Tamann behavior known for fragile glass formers. We find a liquid-glass transition above 50 vol.% that is independent of the particles' concentration and temperature. In an overpacked state at effective volume fractions above 1, the dispersion does not show a liquid phase but undergoes a gel-glass transition at an effective volume fraction of 34 vol.%. At the same concentration, extrema of subdiffusive dynamics are found in the liquid phase at lower weight fractions. We interpret this as dynamic precursors of the glass-gel transition.

Unification of the Rheological Physics of Yield Stress Fluids

The physics above and below the yield stress is unified by a simple model for viscoplasticity that accounts for the nonlinear rheology of multiple yield stress fluids. The model has a rate-dependent relaxation time, allows for plastic deformation below the yield stress, and indicates that rapid elastic deformation aids yielding. A range of commonly observed rheological behaviors are predicted, including the smooth overshoot in the loss modulus and the recently discovered contributions from recoverable and unrecoverable strains in amplitude sweeps.

Glass and Jamming Rheology in Soft Particles Made of PNIPAM and Polyacrylic Acid

The phase behaviour of soft colloids has attracted great attention due to the large variety of new phenomenologies emerging from their ability to pack at very high volume fractions. Here we report rheological measurements on interpenetrated polymer network microgels composed of poly(N-isopropylacrylamide) (PNIPAM) and polyacrylic acid (PAAc) at fixed PAAc content as a function of weight concentration. We found three different rheological regimes characteristic of three different states: a Newtonian shear-thinning fluid, an attractive glass characterized by a yield stress, and a jamming state. We discuss the possible molecular mechanisms driving the formation of these states.

Rheology finds distinct glass and jamming transitions in emulsions

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

LCST polymers with UCST behavior

In this study, temperature dependent behavior of dense dispersions of core crosslinked flower-like micelles is investigated. Micelles were prepared by mixing aqueous solutions of two ABA block copolymers with PEG B-blocks and thermosensitive A-blocks containing PNIPAM and crosslinkable moieties. At a temperature above the lower critical solution temperature (LCST), self-assembly of the polymers resulted in the formation of flower-like micelles with a hydrophilic PEG shell and a hydrophobic core. The micellar core was stabilized by native chemical ligation (NCL). Above the LCST, micelles displayed a radius of ∼35 nm, while a radius of ∼48 nm was found below the LCST due to hydration of the PNIPAM core. Concentrated dispersions of these micelles (≥7.5 wt%) showed glassy state behavior below a critical temperature (Tc: 28 °C) which is close to the LCST of the polymers. Below this Tc, the increase in the micelle volume resulted in compression of micelles together above a certain concentration and formation of a glass. We quantified and compared micelle packing at different concentrations and temperatures. The storage moduli (G') of the dispersions showed a universal dependence on the effective volume fraction, which increased substantially above a certain effective volume fraction of φ = 1.2. Furthermore, a disordered lattice model describing this behavior fitted the experimental data and revealed a critical volume fraction of φc = 1.31 close to the experimental value of φ = 1.2. The findings reported provide insights for the molecular design of novel thermosensitive PNIPAM nanoparticles with tunable structural and mechanical properties.

In situ formed thermogelable hydrogel photonic crystals assembled by thermosensitive IPNs

In this paper, soft thermosensitive photonic crystals are immobilized via a reversible temperature-triggered in situ sol-gel transition above their phase transition temperature (T_p), which may be a significant advance in the field. Specifically, a library of thermosensitive poly(N-isopropylacrylamide)/poly(acrylic acid) (PNIPAm/PAA) interpenetrating nanogels (IPNs) is synthesized, which can achieve a reversible temperature-induced sol-gel transition at a low concentration (1.1 wt%). More interestingly, as the temperature is increased above T_p, the photonic crystals assembled by these IPNs do not disappear but are "immobilized" in the in situ formed hydrogel matrix. Moreover, these colorful IPN dispersions exhibit outstanding syringe-injectability, immediately turning from an aqueous solution into an insoluble hydrogel as they are injected into PBS at 37 °C. Plus, a protein-release study showed that these injectable hydrogels show extended release times and slower release rates in comparison with dilute nanogel dispersions. In brief, these in situ formed hydrogels with brilliant structural colors have potential in optical applications, e.g., color displays, crystal immobilization, and biological applications, e.g., 3D cell culture and drug delivery.

Temperature-Dependent Nanomechanical Properties of Adsorbed Poly-NIPAm Microgel Particles Immersed in Water

The temperature dependence of nanomechanical properties of adsorbed poly-NIPAm microgel particles prepared by a semibatch polymerization process was investigated in an aqueous environment via indentation-based atomic force microscopy (AFM) methods. Poly-NIPAm microgel particles prepared by the classical batch process were also characterized for comparison. The local mechanical properties were measured between 26 and 35 °C, i.e., in the temperature range of the volume transition. Two different AFM tips with different shapes and end radii were utilized. The nanomechanical properties measured by the two kinds of tips showed a similar temperature dependence of the nanomechanical properties, but the actual values were found to depend on the size of the tip. The results suggest that the semibatch synthesis process results in the formation of more homogeneous microgel particles than the classical batch method. The methodological approach reported in this work is generally applicable to soft surface characterization in situ.

Microscopic origin of shear banding as a localized driven glass transition in compressed colloidal pillars

Here we report on compression experiments of colloidal pillars in which the evolution of a shear band can be followed at the particle level during deformation. Quasistatic deformation results in dilation and anisotropic changes in coordination in a localized band of material. Additionally, a transition from solid- to liquidlike mechanical response accompanies the structural change in the band, as evidenced by saturation of the packing fraction at the glass transition point, a diminishing ability to host anelastic strains, and a rapid decay in the long-range strain correlations. Overall, our results suggest that shear banding quantitatively resembles a localized, driven glass transition.

Vibration controlled foam yielding

In rheological terms, foams are time independent yield stress fluids, displaying properties of both solid and liquid materials. Here we measure the propagation of a 2D dry foam in a radially symmetric Hele-Shaw cell forcing local yielding. The yield rate is manipulated by mechanical vibration with frequencies from 0 to 150 Hz. The flow speed is then extracted from the video stream and analyzed using digital image correlation software. The data are modeled analytically by a Guzman-Arrhenius type of energy landscape where the local yielding of foam correlates with the number of oscillations, i.e. attempts to cross the energy barrier. The model is confirmed in an auxiliary experiment where the vibrated foam stays in its flowing state at the same small driving pressures, where the flow of the unvibrated foam ceases. We conclude that the yield stress behaviour of foams under an external perturbation can be summarized using a simple energy landscape model. The vibration affects the films causing the stress to occasionally and locally exceed the yield threshold. This, thus, prevents the foam from jamming as in a static configuration even when the global driving is below the yield point of the foam.

Avalanches, thresholds, and diffusion in mesoscale amorphous plasticity

We present results on a mesoscale model for amorphous matter in athermal, quasistatic (a-AQS), steady-state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size L of (i) statistics of individual relaxation events in terms of stress relaxation S, and individual event mean-squared displacement M, and the subsequent load increments Δγ, required to initiate the next event; (ii) static properties of the system encoded by x=σ_{y}-σ, the distance of local stress values from threshold; and (iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of S is similar to, but distinct from, the distribution of M. We find a strong correlation between S and M for any particular event, with S∼M^{q} with q≈0.65. The exponent q completely determines the scaling exponents for P(M) given those for P(S). For the distribution of local thresholds, we find P(x) is analytic at x=0, and has a value P(x)|_{x=0}=p_{0} which scales with lateral system length as p_{0}∝L^{-0.6}. The size dependence of the average load increment 〈Δγ〉 appears to be asymptotically controlled by the plateau behavior of P(x) rather than by a subsequent apparent power-law behavior. Extreme value statistics arguments lead thus to a scaling relation between the exponents governing P(x) and those governing P(S). Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by 〈Δγ〉 and the scaling properties of P(M) (in particular from 〈M〉) rather than directly from P(S) as one might have naively guessed. Our results (i) further define the a-AQS universality class, (ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, and (iii) clarify the relation between local threshold distributions and event statistics.

Nanogels and Microgels: From Model Colloids to Applications, Recent Developments, and Future Trends

Nanogels and microgels are soft, deformable, and penetrable objects with an internal gel-like structure that is swollen by the dispersing solvent. Their softness and the potential to respond to external stimuli like temperature, pressure, pH, ionic strength, and different analytes make them interesting as soft model systems in fundamental research as well as for a broad range of applications, in particular in the field of biological applications. Recent tremendous developments in their synthesis open access to systems with complex architectures and compositions allowing for tailoring microgels with specific properties. At the same time state-of-the-art theoretical and simulation approaches offer deeper understanding of the behavior and structure of nano- and microgels under external influences and confinement at interfaces or at high volume fractions. Developments in the experimental analysis of nano- and microgels have become particularly important for structural investigations covering a broad range of length scales relevant to the internal structure, the overall size and shape, and interparticle interactions in concentrated samples. Here we provide an overview of the state-of-the-art, recent developments as well as emerging trends in the field of nano- and microgels. The following aspects build the focus of our discussion: tailoring (multi)functionality through synthesis; the role in biological and biomedical applications; the structure and properties as a model system, e.g., for densely packed arrangements in bulk and at interfaces; as well as the theory and computer simulation.

Linear and nonlinear rheology and structural relaxation in dense glassy and jammed soft repulsive pNIPAM microgel suspensions

We present an integrated experimental and quantitative theoretical study of the mechanics of self-crosslinked, slightly charged, repulsive pNIPAM microgel suspensions over a very wide range of concentrations (c) that span the fluid, glassy and putative "soft jammed" regimes. In the glassy regime we measure a linear elastic dynamic shear modulus over 3 decades which follows an apparent power law concentration dependence G' ∼ c5.64, a variation that appears distinct from prior studies of crosslinked ionic microgel suspensions. At very high concentrations there is a sharp crossover to a nearly linear growth of the modulus. To theoretically understand these observations, we formulate an approach to address all three regimes within a single conceptual Brownian dynamics framework. A minimalist single particle description is constructed that allows microgel size to vary with concentration due to steric de-swelling effects. Using a Hertzian repulsion interparticle potential and a suite of statistical mechanical theories, quantitative predictions under quiescent conditions of microgel collective structure, dynamic localization length, elastic modulus, and the structural relaxation time are made. Based on a constant inter-particle repulsion strength parameter which is determined by requiring the theory to reproduce the linear elastic shear modulus over the entire concentration regime, we demonstrate good agreement between theory and experiment. Testable predictions are then made. We also measured nonlinear rheological properties with a focus on the yield stress and strain. A theoretical analysis with no adjustable parameters predicts how the quiescent structural relaxation time changes under deformation, and how the yield stress and strain change as a function of concentration. Reasonable agreement with our observations is obtained. To the best of our knowledge, this is the first attempt to quantitatively understand structure, quiescent relaxation and shear elasticity, and nonlinear yielding of dense microgel suspensions using microscopic force based theoretical methods that include activated hopping processes. We expect our approach will be useful for other soft polymeric particle suspensions in the core-shell family.

Nanoscale mechanics of microgel particles

Microgel particles are highly tuneable materials that are useful for a wide range of industrial applications, such as drug delivery, sensing, nanoactuation, emulsion stabilisation and use as cell substrates. Microgels have also been used as model systems investigating physical phenomena such as crystallization, glass-formation, jamming, ageing and complex flow behaviour. The responsiveness of microgel systems such as poly(N-isopropylacrylamide) (PNIPAm) to external stimuli has been established in fundamental investigations and in applications and recent work has begun to quantify the mechanics of individual particles. However little focus has been placed on determining their internal mechanical properties, which is likely to relate to their nonuniform internal structure. In this work we combine atomic force microscopy, force spectroscopy and dynamic light scattering to mechanically profile the internal structure of microgel particles in the size range of ∼100 nm, which is commonly used both in practical applications and in fundamental studies. Nanoindentation using thermally stable cantilevers allows us to determine the particle moduli and the deformation profiles during particle compression with increasing force, while peak force nanomechanical mapping (PF-QNM) AFM is used to capture high resolution images of the particles' mechanical response. Combining these approaches with dynamic light scattering allows a quantitative profile of the particles' internal elastic response to be determined. Our results provide clear evidence for a radial distribution in particle mechanical response with a softer outer "corona" and a stiffer particle core. We determine the particle moduli in the core and corona, using different force microscopy approaches, and find them to vary systematically both in the core (∼17-50 kPa) and at the outer periphery of the particles (∼3-40 kPa). Importantly, we find that highly crosslinked particles have equivalent moduli across their radial profile, reflecting their significantly lower radial heterogeneity. This ability to accurately and precisely probe microgel radial profiles has clear implications both for fundamental science and for industrial applications.

On the universality of the flow properties of soft-particle glasses

We identify the minimal interparticle interactions necessary for a particle dynamics simulation to predict the structure and flow behaviour of soft particle glasses (SPGs). Generally, two kinds of forces between the particles must be accounted for in simulations of SPGs: viscous or frictional drag forces and elastic contact forces. Far field drag forces are required to dissipate energy in the simulations and capture the effect of the rheology of the suspending fluid. Elastic forces are found to be dominant compared to near-field drag or other forms of friction forces and are the most important component to compute the rheology. The shear stress, the first and second normal stress differences for different interparticle force laws collapse onto universal master curves of the Herschel-Bulkley form by non-dimensionalizing the stress with the yield stress and the shear rate with the viscosity of the suspending fluid divided by the low-frequency shear modulus. The Herschel-Bulkley exponents are close to 0.5 with a slight dependence on the repulsive pairwise elastic forces.

Unusual polysaccharide rheology of aqueous dispersions of soft phytoglycogen nanoparticles

Phytoglycogen is a natural polysaccharide produced in the form of dense, 35 nm diameter nanoparticles by some varieties of plants such as sweet corn. The highly-branched, dendrimeric structure of phytoglycogen leads to interesting and useful properties such as softness and deformability of the particles, and a strong interaction with water. These properties make the particles ideal for use as unique additives in personal care, nutrition and biomedical formulations. In the present study, we describe rheology measurements of aqueous dispersions of phytoglycogen nanoparticles. The viscosity of the dispersions remained Newtonian up to large concentrations (∼20% w/w). For higher concentrations, the zero-shear viscosity increased dramatically, reaching values that exceeded that of the water solvent by six orders of magnitude at a concentration of 30% w/w and were well described by the Vogel-Fulcher-Tammann relation of glassy dynamics. The very large values of the zero-shear viscosity are coupled with significant deformation of the soft nanoparticles. We quantified the softness of the particles by performing osmotic pressure measurements on concentrated dispersions, obtaining a value of 15 kPa for the compressional modulus. For the most concentrated samples, we observed flow at stresses less than the apparent yield stress value determined by fitting the high strain rate data to the Herschel-Bulkley model. This behavior, similar to that of star polymer glasses, suggests the possibility of a hairy colloid particle geometry. Remarkably, phytoglycogen nanoparticles dispersed in water provide a very simple experimental realization of glass-forming dispersions of soft colloidal particles that can be used to validate theoretical models in detail.

Different routes into the glass state for soft thermo-sensitive colloids

We report an experimental and theoretical investigation of glass formation in soft thermo-sensitive colloids following two different routes: a gradual increase of the particle number density at constant temperature and an increase of the radius in a fixed volume at constant particle number density. Confocal microscopy experiments and the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory consistently show that the two routes lead to a dynamically comparable state at sufficiently long aging times. However, experiments reveal the presence of moderate but persistent structural differences. Successive cycles of radius decrease and increase lead instead to a reproducible glass state, indicating a suitable route to obtain rejuvenation without using shear fields.

Structure-property relationships from universal signatures of plasticity in disordered solids

When deformed beyond their elastic limits, crystalline solids flow plastically via particle rearrangements localized around structural defects. Disordered solids also flow, but without obvious structural defects. We link structure to plasticity in disordered solids via a microscopic structural quantity, "softness," designed by machine learning to be maximally predictive of rearrangements. Experimental results and computations enabled us to measure the spatial correlations and strain response of softness, as well as two measures of plasticity: the size of rearrangements and the yield strain. All four quantities maintained remarkable commonality in their values for disordered packings of objects ranging from atoms to grains, spanning seven orders of magnitude in diameter and 13 orders of magnitude in elastic modulus. These commonalities link the spatial correlations and strain response of softness to rearrangement size and yield strain, respectively.

Interpenetration of polymeric microgels at ultrahigh densities

Soft particles such as polymeric microgels can form ultra-dense phases, where the average center-to-center distance a _s can be smaller than the initial unperturbed particle diameter σ ₀, due to their ability to interpenetrate and compress. However, despite of the effort devoted to microgels at ultrahigh densities, we know surprisingly little about their response to their environment at effective volume fractions ϕ _eff above close packing (ϕ _cp ), and the existing information is often contradictory. Here we report direct measurements of the size and shape of poly(N-isopropylacrylamide) microgels at concentrations below and above ϕ _cp using the zero average contrast method in small-angle neutron scattering. We complement these experiments with measurements of the average interparticle distances using small-angle x-ray scattering, and a determination of the glass transition using dynamic light scattering. This allows us to unambiguously decouple interaction effects from density-dependent variations of the particle size and shape at all values of ϕ _eff . We demonstrate that the microgels used in this study significantly interpenetrate and thus change their size and shape only marginally even for ϕ _eff  ≫ ϕ _cp , a finding that may require changes in the interpretation of a number of previously published studies on the structural and dynamic properties of dense soft particle systems.

A simple collision model for small bubbles

In this work, a model for the interaction force between a small bubble and a wall or another bubble is presented. The formulation is especially designed for Lagrangian calculations of bubble or soft sphere trajectories, with or without resolution of the continuous fluid. The force only relies on position and velocity of the bubble. The model does not include any empirical parameter that would have to be calibrated. Therefore, this force model is easy to implement. The formulation of the force is explicit, which means low computational effort. The collision of a small bubble with an inclined top wall is investigated numerically and experimentally. The computational results achieved with the new collision model show good agreement with the experiment.

Introduction to the Colloidal Glass Transition

Colloids are suspensions of small solid particles in a liquid and exhibit glassy behavior when the particle concentration is high. In these samples, the particles are roughly analogous to individual molecules in a traditional glass. This model system has been used to study the glass transition since the 1980s. In this Viewpoint I summarize some of the intriguing behaviors of the glass transition in colloids and discuss open questions.

The glass and jamming transitions of soft polyelectrolyte microgel suspensions

We explore the influence of particle softness on the state diagram of well characterized polyelectrolyte microgel suspensions using dynamic light scattering and rheology. Upon increasing the polymer concentration, we cross successively the well defined glass and jamming transitions which delimit four different states: dilute colloidal suspension, entropic glass, jammed glass, and dense glass. Each state has a specific dynamical fingerprint dictated by two key ingredients related to particle softness: elastic contact interactions, and osmotic or steric deswelling. Soft interactions control yielding and flow of the jammed glasses. The shrinkage of the microgels makes the glass transition look smoother than in hard sphere suspensions. We quantify the relationship between the polymer concentration and the volume fraction, and show that the glass transition behaviour of soft microgels can be mapped to that of hard sphere glasses once the volume fraction is used as the control parameter.

Counter-effect of Brownian and elastic forces on the liquid-to-solid transition of microgel suspensions

Suspensions of microgel particles undergo a transition from liquid-like to solid-like mechanics upon increase of the microgel packing fraction. We study the opposed effects of the microgel softness and size on this transition. We tune the softness of the microgels by varying their polymer crosslinking density, while we simultaneously and independently vary their size and the contribution of Brownian particle motion by investigating two sets of colloidal-scale microgels synthesized by precipitation polymerization, along with one set of granular-scale microgels prepared by droplet-templated polymerization in microfluidic devices. We find that the microgel packing fraction at which the liquid-to-solid transition occurs depends on both the size and the softness of the microgel particles: small and soft microgels undergo this transition at much larger packing fractions than stiff microgels of the same size and than larger microgels with the same softness. This work suggests a systematic strategy to quantitatively predict this transition.

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.

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.

Jamming and unjamming transition of oil-in-water emulsions under continuous temperature change

To analyze the jamming and unjamming transition of oil-in-water emulsions under continuous temperature change, we simulated an emulsion system whose critical volume fraction was 0.3, which was validated with experimental results under oscillatory shear stress. In addition, we calculated the elastic modulus using the phase lag between strain and stress. Through heating and cooling, the emulsion experienced unjamming and jamming. A phenomenon-which is when the elastic modulus does not reach the expected value at the isothermal system-occurred when the emulsion system was cooled. We determined that this phenomenon was caused by the frequency being faster than the relaxation of the deformed droplets. We justified the relation between the frequency and relaxation by simulating the frequency dependency of the difference between the elastic modulus when cooled and the expected value at the same temperature.

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.

Robust scaling of strength and elastic constants and universal cooperativity in disordered colloidal micropillars

We study the uniaxial compressive behavior of disordered colloidal free-standing micropillars composed of a bidisperse mixture of 3- and 6-μm polystyrene particles. Mechanical annealing of confined pillars enables variation of the packing fraction across the phase space of colloidal glasses. The measured normalized strengths and elastic moduli of the annealed freestanding micropillars span almost three orders of magnitude despite similar plastic morphology governed by shear banding. We measure a robust correlation between ultimate strengths and elastic constants that is invariant to relative humidity, implying a critical strain of ∼0.01 that is strikingly similar to that observed in metallic glasses (MGs) [Johnson WL, Samwer K (2005) Phys Rev Lett 95:195501] and suggestive of a universal mode of cooperative plastic deformation. We estimate the characteristic strain of the underlying cooperative plastic event by considering the energy necessary to create an Eshelby-like ellipsoidal inclusion in an elastic matrix. We find that the characteristic strain is similar to that found in experiments and simulations of other disordered solids with distinct bonding and particle sizes, suggesting a universal criterion for the elastic to plastic transition in glassy materials with the capacity for finite plastic flow.

Shear modulus and dilatancy softening in granular packings above jamming

We investigate experimentally the mechanical response to shear of a monolayer of bidisperse frictional grains across the jamming transition. We inflate an intruder inside the packing and use photoelasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 10(-3) and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in: both the shear modulus and the dilatancy shear soften at small strain until a critical strain is reached where effective linearity is recovered. The scaling of the critical strain and the associated critical stresses on the distance to jamming are extracted. We check that the constitutive laws, together with mechanical equilibrium, correctly predict to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition.

Experimental signatures of a nonequilibrium phase transition governing the yielding of a soft glass

We present direct experimental signatures of a nonequilibrium phase transition associated with the yield point of a prototypical soft solid-a binary colloidal glass. By simultaneously quantifying single-particle dynamics and bulk mechanical response, we identified the threshold for the onset of irreversibility with the yield strain. We extracted the relaxation time from the transient behavior of the loss modulus and found that it diverges in the vicinity of the yield strain. This critical slowing down is accompanied by a growing correlation length associated with the size of regions of high Debye-Waller factor, which are precursors to yield events in glasses. Our results affirm that the paradigm of nonequilibrium critical phenomena is instrumental in achieving a holistic understanding of yielding in soft solids.

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.