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

Evidence for Chaotic Behavior during the Yielding of a Soft Particle Glass

Materials comprised of deformable particles such as microgels and concentrated emulsions and foams display complex rheological behavior that includes a yielding transition from an elastic solid to viscous fluid. Most studies of this class of soft matter involve shear flows, and only a handful report both shear and normal stresses. We present measurements of the shear stress and two normal stress differences for a microgel subjected to constant shear rate flows. The shear stress evolves through the yield point in a manner indicative of simple yield stress fluid behavior. Prior to yielding, the normal stress differences are immeasurable; beyond the yield point, they evolve in a reproducibly chaotic manner.

Dynamics of microstructure anisotropy and rheology of soft jammed suspensions

We explore the rheology predicted by a recently proposed constitutive model for jammed suspensions of soft elastic particles derived from particle-level dynamics [Cuny et al., Phys. Rev. Lett., 2021, 127, 218003]. Our model predicts that the orientation of the anisotropy of the microstructure, governed by an interplay between advection and contact elasticity, plays a key role at yielding and in flow. It generates normal stress differences contributing significantly to the yield criterion and Trouton ratio. It gives rise to non-trivial transients such as stress overshoots in step increases of shear rate, residual stresses after flow cessation and power-law decay of the shear rate in creep. Finally, it explains the collapse of storage modulus as measured in parallel superposition for a yielded suspension.

Three-dimensional compaction of soft granular packings

This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to 1, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increases, a transition is observed from a granular-like material with exponential tails of the shear stress distributions to a continuous-like material characterized by Gaussian-like distributions of the shear stresses. We develop an equation that describes the evolution of the packing fraction as a function of the applied pressure. This equation, based on the micromechanical expression of the granular stress tensor, the limit of the Hertz contact law for small deformation, and the power-law relation between the packing fraction and the coordination of the particles, provides good predictions from the jamming point up to very high densities without the need for tuning any parameters.

Microscopic Theory for the Rheology of Jammed Soft Suspensions

We develop a constitutive model allowing for the description of the rheology of two-dimensional soft dense suspensions above jamming. Starting from a statistical description of the particle dynamics, we derive, using a set of approximations, a nonlinear tensorial evolution equation linking the deviatoric part of the stress tensor to the strain-rate and vorticity tensors. The coefficients appearing in this equation can be expressed in terms of the packing fraction and of particle-level parameters. This constitutive equation rooted in the microscopic dynamic qualitatively reproduces a number of salient features of the rheology of jammed soft suspensions, including the presence of yield stresses for the shear component of the stress and for the normal stress difference. More complex protocols like the relaxation after a preshear are also considered, showing a smaller stress after relaxation for a stronger preshear.

Continuum modeling of shear startup in soft glassy materials

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress σ_{y} such that YSFs are solid for stresses σ imposed below σ_{y}, whereas they flow like liquids for σ>σ_{y}. Under an applied shear rate γ[over ̇], the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot," followed by stress relaxation towards a steady state. Such relaxation can be either (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, we use a continuum model based on a spatially resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress σ_{M} and strain γ_{M} as a function of γ[over ̇], which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling σ_{M}(γ[over ̇]) is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF, i.e., whether the steady-state flow profile is homogeneous or shear-banded. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling σ_{M}(γ[over ̇]). This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.

Glassy states in adsorbing surfactant-microgel soft nanocomposites

Mixtures of polymer-colloid hybrids such as star polymers and microgels with non-adsorbing polymeric additives have received a lot of attention. In these materials, the interplay between entropic forces and softness is responsible for a wealth of phenomena. By contrast, binary mixtures where one component can adsorb onto the other one have been far less studied. Yet real formulations in applications often contain low molecular weight additives that can adsorb onto soft colloids. Here we study the microstructure and rheology of soft nanocomposites made of surfactants and microgels using linear and nonlinear rheology, SAXS experiments, and cryo-TEM techniques. The results are used to build a dynamical state diagram encompassing various liquid, glassy, jammed, metastable, and reentrant liquid states, which results from a subtle interplay between enthalpic, entropic, and kinetic effects. We rationalize the rheological properties of the nanocomposites in each domain of the state diagram, thus providing exquisite solutions for designing new rheology modifiers at will.

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.

Investigation of the swollen state of Carbopol molecules in non-aqueous solvents through rheological characterization

We explore how different types of solvent influence the rheological properties of non-aqueous Carbopol dispersions from the dilute to the jammed state. In novel non-aqueous formulations, polar solvents are used more and more frequently, because they can form Carbopol microgels without the need of any neutralizing agents. However, the swelling behaviour of Carbopol molecules in the absence of water, when ionic forces are weak, is still poorly understood. To this end, we study the swelling behaviour of Carbopol 974P NF in different polar solvents, i.e. glycerol, PEG400 and mixtures of the two solvents, by mapping the rheological behaviour of Carbopol suspensions from very dilute to highly concentrated conditions. The rheological study reveals that the onset of the jamming transition occurs at different critical polymer concentrations depending on the solvents used. Nevertheless, once the jammed state is reached, both elastic and yielding behaviours are scalable with the particle volume fraction. These results suggest that the type of solvent influences the final volume of the single Carbopol particles but does not alter the interactions between the particles. The final radius of the swollen particles is estimated from shear rheology measurements in dilute conditions, showing a decrease of the final swelling ratio of Carbopol molecules of almost 50% for PEG400 solutions, a result that confirms the shift to higher values of the critical jamming concentration obtained from linear viscoelasticity for the same solutions.

Two-step yielding behavior of densely packed microgel mixtures with chemically dissimilar surfaces and largely different sizes

Steady-state flow and elastic behavior is investigated for the moderately concentrated binary suspensions of soft microgels (pastes) with chemically dissimilar surfaces, and various degrees of size- and stiffness disparities. The pastes of poly(N-isopropyl acrylamide) (N) and poly(N-isopropyl methacrylamide) (NM) microgels with different values of yield strain γc (γNc > γNMc) are employed as the components. For the single microgel pastes (φ ≈ 1 where φ is apparent volume fraction), the values of γc are governed by the chemical species of constituent polymer in microgel surface whereas γc is insensitive to cross-link density and particle size. We demonstrate that the binary N/NM pastes with large size disparity (RN/NM = DN/DNM < 0.26 where D is the microgel diameter) at low φN (φN: weight fraction of small N microgels) exhibit the peculiarities in several rheological aspects, i.e., the two-step yielding in steady-state flow, and their values of γc and equilibrium shear modulus (G0) being equivalent to those of the single large NM microgel paste. These peculiarities are attributed to the characteristic packing resulting from large size disparity in which all or almost of the small N microgels tend to be accommodated in the gap between the large NM microgels even in moderately concentrated state. This characteristic packing substantially masks the contribution of the small N microgels at low φN, explaining the φN-independent G0 and γc as well as the first yielding governed solely by the large NM microgels. The second yielding results from the emerged contribution of the small N microgels expelled out from the gap by the positional rearrangements after the first yielding. The binary homo-N/N pastes with the similarly large size disparity at low φsmall also exhibit the φsmall-independent values of G0, but they show one-step yielding, indicating that the two-step yielding requires not only sufficiently large size disparity but also chemical dissimilarity (different values of γc) between the two components.

The hierarchical emergence of worm-like chain behaviour from globular domain polymer chains

Biological organisms make use of hierarchically organised structures to modulate mechanical behaviour across multiple lengthscales, allowing microscopic objects to generate macroscopic effects. Within these structural hierarchies, the resultant physical behaviour of the entire system is determined not only by the intrinsic mechanical properties of constituent subunits, but also by their organisation in three-dimensional space. When these subunits are polyproteins, colloidal chains or other globular domain polymers, the Kratky-Porod model is often assumed for the individual subunits. Hence, it is implicitly asserted that the polymeric object has an intrinsic parameter, the persistence length, that defines its flexibility. However, the persistence lengths extracted from experiment vary, and are often relatively small. Through a series of simulations on polymer chains formed of globular subunits, we show that the persistence length itself is a hierarchical structural property, related not only to the intrinsic mechanical properties of the underlying monomeric subunits, but emerging due to the organisation of inhomogenous geometry along the polymer contour.