Unified study of glass and jamming rheology in soft particle systems

Rheology of high internal phase ratio emulsions and foams

A comprehensive review of the rheology and related phenomena of high internal phase ratio emulsions (referred to as HIPREs) and foams is presented. Emulsions and foams with Brownian and non-Brownian inclusions (droplets/bubbles) are considered. The topics covered are osmotic pressure, modelling and experiments of the rheology of HIPREs/foams, time-dependent rheology (thixotropy/rheopexy), normal stresses, shear banding and slip effects in flow of HIPREs/foams, influence of solid particle stabilizers (Pickering emulsion/foam), and finally pipe rheology and flow of HIPREs/foams. This is the first review article that covers all aspects of the rheology of HIPREs/foams. The theoretical and empirical models describing the osmotic pressure and rheology (yield stress, storage modulus, viscosity, etc.) of HIPREs/foams are presented and their limitations pointed out. The contributions of entropic effects in the rheology of HIPREs/foams consisting of Brownian inclusions (droplets/bubbles) are given special consideration. The key experimental studies available in the literature are reviewed including measurements of yield stress, storage modulus, and viscosity of HIPREs/foams. Comparisons of experimental data with the theoretical and semi-theoretical models are made and the limitations of the models are identified. Experimental studies elaborating special effects in HIPREs/foams rheology such as thixotropy, rheopexy, normal stresses in fixed shear strain and steady shear, shear banding in thixotropic HIPREs/foams, and slip effects are also reviewed. The effects of average size and size distribution of inclusions (droplets/bubbles) on the rheology of HIPREs/foams are evaluated. The rheology of Pickering HIPREs/foams stabilized with solid nanoparticles at the interface is reviewed and compared with the rheology of surfactant-stabilized systems. Finally, the experimental work published on the pipe flow of HIPREs/foams and its connection to rheology is presented and discussed. The gaps in the existing knowledge of the rheology of HIPREs/foams are identified and future research directions in the area are given.

A Free Energy Model for the Plateau Shear Modulus in Thermosensitive Microgel Suspensions

Polymer microgels exhibit intriguing macroscopic flow properties arising from their unique microscopic structure. Microgel colloids usually comprise a cross-linked polymer network with a radially decaying density profile, resulting in a dense core surrounded by a fuzzy corona. Notably, microgels synthesized from poly(N-isopropylacrylamide) (PNIPAM) are thermoresponsive and capable of adjusting their size and density profile based on temperature. Above the lower critical solution temperature (T LCST ∼ 33 °C), the microgel's polymer network collapses, expulsing water through a reversible process. Conversely, below 33 °C, the microgel's network swells, becoming highly compressible and allowing overpacking to effective volume fractions exceeding one. Under conditions of dense packing, microgels undergo deformation in distinct stages: corona compression and faceting, interpenetration, and finally, isotropic compression. Each stage exhibits a characteristic signature in the dense microgel suspensions' yield stress and elastic modulus. Here, we introduce a model for the linear elastic shear modulus by minimizing a quasi-equilibrium free energy, encompassing all relevant energetic contributions. We validate our model by comparing its predictions to experimental results from oscillatory shear rheology tests on microgel suspensions at different densities and temperatures. Our findings demonstrate that combining macroscopic rheological measurements with the model allows for temperature-dependent characterization of polymer interaction parameters.

Rigidity transition of a highly compressible granular medium

A wide range of disordered materials, from biological to geological assemblies, feature discrete elements undergoing large shape changes. How significant geometrical variations at the microscopic scale affect the response of the assembly, in particular rigidity transitions, is an ongoing challenge in soft matter physics. However, the lack of a model granular-like experimental system featuring large and versatile particle deformability impedes advances. Here, we explore the oscillatory shear response of a sponge-like granular assembly composed of highly compressible elastic rings. We highlight a progressive rigidity transition, switching from a yielded phase to a solid one by increasing density or decreasing shear amplitude. The rearranging yielded state consists of crystal clusters separated by melted regions; in contrast, the solid state remains amorphous and absorbs all imposed shear elastically. We rationalize this transition by uncovering an effective, attractive shear force between rings that emerges from a friction-geometry interplay. If friction is sufficiently high, the extent of the contacts between rings, captured analytically by elementary geometry, controls the rigidity transition.

Viscoelastic properties of colloidal systems with attractive solid particles at low concentration: A review, new results and interpretations

This paper concerns the viscoelastic properties and the resulting structure of colloidal systems with short-range attractions in the regime where the volume fraction f is small. Unlike the high ϕ regime, which is well understood in terms of mode-coupling theory (MCT), the low ϕ regime is still the subject of a debate based on different concepts such as percolation, diffusion-limited colloidal aggregation (DLCA), jamming, or cluster mode-coupling approach. Prior to the analysis of three examples of attractive systems at low ϕ values, a summary of concepts relevant to understanding the formation and properties of such attractive particles is discussed in the present study. Afterwards, we re-analyze the behaviour at a low ϕ of i) suspensions of carbon black (CB) particles, ii) suspensions of poly(methyl methacrylate) (PMMA) hard spheres with a depletion attraction induced by the addition of polystyrene (PS), and iii) suspensions of amino acid organogelator molecules which form rod-like objects. The rheological properties of these systems have been studied in detail and their response has been interpreted as being due either to a solid network discussed in relation to the jamming state diagram or to a suspension formed by jamming of clusters. Our analysis shows that these three systems are in fact cluster fluids and that their solid-like response corresponds to a change in their viscoelastic response, the elastic component G' becoming greater than the viscous component G" at low frequencies. Due to the presence of weak interparticle interactions in the tens range from 1 to 15 kBT, a liquid-like state is reversibly achieved at high frequencies, as indicated by the crossover of G' and G" as a function of frequency for a given concentration. Moreover, all these attractive particle systems at low ϕ show for both moduli a master curve which characterizes these cluster fluids and allows for the classification of these attractive particle systems.

Long-range correlations in elastic moduli and local stresses at the unjamming transition

We explore the behaviour of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic p2 dependence of the correlations as the pressure p approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.

Considerations on the relaxation time in shear-driven jamming

We study the jamming transition in a model of elastic particles under shear at zero temperature, with a focus on the relaxation time τ_{1}. This relaxation time is from two-step simulations where the first step is the ordinary shearing simulation and the second step is the relaxation of the energy after stopping the shearing. τ_{1} is determined from the final exponential decay of the energy. Such relaxations are done with many different starting configurations generated by a long shearing simulation in which the shear variable γ slowly increases. We study the correlations of both τ_{1}, determined from the decay, and the pressure, p_{1}, from the starting configurations as a function of the difference in γ. We find that the correlations of p_{1} are longer lived than the ones of τ_{1} and find that the reason for this is that the individual τ_{1} is controlled both by p_{1} of the starting configuration and a random contribution which depends on the relaxation path length-the average distance moved by the particles during the relaxation. We further conclude that it is γ_{τ}, determined from the correlations of τ_{1}, which is the relevant one when the aim is to generate data that may be used for determining the critical exponent that characterizes the jamming transition.

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (η) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction (ϕS). The increase in η up to ϕS is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, η is a constant above ϕS. To determine the mechanism of this unusual dependence of η on ϕ, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above ϕS but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.

Onset of glassiness in two-dimensional ring polymers: Interplay of stiffness and crowding

The effect of ring stiffness and pressure on the glassy dynamics of a thermal assembly of two-dimensional ring polymers is investigated using extensive coarse-grained molecular dynamics simulations. In all cases, dynamical slowing down is observed with increasing pressure, and thereby, a phase space for equilibrium dynamics is identified in the plane of the obtained monomer density and ring stiffness. When the rings are highly flexible, i.e., have low ring stiffness, glassiness sets in via the crowding of crumpled polymers, which take on a globular form. In contrast, at large ring stiffness, when the rings tend to have large asphericity under compaction, we observe the emergence of local domains having orientational ordering at high pressures. Therefore, our simulations highlight how varying the deformability of rings leads to contrasting mechanisms in driving the system toward the glassy regime.

A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming

Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.

Fluid-Glass-Jamming Rheology of Soft Active Brownian Particles

We numerically study the shear rheology of a binary mixture of soft active Brownian particles, from the fluid to the disordered solid regime. At low shear rates, we find a Newtonian regime, where a Green-Kubo relation with an effective temperature provides the linear viscosity. It is followed by a shear-thinning regime at high shear rates. At high densities, solidification is signaled by the emergence of a finite yield stress. We construct a "fluid-glass-jamming" phase diagram with activity replacing temperature. While both parameters gauge fluctuations, activity also changes the exponent characterizing the decay of the diffusivity close to the glass transition and the shape of the yield stress surface. The dense disordered active solid appears to be mostly dominated by athermal jamming rather than glass rheology.

Strain-Controlled Critical Slowing Down in the Rheology of Disordered Networks

Networks and dense suspensions frequently reside near a boundary between soft (or fluidlike) and rigid (or solidlike) regimes. Transitions between these regimes can be driven by changes in structure, density, or applied stress or strain. In general, near the onset or loss of rigidity in these systems, dissipation-limiting heterogeneous nonaffine rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe a simple quantitative relationship between nonaffinity and the excess viscosity. We test this nonaffinity-viscosity relationship computationally and demonstrate its rheological consequences in simulations of strained filament networks and dense suspensions. We also predict critical signatures in the rheology of semiflexible and stiff biopolymer networks near the strain stiffening transition.

Dependence of the Glass Transition and Jamming Densities on Spatial Dimension

We investigate the dynamics of soft sphere liquids through computer simulations for spatial dimensions from d=3 to 8, over a wide range of temperatures and densities. Employing a scaling of density-temperature-dependent relaxation times, we precisely identify the density ϕ_{0}, which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between ϕ_{0} and the athermal jamming density ϕ_{J}, small in 3 and 4 dimensions, increases with dimension, with ϕ_{0}>ϕ_{J} for d>4. We compare our results with recent theoretical calculations.

Scaling relationships between viscosity and diffusivity in shear-thickening suspensions

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated state to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity η and diffusivity D/ of the particles increase under characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relationship between viscosity and diffusivity using the length scale ξ associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that η and D/ are controlled by ξ in two distinct flow regimes, i.e. in the frictionless and frictional states, where the one-to-one relationship is described as a crossover from D/ ∼ η (frictionless) to η1/3 (frictional). We also confirm that the proposed power laws are insensitive to the interparticle friction and system size.

Glassy and compressed nanoemulsions stabilized with sodium dodecyl sulfate in the presence of poly(ethylene glycol)-diacrylate

The rheology of concentrated nanoemulsions is critical for their formulation in various applications, such as pharmaceuticals, foods, cosmetics, and templating advanced materials. The rheological properties of nanoemulsions depend on interdroplet interactions, Laplace pressure, dispersed phase volume fraction, and continuous phase properties. The interdroplet forces can be tuned by background electrolytes (i.e., charge screening), surfactant type, the excess surfactant micelle concentration, and depletant molecules such as polymer chains. In the current research, we study the effect of varying the content of poly(ethylene glycol)-diacrylate (PEGDA) on the interfacial tension of the water-oil phase and rheological properties of concentrated nanoemulsions with 50% and 60% volume fractions. Sodium dodecyl sulfate (SDS) is used as the ionic surfactant. The final concentrated nanoemulsions are repulsive according to overall interaction potentials and are in the glass and compressed states based on the effective volume fraction estimation. They contain nearly same SDS concentration on the droplet surface and also in the bulk, but a different amount of PEGDA. The scaled rheological properties of the glassy nanoemulsions show a higher dependency on the PEGDA content and the possible effect of polymer-surfactant complexations compared to those of the compressed ones. This dependency is more pronounced in small strain amplitudes but not in large strains in the non-linear regime. These results provide insights into formulating concentrated nanoemulsions with controlled rheology for expanded application areas.

pH- and temperature-responsive supramolecular assemblies with highly adjustable viscoelasticity: a multi-stimuli binary system

Stimuli-responsive materials are increasingly needed for the development of smart electronic, mechanical, and biological devices and systems relying on switchable, tunable, and adaptable properties. Herein, we report a novel pH- and temperature-responsive binary supramolecular assembly involving a long-chain hydroxyamino amide (HAA) and an inorganic hydrotrope, boric acid, with highly tunable viscous and viscoelastic properties. The system under investigation demonstrates a high degree of control over its viscosity, with the capacity to achieve over four orders of magnitude of control through the concomitant manipulation of pH and temperature. In addition, the transformation from non-Maxwellian to Maxwellian fluid behavior could also be induced by changing the pH and temperature. Switchable rheological properties were ascribed to the morphological transformation between spherical vesicles, aggregated/fused spherical vesicles, and bicontinuous gyroid structures revealed by cryo-TEM studies. The observed transitions are attributed to the modulation of the head group spacing between HAA molecules under different pH conditions. Specifically, acidic conditions induce electrostatic repulsion between the protonated amino head groups, leading to an increased spacing. Conversely, under basic conditions, the HAA head group spacing is reduced due to the intercalation of tetrahydroxyborate, facilitated by hydrogen bonding.

Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian

We provide a first-principles derivation of the Langevin equation with shear flow and its corresponding fluctuation-dissipation theorems. Shear flow of simple fluids has been widely investigated by numerical simulations. Most studies postulate a Markovian Langevin equation with a simple shear drag term in the manner of Stokes. However, this choice has never been justified from first principles. We start from a particle-bath system described by a classical Caldeira-Leggett Hamiltonian modified by adding a term proportional to the strain-rate tensor according to Hoover's DOLLS method, and we derive a generalized Langevin equation for the sheared system. We then compute, analytically, the noise time-correlation functions in different regimes. Based on the intensity of the shear rate, we can distinguish between close-to-equilibrium and far-from-equilibrium states. According to the results presented here, the standard, simple, and Markovian form of the Langevin equation with shear flow postulated in the literature is valid only in the limit of extremely weak shear rates compared to the effective vibrational temperature of the bath. For even marginally higher shear rates, the (generalized) Langevin equation is strongly non-Markovian, and nontrivial fluctuation-dissipation theorems are derived.

Paediatric Solid Oral Dosage Forms for Combination Products: Improving In Vitro Swallowability of Minitablets Using Binary Mixtures with Pellets

There is a growing interest in enhancing the acceptability of paediatric pharmaceutical formulations. Solid oral dosage forms (SODF) are being considered as an alternative to liquid formulations, but they may compromise palatability as large volumes may be required. We hypothesised that a binary mixture of paediatric SODF, designed to increase the formulation maximum packing fraction, could reduce the suspension viscosity and facilitate swallowing. Using the Paediatric Soft Robotic Tongue (PSRT) - an in vitro device inspired by the anatomy and physiology of 2-year-old children - we investigated the oral phase of swallowing for multi-particulate formulations, i.e., pellets (350 and 700 µm particles), minitablets (MTs, 1.8 mm), and their binary mixtures (BM), by evaluating oral swallowing time, the percentage of particles swallowed, and post-swallow residues. We also conducted a systematic analysis of the effect of feeding method, bolus volume, carrier type, particle size, and particle volume fraction on pellets swallowability. The results demonstrated that the introduction of pellets affected the flowing ability of the carriers, increasing shear viscosity. The size of the pellets did not appear to influence particle swallowability but raising the particle volume fraction (v.f.) above 10% resulted in a decrease in the percentage of particles swallowed. At v.f. 0.4, pellets were easier to swallow (+ 13.1%) than MTs, being the administration method used highly dependent on the characteristics of the multi-particulate formulation under consideration. Finally, mixing MTs with only 24% of pellets improved particle swallowability, achieving swallowing levels similar to those of pellets alone. Thus, combining SODF, i.e., MTs and pellets, improves MT swallowability, and offers new possibilities for adjusting product palatability, being particularly attractive for combination products.

On the origin of universal cell shape variability in confluent epithelial monolayers

Cell shape is fundamental in biology. The average cell shape can influence crucial biological functions, such as cell fate and division orientation. But cell-to-cell shape variability is often regarded as noise. In contrast, recent works reveal that shape variability in diverse epithelial monolayers follows a nearly universal distribution. However, the origin and implications of this universality remain unclear. Here, assuming contractility and adhesion are crucial for cell shape, characterized via aspect ratio (r), we develop a mean-field analytical theory for shape variability. We find that all the system-specific details combine into a single parameter α that governs the probability distribution function (PDF) of r; this leads to a universal relation between the standard deviation and the average of r. The PDF for the scaled r is not strictly but nearly universal. In addition, we obtain the scaled area distribution, described by the parameter μ. Information of α and μ together can distinguish the effects of changing physical conditions, such as maturation, on different system properties. We have verified the theory via simulations of two distinct models of epithelial monolayers and with existing experiments on diverse systems. We demonstrate that in a confluent monolayer, average shape determines both the shape variability and dynamics. Our results imply that cell shape distribution is inevitable, where a single parameter describes both statics and dynamics and provides a framework to analyze and compare diverse epithelial systems. In contrast to existing theories, our work shows that the universal properties are consequences of a mathematical property and should be valid in general, even in the fluid regime.

Beyond simple self-healing: How anisotropic nanogels adapt their shape to their environment

The response of soft colloids to crowding depends sensitively on the particles’ compressibility. Nanogel suspensions provide model systems that are often studied to better understand the properties of soft materials and complex fluids from the formation of colloidal crystals to the flow of viruses, blood, or platelet cells in the body. Large spherical nanogels, when embedded in a matrix of smaller nanogels, have the unique ability to spontaneously deswell to match their size to that of the nanogel composing the matrix. In contrast to hard colloids, this self-healing mechanism allows for crystal formation without giving rise to point defects or dislocations. Here, we show that anisotropic ellipsoidal nanogels adapt both their size and their shape depending on the nature of the particles composing the matrix in which they are embedded. Using small-angle neutron scattering with contrast variation, we show that ellipsoidal nanogels become spherical when embedded in a matrix of spherical nanogels. In contrast, the anisotropy of the ellipsoid is enhanced when they are embedded in a matrix of anisotropic nanogels. Our experimental data are supported by Monte Carlo simulations that reproduce the trend of decreasing aspect ratio of ellipsoidal nanogels with increasing crowding by a matrix of spherical nanogels.

Structural Measures as Guides to Ultrastable States in Overjammed Packings

Jammed, disordered packings of given sets of particles possess a multitude of equilibrium states with different mechanical properties. Identifying and constructing desired states, e.g., of superior stability, is a complex task. Here, we show that in two-dimensional particle packings the energy of all metastable states (inherent structures) is reliably classified by simple scalar measures of local steric packing. These structural measures are insensitive to the particle interaction potential and so robust that they can be used to guide a modified swap algorithm that anneals polydisperse packings toward low-energy metastable states exceptionally fast. The low-energy states are extraordinarily stable against applied shear, so that the approach also efficiently identifies ultrastable packings.

Rheological response of a glass-forming liquid having large bidispersity

Using extensive numerical simulations, we investigate the flow behaviour of a model glass-forming binary mixture whose constituent particles have a large size ratio. The rheological response to applied shear is studied in the regime where the larger species are spatially predominant. We demonstrate that the macroscopic rigidity that emerges with increasing density occurs in the regime where the larger species undergo a glass transition while the smaller species continue to be highly diffusive. We analyse the interplay between the timescale imposed by the shear and the quiescent relaxation dynamics of the two species to provide a microscopic insight into the observed rheological response. Finally, by tuning the composition of the mixture, we illustrate that the systematic insertion of the smaller particles affects the rheology by lowering of viscosity of the system.

The rheology of confined colloidal hard disks

Colloids may be treated as “big atoms” so that they are good models for atomic and molecular systems. Colloidal hard disks are, therefore, good models for 2d materials, and although their phase behavior is well characterized, rheology has received relatively little attention. Here, we exploit a novel, particle-resolved, experimental setup and complementary computer simulations to measure the shear rheology of quasi-hard-disk colloids in extreme confinement. In particular, we confine quasi-2d hard disks in a circular “corral” comprised of 27 particles held in optical traps. Confinement and shear suppress hexagonal ordering that would occur in the bulk and create a layered fluid. We measure the rheology of our system by balancing drag and driving forces on each layer. Given the extreme confinement, it is remarkable that our system exhibits rheological behavior very similar to unconfined 2d and 3d hard particle systems, characterized by a dynamic yield stress and shear-thinning of comparable magnitude. By quantifying particle motion perpendicular to shear, we show that particles become more tightly confined to their layers with no concomitant increase in density upon increasing the shear rate. Shear thinning is, therefore, a consequence of a reduction in dissipation due to weakening in interactions between layers as the shear rate increases. We reproduce our experiments with Brownian dynamics simulations with Hydrodynamic Interactions (HI) included at the level of the Rotne–Prager tensor. That the inclusion of HI is necessary to reproduce our experiments is evidence of their importance in transmission of momentum through the system.

Beyond the Average: Spatial and Temporal Fluctuations in Oxide Glass-Forming Systems

Atomic structure dictates the performance of all materials systems; the characteristic of disordered materials is the significance of spatial and temporal fluctuations on composition-structure-property-performance relationships. Glass has a disordered atomic arrangement, which induces localized distributions in physical properties that are conventionally defined by average values. Quantifying these statistical distributions (including variances, fluctuations, and heterogeneities) is necessary to describe the complexity of glass-forming systems. Only recently have rigorous theories been developed to predict heterogeneities to manipulate and optimize glass properties. This article provides a comprehensive review of experimental, computational, and theoretical approaches to characterize and demonstrate the effects of short-, medium-, and long-range statistical fluctuations on physical properties (e.g., thermodynamic, kinetic, mechanical, and optical) and processes (e.g., relaxation, crystallization, and phase separation), focusing primarily on commercially relevant oxide glasses. Rigorous investigations of fluctuations enable researchers to improve the fundamental understanding of the chemistry and physics governing glass-forming systems and optimize structure-property-performance relationships for next-generation technological applications of glass, including damage-resistant electronic displays, safer pharmaceutical vials to store and transport vaccines, and lower-attenuation fiber optics. We invite the reader to join us in exploring what can be discovered by going beyond the average.

Turbulent-like velocity fluctuations in two-dimensional granular materials subject to cyclic shear

We perform a systematic experimental study to investigate the velocity fluctuations in the two-dimensional granular matter of low and high friction coefficients subjected to cyclic shear of a range of shear amplitudes, whose velocity fields are strikingly turbulent-like with vortices of different scales. The scaling behaviors of both the transverse velocity power spectra E_T(k) ∝ k^-α_T and, more severely, the longitudinal velocity power spectra E_L(k) ∝ k^-α_L are affected by the prominent peak centered around k ≈ 2π of the inter-particle distance due to the static structure factor of the hard-particle nature in contrast to the real turbulence. To reduce the strong peak effect to the actual values of α_ν (the subscript 'ν' refers to either T or L), we subsequently analyze the second-order velocity structure functions of S(2)ν(r) in real space, which show the power-law scalings of S(2)ν(r) ∝ r^β_ν for both modes. From the values of β_ν, we deduce the corresponding α_ν from the scaling relations of α_ν = β_ν + 2. The deduced values of α_ν increase continuously with the shear amplitude γ_m, showing no signature of yielding transition, and are slightly larger than α_ν = 2.0 at the limit of γ_m → 0, which corresponds to the elastic limit of the system, for all γ_m. The inter-particle friction coefficients show no significant effect on the turbulent-like velocity fluctuations. Our findings suggest that the turbulent-like collective particle motions are governed by both the elasticity and plasticity in cyclically sheared granular materials.

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.

Configurational fingerprints of multicellular living systems

Cells cooperate as groups to achieve structure and function at the tissue level, during which specific material characteristics emerge. Analogous to phase transitions in classical physics, transformations in the material characteristics of multicellular assemblies are essential for a variety of vital processes including morphogenesis, wound healing, and cancer. In this work, we develop configurational fingerprints of particulate and multicellular assemblies and extract volumetric and shear order parameters based on this fingerprint to quantify the system disorder. Theoretically, these two parameters form a complete and unique pair of signatures for the structural disorder of a multicellular system. The evolution of these two order parameters offers a robust and experimentally accessible way to map the phase transitions in expanding cell monolayers and during embryogenesis and invasion of epithelial spheroids.

Instantaneous Normal Modes Reveal Structural Signatures for the Herschel-Bulkley Rheology in Sheared Glasses

The Herschel-Bulkley law, a universal constitutive relation, has been empirically known to be applicable to a vast range of soft materials, including sheared glasses. Although the Herschel-Bulkley law has attracted public attention, its structural origin has remained an open question. In this Letter, by means of atomistic simulation of binary Lennard-Jones glasses, we report that the instantaneous normal modes with negative eigenvalues, or so-called imaginary modes, serve as the structural signatures for the Herschel-Bulkley rheology in sheared glasses.

Rheology of granular liquids in extensional flows: Beyond the μ(I)-law

The Granular Integration Through Transients (GITT) formalism gives a theoretical description of the rheology of moderately dense granular flows and suspensions. In this work, we extend the GITT equations beyond the case of simple shear flows studied before. Applying this to the particular example of extensional flows, we show that the predicted behavior is somewhat different from that of the more frequently studied simple shear case, as illustrated by the possibility of nonmonotonous evolution of the effective friction coefficient μ with the inertial number I. By the reduction of the GITT equations to simple toy models, we provide a generalization of the μ(I)-law true for any type of flow deformation. Our analysis also includes a study of the Trouton ratio, which is shown to behave quite similarly to that of dense colloidal suspensions.

Long-range correlations in pinned athermal networks

We derive exact results for displacement fields that develop as a response to external pinning forces in two-dimensional athermal networks. For a triangular lattice arrangement of particles interacting through soft potentials, we develop a Green's function formalism which we use to derive exact results for displacement fields produced by localized external forces. We show that in the continuum limit the displacement fields decay as 1/r at large distances r away from a force dipole. Finally, we extend our formulation to study correlations in the displacement fields produced by the external pinning forces. We show that uncorrelated pinned forces at each vertex give rise to long-range correlations in displacements in athermal systems, with a nontrivial system size dependence. We verify our predictions with numerical simulations of athermal networks in two dimensions.

Carbomer microgels as model yield-stress fluids

The review presents current research results for Carbopol-based microgels as yield-stress materials, covering three aspects: chemical, physical and rheological. Such a joint three-aspect study has no analog in the literature. The chemical aspects of Carbopol polymers are presented in terms of a cross-linking polymerization of acrylic acid, their molecular structure, microgel formulation, polyacid dissociation and neutralization, osmotic pressure and associated immense microgel swelling. The physical characterization is focused on models of the shear-induced solid-to-liquid transition of microgels, which are formed of mesoscopic particles typical for soft matter materials. Models that describe interparticle effects are presented to explain the energy states of microgel particles at the mesoscale of scrutiny. Typical representatives of the models utilize attributes of jamming dispersions, micromechanical and polyelectrolyte reactions. Selected relationships that result from the models, such as scaling rules and nondimensional flow characteristics are also presented. The rheological part presents the discussion of problems of yield stress in 2D and 3D deformations, appearance and magnitude of the wall slip. The theory and characteristics of Carbopol microgel deformation in rotational rheometers are presented with graphs for the steady-state measurements, stress-controlled oscillation and two types of transient shear deformation. The review is concluded with suggestions for future research.

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.

How size ratio and segregation affect the packing of binary granular mixtures

For reaching high packing fractions, grains of various sizes are often mixed together allowing the small grains to fill the voids created by the large ones. However, in most cases, granular segregation occurs leading to lower packing fractions. We performed a wide set of experiments with different binary granular systems, proving that two main parameters are respectively the volume fraction f of small beads and the grain size ratio α. In addition, we show how granular segregation affects the global packing fraction. We propose a model with a strong dependency on α that takes into account possible granular segregation. Our model is in good agreement with both earlier experimental and simulation data.

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.

Integration through transients approach to the μ(I) rheology

This work generalizes the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)10.1103/PhysRevLett.121.148002] to the determination of the pressure. We focus on the Bagnold regime and provide theoretical support to the empirical μ(I) rheology laws that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the μ(I) laws apply.

Soft granular particles sheared at a controlled volume: rate-dependent dynamics and the solid-fluid transition

We study the responses of fluid-immersed soft hydrogel spheres that are sheared under controlled volume fractions. Slippery, deformable particles along with the density-matched interstitial fluid are sandwiched between two opposing rough cones, allowing studies for a wide range of volume fraction φ both above and below the jamming of granular suspension. We utilize sudden cessations of shearing, accompanied by refraction-matched internal imaging, to supplement the conventional flow-curve measurements. At sufficiently high volume fractions, the settling of particles after the cessations exhibits a continuous yet distinct transition over the change of the shear rate. Such changes back out the qualitative difference in the state of flowing prior to the cessations: the quasi-static yielding of a tightly packed network, as opposed to the rapid sliding of particles mediated by the interstitial fluid whose dynamics depends on the driving rate. In addition, we determine the solid-fluid transition using two independent methods: the extrapolation of stress residues and the estimated yield stress from high values of φ, and the settling of particles upon shear cessations as φ goes across the transition. We also verify the power law on values of characteristic stress with respect to the distance from jamming φ - φc, with an exponent close to 2. These results demonstrate a multitude of relaxation timescales behind the dynamics of soft particles, and raise questions on how we extend the existing paradigms of the flow of a densely packed system when the softness is actively involved.

Rheology of colloidal and metallic glass formers

Colloidal hard-sphere suspensions are convenient experimental models to understand soft matter, and also by analogy the structural-relaxation behavior of atomic or small-molecular fluids. We discuss this analogy for the flow and deformation behavior close to the glass transition. Based on a mapping of temperature to effective hard-sphere packing, the stress–strain curves of typical bulk metallic glass formers can be quantitatively compared with those of hard-sphere suspensions. Experiments on colloids give access to the microscopic structure under deformation on a single-particle level, providing insight into the yielding mechanisms that are likely also relevant for metallic glasses. We discuss the influence of higher-order angular signals in connection with non-affine particle rearrangements close to yielding. The results are qualitatively explained on the basis of the mode-coupling theory. We further illustrate the analogy of pre-strain dependence of the linear-elastic moduli using data on PS-PNiPAM suspensions.

Shear jamming, discontinuous shear thickening, and fragile states in dry granular materials under oscillatory shear

We numerically study the linear response of two-dimensional frictional granular materials under oscillatory shear. The storage modulus G^{'} and the loss modulus G^{''} in the zero strain rate limit depend on the initial strain amplitude of the oscillatory shear before measurement. The shear jammed state (satisfying G^{'}>0) can be observed at an amplitude greater than a critical initial strain amplitude. The fragile state is defined by the emergence of liquid-like and solid-like states depending on the form of the initial shear. In this state, the observed G^{'} after the reduction of the strain amplitude depends on the phase of the external shear strain. The loss modulus G^{''} exhibits a discontinuous jump corresponding to discontinuous shear thickening in the fragile state.

Stress Relaxation above and below the Jamming Transition

We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending on whether the transition is approached from the jammed or unjammed phase. This contrasts sharply with conventional dynamic critical scaling scenarios, where a single exponent characterizes both sides. We explain this surprising difference in terms of the vibrational density of states, which is a key ingredient of linear viscoelastic theory. The vibrational density of states exhibits an extra slow mode that emerges below jamming, which we utilize to demonstrate the anomalous exponent below jamming.

Dynamical Heterogeneity near Glass Transition Temperature under Shear Conditions

We experimentally studied the shear effect on dynamical heterogeneity near glass transition temperature. X-ray photon correlation spectroscopy was utilized to study the dynamics of polyvinyl acetate with tracer particles near its glass transition temperature, to determine the local shear rate from the anisotropic behavior of the time autocorrelation function and to calculate the dynamical heterogeneity using higher-order correlation function. The obtained results show a decrease in the dynamical heterogeneity and faster dynamics with increasing shear rate. This is the first experimental result that proved the predictions of previous molecular dynamics simulations.

Micro-mechanical theory of shear yield stress for strongly flocculated colloidal gel

Shear yield stress is an important parameter in the processing of colloidal suspensions as it characterizes the solid-to-fluid transition. Although shear rheology of colloidal gel is of widespread academic and industrial interest, first principles theory that connects the microscopic properties to the macroscopic mechanical response in a self-consistent manner is lacking. In this work, we derive a constitutive relation to predict the yield stress for a strongly attractive gel undergoing quasi-static shear deformation as a function of volume fraction, inter-particle potential, contact scale properties and the micro-structure of a strongly-aggregated colloidal gel. The model also predicts the strain at which the colloidal gel network will yield under shear load. To test the model, discrete element simulation is performed using a non-central potential with friction while accounting for the rolling resistance, which is important in real colloidal gel systems. The theoretical predictions are not only in good agreement with the simulation results, but also with previous experiments.

Universal Relaxation Dynamics of Sphere Packings below Jamming

We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic timescale that diverges at jamming. This slow timescale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.

Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.

Slow Coarsening in Jammed Athermal Soft Particle Suspensions

We simulate a densely jammed, athermal assembly of repulsive soft particles immersed in a solvent. Starting from an initial condition corresponding to a quench from a high temperature, we find nontrivial slow dynamics driven by a gradual release of stored elastic energy, with the root mean squared particle speed decaying as a power law in time with a fractional exponent. This decay is accompanied by the presence within the assembly of spatially localized and temporally intermittent "hot spots" of nonaffine deformation, connected by long-ranged swirls in the velocity field, reminiscent of the local plastic events and long-ranged elastic propagation that have been intensively studied in sheared amorphous materials. The pattern of hot spots progressively coarsens, with the hot-spot size and separation slowly growing over time, and the associated correlation length in particle speed increasing as a sublinear power law. Each individual spot, however, exists only transiently within an overall picture of strongly intermittent dynamics.