Soft Glassy Materials Research Articles

Squeeze flow behavior of (soft glassy) thixotropic material

We study the flow behavior of a model soft glassy material − an aqueous suspension of Laponite − when it is squeezed between two circular parallel plates of different roughness. Aqueous suspension of Laponite shows a time dependent aging behavior as reflected in increased elastic modulus as well as yield stress, both of which however also decrease with an increase in the strength of deformation field thereby demonstrating typical thixotropic character. In a squeeze flow situation, under both force as well as velocity controlled modes; we find the behavior to be independent of the initial gap between the plates. In a constant force mode, the gap between the plates decreases until it reaches a finite limiting value, which is found to increase with an increase in age of the material as well as with a decrease in the applied force. In constant velocity experiments, at large gaps between the plates, normal force varies inversely with plate separation. The normal force is higher for a sample aged for a longer time as well as for a larger velocity of the top plate. We observe that the experimental behavior follows prediction of Herschel–Bulkley model solved for the squeeze flow (with different friction coefficients at the two plates) reasonably well under weak deformation fields. However, under strong deformation fields, experimental behavior deviates significantly from the prediction of Herschel–Bulkley model. This deviation arises due to melting or partial yielding of Laponite suspension under large deformation fields causing decrease in the viscosity, elastic modulus and the yield stress.

Glass physics: from fundamentals to applications

A new focus on glass physics has arisen with the emergence, on the one hand, of soft glassy materials in technologically significant and biological contexts, and, on the other hand, of metallic glasses that present intriguing opportunities for the efficient manufacture of valuable high strength components. The slow dynamics that develops in liquids cooled toward the glass transition temperature and the nature of the glass transition that follows remain at the core of the glass puzzle, and endure as grand theoretical challenges in understanding condensed matter. However, a focus on the applications of these new materials has resulted in a flowering of investigations on the origin of aging, dynamical heterogeneity and slow relaxation with a focus on relating glass structure to the prediction of important properties such as fragility, glass formability, rheology and elastic and plastic responses to mechanical stress. Simultaneously the scope of research has expanded in new directions owing to advances in research tools ranging from more powerful computational capabilities to improved scattering facilities and advanced imaging techniques. Sustained engagement between physical scientists and the materials science communities working to unlock the technological capabilities of specific glasses has generated a renewed interest in previously underappreciated gaps in our understanding, expanding the productive interface between fundamental and applied investigations in glass physics. This special issue in European Physical Journal E brings together a cross-section of research advances, highlighting the diversity of basic and applied interest in glassy behavior in a wide range of systems (colloidal, polymer, chalcogenide, metallic, granular, biomolecular, organic and oxide glasses). Several papers discuss theoretical and computational investigations of model glass formers such as a critique of structure-based microscopic theories of dynamics and a field-theoretic description of dynamical heterogeneity. The papers in this issue showcase examples of cross-fertilization, such as the application of mode-coupling theory, extensively employed in analyzing slow dynamics in glass-forming liquids, to analyzing motion under shear, but also energy-landscape analysis of mechanical deformation, the study of heterogeneity effects in polymer thin films and the jamming behavior in polymer solutions, to name but a few examples. We hope that this compilation will serve the purpose of furthering the interaction across the boundaries between fundamental and applied research, and among practitioners in different sub-areas, leading to the emergence of new thrust directions, concepts, and exciting developments.

Effects of Spark Plasma Sintering Parameters on the Crystallization and Densification of Fe76Si9B10P5 Atomization Powders

A soft magnetic Fe76Si9B10P5 glassy bulk material was prepared by the spark plasma sintering technique below the glass transition temperature. The glassy powders were consolidated into bulk forms with relative densities above 98.7%. The sintering parameters were a temperature of 467 °C, a pressure of 600 MPa, a heating rate of 100 °C/min, and a holding time of 6 min while the samples were still in a glassy state. The effects of these parameters on the crystallization and densification of Fe76Si9B10P5 were investigated by X-ray diffraction and differential scanning calorimetry.

Shear banding from lattice kinetic models with competing interactions

We present numerical simulations based on a Boltzmann kinetic model with competing interactions, aimed at characterizing the rheological properties of soft-glassy materials. The lattice kinetic model is shown to reproduce typical signatures of driven soft-glassy flows in confined geometries, such as Herschel-Bulkley rheology, shear banding and hysteresis. This lends further credit to the present lattice kinetic model as a valuable tool for the theoretical/computational investigation of the rheology of driven soft-glassy materials under confinement.

Theoretical perspective on the glass transition and amorphous materials

We provide a theoretical perspective on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations to study and understand the dynamics of systems close to the glass transition at the molecular level is spelled out. We review the recent progress on the subject of the spatially heterogeneous dynamics that characterizes structural relaxation in materials with slow dynamics. We then present the main theoretical approaches describing the glass transition in supercooled liquids, focusing on theories that have a microscopic, statistical mechanics basis. We describe both successes and failures, and critically assess the current status of each of these approaches. The physics of aging dynamics in disordered materials and the rheology of soft glassy materials are then discussed, and recent theoretical progress is described. For each section, we give an extensive overview of the most recent advances, but we also describe in some detail the important open problems that, we believe, will occupy a central place in this field in the coming years.

Shear-transformation-zone theory of linear glassy dynamics

We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both metallic glasses and soft glassy materials such as colloidal suspensions. We find that the frequency-dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an α peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.

Linear Response Theory for Hard and Soft Glassy Materials

Despite qualitative differences in their underlying physics, both hard and soft glassy materials exhibit almost identical linear rheological behaviors. We show that these nearly universal properties emerge naturally in a shear-transformation-zone theory of amorphous plasticity, extended to include a broad distribution of internal thermal-activation barriers. The principal features of this barrier-height distribution are predicted by nonequilibrium, effective-temperature thermodynamics. Our theoretical loss modulus G''(ω) has a peak at the α relaxation rate, and a power law decay of the form ω(-ζ) for higher frequencies, in quantitative agreement with experimental data.

Prediction of Long and Short Time Rheological Behavior in Soft Glassy Materials

We present an effective time approach to predict long and short time rheological behavior of soft glassy materials from experiments carried out over practical time scales. Effective time approach takes advantage of relaxation time dependence on aging time that allows time-aging time superposition even when aging occurs over the experimental time scales. Interestingly, experiments on a variety of soft materials demonstrate that the effective time approach successfully predicts superposition for diverse aging regimes ranging from subaging to hyperaging behaviors. This approach can also be used to predict behavior of any response function in molecular as well as spin glasses.

Glass Transition Seen through Asymptotic Expansions

Soft glassy materials exhibit the so-called glassy transition, which means that the behavior of the model at a low shear rate changes when a certain parameter (which we call the glass parameter) crosses a critical value. This behavior goes from a Newtonian behavior to a Herschel–Bulkley behavior through a power-law-type behavior at the transition point. In a previous paper we rigorously proved that the Hébraud–Lequeux model, a Fokker–Planck-like description of soft glassy material, exhibits such a glass transition. But the method we used was very specific to the one-dimensional setting of the model, and as a preparation for generalizing this model to take into account multidimensional situations, we look for another technique to study the glass transition of this type of model. In this paper we shall use matched asymptotic expansions for such a study. The difficulties encountered when using asymptotic expansions for the Hébraud–Lequeux model are that multiple ansaetze have to be used, even though the initial model is unique, due to the glass transition. We shall delineate the various regimes and give a rigorous justification of the expansion by means of an implicit function argument. The use of a two parameter expansion plays a crucial role in elucidating the reasons for the scalings which occur.

A kinetic elasto-plastic model exhibiting viscosity bifurcation in soft glassy materials

A kinetic elasto-plastic model of the dynamics of a flowing jammed material is proposed, supplemented with a phenomenological equation describing the coupling of the flow and the structure of the fluid. Coarse graining these equations yields a non-local constitutive law for the flow, with the introduction of the number of plastic events per unit time, called the fluidity, as a key dynamical parameter. Above a given threshold, the weakening of the structure caused by the flow induces a macroscopic phase separation that causes viscosity bifurcation.

Work hardening of soft glassy materials, or a metallurgist’s view of peanut butter

The non-linear rheology of colloidal gels, glasses, and pastes is rather complex. For instance, colloidal glasses and pastes yield at a certain strain, followed by shear thinning. A detailed understanding of the yielding point, and what causes it, is lacking. Here, we perform constant shear rate rheology on a pre-sheared material, smooth peanut butter, which is a glassy colloidal paste. Controlling the ageing appears to control the yield stress value, whose associated stress scales with the applied pre-shear with a power law of 1/2. This corresponds to the governing formula for the work hardening mechanism in metals, from which an analogy is drawn.

Self-similarity in electrorheological behavior

In this work we study creep flow behavior of suspension of Polyaniline (PANI) particles in silicone oil under application of electric field. Suspension of PANI in silicone oil, a model electrorheological fluid, shows enhancement in elastic modulus and yield stress with increase in the magnitude of electric field. Under creep flow field, application of greater magnitude of electric field reduces strain induced in the material while application of greater magnitude of shear stress at any electric field enhances strain induced in the material. Remarkably, time evolution of strain in PANI suspension at different stresses, electric field strengths and concentrations show superposition after appropriate shifting of the creep curves on time and strain axes. Observed electric field - shear stress - creep time - concentration superposition demonstrates self-similarity in electrorheological behavior. We analyze the experimental data using Bingham and Klingenberg - Zukoski model and observe that the latter predicts the experimental behavior very well. We conclude by discussing remarkable similarities between observed rheological behavior of ER fluids and rheological behavior of aging soft glassy materials.

Understanding and predicting viscous, elastic, plastic flows

Foams, gels, emulsions, polymer solutions, pastes and even cell assemblies display both liquid and solid mechanical properties. On a local scale, such "soft glassy" systems are disordered assemblies of deformable rearranging units, the complexity of which gives rise to their striking flow behaviour. On a global scale, experiments show that their mechanical behaviour depends on the orientation of their elastic deformation with respect to the flow direction, thus requiring a description by tensorial equations for continuous materials. However, due to their strong non-linearities, the numerous candidate models have not yet been solved in a general multi-dimensional geometry to provide stringent tests of their validity. We compute the first solutions of a continuous model for a discriminant benchmark, namely the flow around an obstacle. We compare it with experiments of a foam flow and find an excellent agreement with the spatial distribution of all important features: we accurately predict the experimental fields of velocity, elastic deformation, and plastic deformation rate in terms of magnitude, direction, and anisotropy. We analyse the role of each parameter, and demonstrate that the yield strain is the main dimensionless parameter required to characterize the materials. We evidence the dominant effect of elasticity, which explains why the stress does not depend simply on the shear rate. Our results demonstrate that the behaviour of soft glassy materials cannot be reduced to an intermediate between that of a solid and that of a liquid: the viscous, the elastic and the plastic contributions to the flow, as well as their couplings, must be treated simultaneously. Our approach opens the way to the realistic multi-dimensional prediction of complex flows encountered in geophysical, industrial and biological applications, and to the understanding of the link between structure and rheology of soft glassy systems.

Yielding and Shear Banding in Soft Glassy Materials

Yield stress fluids have proven difficult to characterize, and a reproducible determination of the yield stress is difficult. We study two types of yield stress fluids (YSF) in a single system: simple and thixotropic ones. This allows us to show that simple YSF are simply a special case of thixotropic ones, and to pinpoint the difference between static and dynamic yield stresses, one of the major problems in the field. The thixotropic systems show a strong time dependence of the viscosity due to the existence of an internal percolated structure that confers the yield stress to the material. Using loaded emulsions to control the thixotropy, we show that the transition to flow at the yield stress is discontinuous for thixotropic materials, and continuous for ideal ones. The discontinuity leads to a critical shear rate below which no steady flows can be observed, accounting for the ubiquitous shear banding observed in these materials.

Rheological fingerprinting of an aging soft colloidal glass

We investigate the complex flow behavior of a well-characterized colloidal star glass using linear and nonlinear rheology. The results are integrated into a generic state diagram which specifies the states of the glass for different initial conditions and mechanical histories: viscoelastic liquid and solid, homogeneous shear-thinned solution, and shear-banded material. Aging takes different forms which can be interpreted as kinetic pathways through the state diagram. Shear-banding appears to be an intrinsic mechanical instability which occurs when the solid state of the glass is shear-melted. Our results provide a straightforward methodology to fingerprint the material behavior of soft glassy materials undergoing rheological transitions which can be used as predictive tool to design systems with a desired rheological response.

Time–aging time–stress superposition in soft glass under tensile deformation field

We have studied the tensile deformation behaviour of thin films of aging aqueous suspension of Laponite, a model soft glassy material, when subjected to a creep flow field generated by a constant engineering normal stress. Aqueous suspension of Laponite demonstrates aging behaviour wherein it undergoes time dependent enhancement of its elastic modulus as well as its characteristic relaxation time. However, under application of the normal stress, the rate of aging decreases and in the limit of high stress, the aging stops with the suspension now undergoing a plastic deformation. Overall, it is observed that the aging that occurs over short creep times at small normal stresses is same as the aging that occurs over long creep times at large normal stresses. This observation allows us to suggest an aging time - process time - normal stress superposition principle, which can predict rheological behaviour at longer times by carrying out short time tests.

Three-dimensional jamming and flows of soft glassy materials

Various disordered dense systems, such as foams, gels, emulsions and colloidal suspensions, undergo a jamming transition from a liquid state (they flow) to a solid state below a yield stress. Their structure, which has been thoroughly studied with powerful means of three-dimensional characterization, shows some analogy with that of glasses, which led to them being named soft glassy materials. However, despite its importance for geophysical and industrial applications, their rheological behaviour, and its microscopic origin, is still poorly known, in particular because of its nonlinear nature. Here we show from two original experiments that a simple three-dimensional continuum description of the behaviour of soft glassy materials can be built. We first show that when a flow is imposed in some direction there is no yield resistance to a secondary flow: these systems are always unjammed simultaneously in all directions of space. The three-dimensional jamming criterion seems to be the plasticity criterion encountered in most solids. We also find that they behave as simple liquids in the direction orthogonal to that of the main flow; their viscosity is inversely proportional to the main flow shear rate, as a signature of shear-induced structural relaxation, in close similarity to the structural relaxations driven by temperature and density in other glassy systems.

How does a soft glassy material flow: finite size effects, non local rheology, and flow cooperativity

In this paper, we investigate the rheological behavior of jammed emulsions in microchannels on the basis of microvelocimetry techniques. We demonstrate that velocity profiles in this confined geometry cannot be accounted for by the bulk - Herschel-Bulkley - rheological flow curve measured independently in a rheometer. A strong dependence of the flow behavior on the confinement, pressure drop and surface roughness is evidenced, which cannot be described by classical rheological descriptions. We show that these behaviors can be rationalized on the basis of a non local rheological model, introducing the notion of local fluidity as a key rheological quantity. The model reproduces the experimental velocity profiles for any confinements and any surface nature. The non-locality is quantified by a length, ζ, characterizing the flow cooperativity of jammed emulsions, and typically of the order of several emulsion droplet diameters. We study the influence of volume fraction, droplet diameter, and emulsions polydispersity on this length.

Graphics processing unit implementation of lattice Boltzmann models for flowing soft systems

A graphic processing unit (GPU) implementation of the multicomponent lattice Boltzmann equation with multirange interactions for soft-glassy materials ["glassy" lattice Boltzmann (LB)] is presented. Performance measurements for flows under shear indicate a GPU/CPU speed up in excess of 10 for 1024(2) grids. Such significant speed up permits to carry out multimillion time-steps simulations of 1024(2) grids within tens of hours of GPU time, thereby considerably expanding the scope of the glassy LB toward the investigation of long-time relaxation properties of soft-flowing glassy materials.

On secondary loops in LAOS via self-intersection of Lissajous–Bowditch curves

When the shear stress measured in large amplitude oscillatory shear (LAOS) deformation is represented as a 2-D Lissajous–Bowditch curve, the corresponding trajectory can appear to self-intersect and form secondary loops. This self-intersection is a general consequence of a strongly nonlinear material response to the imposed oscillatory forcing and can be observed for various material systems and constitutive models. We derive the mathematical criteria for the formation of secondary loops, quantify the location of the apparent intersection, and furthermore suggest a qualitative physical understanding for the associated nonlinear material behavior. We show that when secondary loops appear in the viscous projection of the stress response (the 2-D plot of stress vs. strain rate), they are best interpreted by understanding the corresponding elastic response (the 2-D projection of stress vs. strain). The analysis shows clearly that sufficiently strong elastic nonlinearity is required to observe secondary loops on the conjugate viscous projection. Such a strong elastic nonlinearity physically corresponds to a nonlinear viscoelastic shear stress overshoot in which existing stress is unloaded more quickly than new deformation is accumulated. This general understanding of secondary loops in LAOS flows can be applied to various molecular configurations and microstructures such as polymer solutions, polymer melts, soft glassy materials, and other structured fluids.