Aging in a colloidal glass in creep flow: time-stress superposition

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.

Elastoviscoplasticity, hyperaging, and time-age-time-temperature superposition in aqueous dispersions of bentonite clay

Clay slurries are both ubiquitous and essential in the oil exploration industry, and are most commonly employed as drilling fluids. Due to its natural abundance, bentonite clay is often the de facto choice for these materials. Understanding and predicting the mechanical response of these fluids is critical for safe and efficient drilling operations. However, rheological modeling of bentonite clay suspensions is complicated by the fact that thermally-driven microscopic arrangements of particle aggregates lead to a continual evolution of the viscoelastic properties and the yield stress of the suspension with time. Ergodic relations fundamental to linear viscoelastic theory, such as the Boltzmann superposition principle, do not hold in this scenario of 'rheological aging'. We present an approach for modeling the linear viscoelastic response of aging bentonite suspensions across a range of temperatures that is based on the transformation from laboratory time to an effective 'material time' domain in which time-translation invariance holds, and the typical relations of non-aging linear viscoelastic theory apply. In particular, we model the constitutive relationship between stress and strain-rate in the bentonite suspensions as fractional Maxwell gels with constant relaxation dynamics in the material time domain, in parallel with a non-aging Newtonian viscous contribution to the total stress. This approach is supported by experimental measurements of the stress relaxation and rapid time-resolved measurements of the linear viscoelastic properties performed using optimized exponential chirps. This data is then reduced to master curves in the material domain using time-age-time superposition to obtain best fits of the model parameters over a range of operating temperatures.

Antibodies Adsorbed to the Air-Water Interface Form Soft Glasses

When monoclonal antibodies are exposed to an air-water interface, they form aggregates, which negatively impacts their performance. Until now, the detection and characterization of interfacial aggregation have been difficult. Here, we exploit the mechanical response imparted by interfacial adsorption by measuring the interfacial shear rheology of a model antibody, anti-streptavidin immunoglobulin-1 (AS-IgG1), at the air-water interface. Strong viscoelastic layers of AS-IgG1 form when the protein is adsorbed from the bulk solution. Creep experiments correlate the compliance of the interfacial protein layer with the subphase solution pH and bulk concentration. These, along with oscillatory strain amplitude and frequency sweeps, show that the viscoelastic behavior of the adsorbed layers is that of a soft glass with interfacial shear moduli on the order of 10-3 Pa m. Shifting the creep compliance curves under different applied stresses forms master curves consistent with stress-time superposition of soft interfacial glasses. The interfacial rheology results are discussed in the context of the interface-mediated aggregation of AS-IgG1.

Structural and rheological aging in model attraction-driven glasses by Rheo-SANS

Aging in a model colloidal suspension comprised of particles with a thermoreversible attraction is studied using Rheo-SANS techniques in the attractive-driven glass state. Multiple thermal pathways lead to a common rheological and microstructural aging trajectory, as was observed previously for a thermoreversible gel. SANS measurements of the colloidal glass microstructure as a function of temperature and time during various quench protocols are quantitatively characterized in terms of an effective interaction strength that becomes an order parameter defining the microstructural state of the glass. Using previously validated concepts of a fictive temperature, a semi-empirical, quantitative relationship similar to an Avrami relationship is established between the mechanical aging (elastic modulus) and microstructural aging (order parameter) that is independent of thermal history for the thermal profiles studied herein at long times. Furthermore, shear rejuvenation is studied, and while shear may only partially reduce the degree of structure in the glass, aging upon flow cessation is found to follow a common trajectory when viewed in terms of the microstructural order parameter.

Microstructure and Soft Glassy Dynamics of an Aqueous Laponite Dispersion

Synthetic hectorite clay Laponite RD/XLG is composed of disk-shaped nanoparticles that acquire dissimilar charges when suspended in an aqueous medium. Owing to their property to spontaneously self-assemble, Laponite is used as a rheology modifier in a variety of commercial water-based products. In particular, an aqueous dispersion of Laponite undergoes a liquid-to-solid transition at about 1 vol % concentration. The evolution of the physical properties as the dispersion transforms to the solid state is reminiscent of physical aging in molecular as well as colloidal glasses. The corresponding soft glassy dynamics of an aqueous Laponite dispersion, including the rheological behavior, has been extensively studied in the literature. In this feature article, we take an overview of recent advances in understanding soft glassy dynamics and various efforts taken to understand the peculiar rheological behavior. Furthermore, the continuously developing microstructure that is responsible for the eventual formation of a soft solid state that supports its own weight against gravity has also been a topic of intense debate and discussion. In particularly, extensive experimental and theoretical studies lead to two types of microstructures for this system: an attractive gel-like or a repulsive glass-like structure. We carefully examine and critically analyze the literature and propose a state (phase) diagram that suggests an aqueous Laponite dispersion to be present in an attractive gel state.

Physical aging and structural recovery in a colloidal glass subjected to volume-fraction jump conditions

Three important kinetic phenomena have been cataloged by Kovacs in the investigation of molecular glasses during structural recovery or physical aging. These are responses to temperature-jump histories referred to as intrinsic isotherms, asymmetry of approach, and memory effect. Here we use a thermosensitive polystyrene-poly (N-isopropylacrylamide)-poly (acrylic acid) core-shell particle-based dispersion as a colloidal model and by working at a constant number concentration of particles we use temperature changes to create volume-fraction changes. This imposes conditions similar to those defined by Kovacs on the colloidal system. We use creep experiments to probe the physical aging and structural recovery behavior of colloidal glasses in the Kovacs-type histories and compare the results with those seen in molecular glasses. We find that there are similarities in aging dynamics between molecular glasses and colloidal glasses, but differences also persist. For the intrinsic isotherms, the times t_{eq} needed for relaxing or evolving into the equilibrium (or stationary) state are relatively insensitive to the volume fraction and the values of t_{eq} are longer than the α-relaxation time τ_{α} at the same volume fraction. On the other hand, both of these times grow at least exponentially with decreasing temperature in molecular glasses. For the asymmetry of approach, similar nonlinear behavior is observed for both colloidal and molecular glasses. However, the equilibration time t_{eq} is the same for both volume-fraction up-jump and down-jump experiments, different from the finding in molecular glasses that it takes longer for the structure to evolve into equilibrium for the temperature up-jump condition than for the temperature down-jump condition. For the two-step volume-fraction jumps, a memory response is observed that is different from observations of structural recovery in two-step temperature histories in molecular glasses. The concentration dependence of the dynamics of the colloidal dispersions is also examined in the equilibrium state and we find that the dynamic fragility index m is sensitive to the degree of softness of the soft colloidal dispersion, indicating that soft colloids make stronger glasses. Finally, we compare the present results with prior findings for similar thermoresponsive systems obtained with diffusing wave spectroscopy and discuss similarities and differences.

Creep and aging of hard-sphere glasses under constant stress

We investigate the aging behavior of glassy suspensions of nearly hard-sphere colloids submitted to a constant shear stress. For low stresses, below the yield stress, the system is subject to creep motion. As the sample ages, the shear rate exhibits a power-law decrease with time with exponents that depend on the sample age. We use a combination of rheological experiments with time-resolved photon correlation spectroscopy to investigate the time evolution of the sample dynamics under shear on various time and length scales. Long-time light-scattering experiments reveal the occurrence of microscopic rearrangement events that are linked with the macroscopic strain deformation of the sample. Dynamic time sweep experiments indicate that while the internal microscopic dynamics slow down continuously with waiting time, the storage and loss moduli are almost constant after a fast, weak decrease, resembling the behavior of quenched systems with partially frozen-in stresses.

A model for aging under deformation field, residual stresses and strains in soft glassy materials

A model is proposed that considers aging and rejuvenation in a soft glassy material as, respectively, a decrease and an increase in free energy. The aging term is weighted by an inverse of characteristic relaxation time suggesting that greater mobility of the constituents induces faster aging in a material. A dependence of relaxation time on free energy is proposed, which under quiescent conditions leads to a power law dependence of relaxation time on waiting time as observed experimentally. The model considers two cases, namely, a constant modulus when aging is entropy controlled and a time dependent modulus. In the former and the latter cases the model has, respectively, two and three experimentally measurable parameters that are physically meaningful. Overall, the model predicts how the material undergoes aging and approaches a rejuvenated state under the application of a deformation field. In particular, the model proposes distinctions between various kinds of rheological effects for different combinations of parameters. Interestingly, when the relaxation time evolution is stronger than linear, the model predicts various features observed in soft glassy materials such as thixotropic and constant yield stress, thixotropic shear banding, and the presence of residual stress and strain.

Comparison of the physical aging behavior of a colloidal glass after shear melting and concentration jumps

Colloidal systems are considered good models of molecular glasses and we further explore the range of validity of this paradigm using a thermosensitive core-shell particle dispersion to study the aging response of a colloidal glass subsequent to both shear-melting and temperature (concentration)-jump perturbations in the vicinity of the glass transition concentration or temperature. Sequential creep experiments were used to probe the different aging responses of the system. The colloidal glass displays aging behavior after both types of perturbation and our results indicate that this colloidal glass is similar to a molecular glass, in that shift rates are found to be below unity and to decrease towards zero as the glass temperature (or concentration) is approached as temperature increases. However, the kinetics of the aging in the two cases are different indicating that the structural changes induced by the mechanical perturbation are different from those induced by the temperature or concentration jump-similar to findings on mechanical rejuvenation of molecular glasses. We also find differences between the colloidal glass and molecular glasses: In the case of the colloidal glass the structural recovery or equilibration times do not diverge, while the mechanical relaxation times do. On the other hand, for the molecular glass, both times change very rapidly with decreasing temperature, apparently towards a distant point of divergence.

Dynamics of colloidal glasses and gels

Many household and industrially important soft colloidal materials, such as pastes, concentrated suspensions and emulsions, foams, slurries, inks, and paints, are very viscous and do not flow over practical timescales until sufficient stress is applied. This behavior originates from restricted mobility of the constituents arrested in disordered structures of varying length scales, termed colloidal glasses and gels. Usually these materials are thermodynamically out of equilibrium, which induces a time-dependent evolution of the structure and the properties. This review presents an overview of the rheological behavior of this class of materials. We discuss the experimental observations and theoretical developments regarding the microstructure of these materials, emphasizing the complex coupling between the deformation field and nonequilibrium structures in colloidal glasses and gels, which leads to a rich array of rheological behaviors with profound implications for various industrial processes and products.

Creep in colloidal glasses

We investigate the nonlinear response to shear stress of a colloidal hard-sphere glass, identifying several regimes depending on time, sample age, and the magnitude of applied stress. This emphasizes a connection between stress-imposed deformation of soft and hard matter, in particular, colloidal and metallic systems. A generalized Maxwell model rationalizes logarithmic creep for long times and low stresses. We identify diverging time scales approaching a critical yield stress. At intermediate times, strong aging effects are seen, which we link to a stress overshoot seen in stress-strain curves.

Hyper-aging dynamics of nanoclay suspension

Aqueous suspension of nanoclay Laponite undergoes structural evolution as a function of time, which enhances its elasticity and relaxation time. In this work, we employ an effective time approach to investigate long-term relaxation dynamics by carrying out creep experiments. Typically, we observe that the monotonic evolution of elastic modulus shifts to lower aging times, while maxima in viscous moduli get progressively broader for experiments carried out on a later date after preparation (idle time) of the nanoclay suspension. Application of effective time theory produces a superposition of all the creep curves irrespective of their initial state. The resulting dependence of the relaxation time on aging time shows very strong hyper-aging dynamics at short idle times, which progressively weakens to demonstrate a linear dependence in the limit of very long idle times. Remarkably, this behavior of nanoclay suspensions is akin to that observed for polymeric glasses. Consideration of aging as a first-order process suggests that continued hyper-aging dynamics causes cessation of aging. The dependence of relaxation time on aging time, therefore, must attenuate eventually producing linear or weaker dependence on time in order to approach a progressively low-energy state in the limit of very long times as observed experimentally. We also develop a simple scaling model based on a concept of aging of an energy well, which qualitatively captures various experimental observations very well, leading to profound insight into the hyper-aging dynamics of nanoclay suspensions.

Thermal jamming of a colloidal glass

We investigate the effect of temperature on structure and dynamics of a colloidal glass created by tethering polymers to the surface of inorganic nanoparticles. Contrary to the conventional assumption, an increase in temperature slows down glassy dynamics of the material, yet causes no change in its static structure factor. We show that these findings can be explained within the soft glassy rheology framework if the noise temperature X of the glass phase is correlated with thermodynamic temperature.

Strain-accelerated dynamics of soft colloidal glasses

We have investigated strain-accelerated dynamics of soft glasses theoretically and experimentally. Mechanical rheology measurements performed on a variety of systems reveal evidence for the speeding-up of relaxation at modest shear strains in both step and oscillatory shear flows. Using the soft glassy rheology (SGR) model framework, we show that the observed behavior is a fundamental, but heretofore unexplored attribute of soft glasses.

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.

Subdiffusion and intermittent dynamic fluctuations in the aging regime of concentrated hard spheres

We study the nonequilibrium aging dynamics in a system of quasihard spheres at large density by means of computer simulations. We find that, after a sudden quench to large density, the relaxation time initially increases exponentially with the age of the system. After a surprisingly large crossover time, the system enters the asymptotic aging regime characterized by a nearly linear increase in the relaxation time with age. In this aging regime, single-particle motion is strongly non-fickian, with a mean-squared displacement increasing subdiffusively, associated with broad non-gaussian tails in the distribution of particle displacements. We find that the system ages through temporally intermittent relaxation events, and a detailed finite-size analysis of these collective dynamic fluctuations reveals that these events are not spanning the entire system, but remain spatially localized.

Solid-liquid transition and rejuvenation similarities in complex flows of thixotropic materials studied by NMR and MRI

We study the flow of a typical thixotropic material subjected to very different deformation histories (squeeze, shear, and extrusion) with either local (proton NMR and magnetic resonance imaging) or macroscopic measurements after different times of rest. Specifically, we measure the velocity fields and the spin-spin NMR relaxation of the material after different flow histories. The relaxation data exhibits a long relaxing component revealing information about the reversible microstructural evolution of the sample during aging-rejuvenation cycles. We show that for each deformation process, the evolution of the viscosity during the solid-liquid transition is similar by a factor related to the initial state of the material. Moreover, results examining the impact of the rate at which the deformation is imposed suggest that the state of the material during this transition may be described by a single parameter reflecting the average size and deformation of the material's flocs. These results also show that localization of flow occurs as a result of a progressive differential evolution of the material in different regions of the flow, and thus are determined by the boundary conditions of the flow.

Ageing and yield behaviour in model soft colloidal glasses

We use multi-arm star polymers as model soft colloids with tuneable interactions and explore their behaviour in the glassy state. In particular, we perform a systematic rheological study with a well-defined protocol and address aspects of ageing and shear melting of star glasses. Ageing proceeds in two distinct steps: a fast step of O(10(3) s) and a slow step of O(10(4) s). We focus on creep and recovery tests, which reveal a rich, albeit complex response. Although the waiting time, the time between pre-shear (rejuvenation) of the glassy sample and measurement, affects the material's response, it does not play the same role as in other soft glasses. For stresses below the yield value, the creep curve is divided into three regimes with increasing time: viscoplastic, intermediate steady flow (associated with the first ageing step) and long-time evolving elastic solid. This behaviour reflects the interplay between ageing and shear rejuvenation. The yield behaviour, as investigated with the stress-dependent recoverable strain, indicates a highly nonlinear elastic response intermediate between a low-stress Hookean solid and a high-stress viscoelastic liquid, and exemplifies the distinct characteristics of this class of hairy colloids. It appears that a phenomenological classification of different colloidal glasses based on yielding performance may be possible.

Glass transition and aging in dense suspensions of thermosensitive microgel particles

We report a thermosensitive microgel suspension that can be tuned reversibly between the glass state at low temperature and the liquid state at high temperature. Unlike hard spheres, we find that the glass transition for these suspensions is governed by both the volume fraction and the softness of the particles, where softer suspensions form a glass at higher effective volume fractions. In the glass state, these suspensions show aging where the relaxation times increase linearly with age, irrespective of the degree of particle softness. This relaxation scaling is in contrast with hard sphere behavior but consistent with the soft glassy rheology model.