Hard-sphere Colloidal Glasses Research Articles

Mechanical testing of colloidal solids with millipascal stress and single-particle strain resolution.

We introduce a technique, traction rheoscopy, to carry out mechanical testing of colloidal solids. A confocal microscope is used to directly measure stress and strain during externally applied deformation. The stress is measured, with single-mPa resolution, by determining the strain in a compliant polymer gel in mechanical contact with the colloidal solid. Simultaneously, the confocal microscope is used to measure structural change in the colloidal solid with single particle resolution during the deformation. To demonstrate the utility and sensitivity of this technique, we deform a hard-sphere colloidal glass in simple shear, and from the macroscopic shear strain and measured stress determine the stress-strain curve. Using the stress-strain curve and measured shear modulus, we decompose the macroscopic shear strain into an elastic and a plastic component. We also determine a local strain tensor for each particle using the changes in its nearest-neighbor distances. These local strains are spatially heterogeneous throughout the sample, but, when averaged, match the macroscopic strain. A microscopic yield criterion is used to split the local strains into subyield and yielded partitions; averages over these partitions complement the macroscopic elastic-plastic decomposition obtained from the stress-strain curve. By combining mechanical testing with single-particle structural measurements, traction rheoscopy is a unique tool for the study of deformation mechanisms in a diverse range of soft materials.

Mechanical oscillation accelerating nucleation and nuclei growth in hard-sphere colloidal glass

Crystallization from amorphous solids is generally caused by activating phonons in a wide frequency range during heat treatment. In contrast, the activation of phonons in a narrow frequency range using ultrasonic treatment also causes crystallization below the glass transition temperature. These behaviors indicate that crystallization is related to the atomic motion in the glass state, and it is suggested that the activation of specific atomic motion can cause crystallization without increasing temperature. In this study, we observe nucleation and nuclei growth caused by mechanical oscillation in a hard-sphere colloidal glass and evaluate the effect of mechanical oscillation on the structural evolution in the early stage of the crystallization. Oscillation between 5 and 100 Hz is applied to the colloidal glass, and it is observed that the nucleation rate increases under the 70 Hz oscillation, resulting in formation of stable nuclei in a short amount of time. The nuclei growth is also accelerated by the 70 Hz oscillation, whereas increases in the nucleation rate and nuclei growth were not observed at other frequencies. Finally, activation of the diffusion-based rattling of particles by caging is considered as a possible mechanism of the observations.

Rheological signatures of aging in hard sphere colloidal glasses

Colloidal glasses are out-of-equilibrium in nature. When such materials are quenched from a shear-melted state into a quiescent one, their structure freezes due to entropic caging of the constituents. However, thermal fluctuations allow slow structural evolution, a process known as aging, in favor of minimizing free energy. Here, we examine the rheological signatures of aging, in a model system of nearly hard sphere colloidal glass. Subtle changes in the linear viscoelastic properties are detected with the age of the colloidal glass where viscous modulus shows a decrease with aging whereas the elastic modulus remains unaffected. This is associated with the slowing-down of long-time out-of-cage dynamics as the glass ages. On the contrary, nonlinear rheological measurements such as start-up shear flow, stress relaxation, and creep experiments show a strong dependence on sample age. Moreover, creep and stress relaxation experiments show ample evidence of avalanche type processes that occur during aging of colloidal glasses. Finally, comparison of creep and start-up shear flow measurements indicate that the latter is more energy efficient in inducing flow in colloidal glasses irrespective of aging dynamics.

A high-frequency piezoelectric rheometer with validation of the loss angle measuring loop: application to polymer melts and colloidal glasses

We revisit and improve the technique of piezo-operated sliding-plate rheometry in order to provide a versatile platform for measuring the linear viscoelastic properties of various soft matter systems at frequencies from 10 to 1.000 Hz. The sensitive loss angle measuring loop is validated explicitly against reference data from entangled amorphous polymer melts obtained with conventional rotational rheometers by means of time-temperature superposition (tTS). Frequency range limiting factors such as sample and tool inertia are discussed while errors are traced and theoretical correction is shown to be feasible when strong nonlinear behavior of the measuring cell is present. This gives confidence in measuring more complex systems where tTS does not apply. We also demonstrate the ability to probe the short-time dynamics of hard-sphere colloidal glasses. Important high-frequency features such as the behavior of the elastic modulus, G′, the moduli crossover frequency fc related to β-relaxation, and the associated limiting in-phase (with strain-rate), dynamic viscosity η∞′, are captured. This validates the suitability of this high-frequency rheometric technique to provide insights into interactions at nanometric particle separations.

Observation of structural change in hard-sphere colloidal glass

Observation of structural change in hard-sphere colloidal glass

Shear-density coupling for a compressible single-component yield-stress fluid.

Flow behavior of a single-component yield stress fluid is addressed on the hydrodynamic level. A basic ingredient of the model is a coupling between fluctuations of density and velocity gradient via a Herschel-Bulkley-type constitutive model. Focusing on the limit of low shear rates and high densities, the model approximates well-but is not limited to-gently sheared hard sphere colloidal glasses, where solvent effects are negligible. A detailed analysis of the linearized hydrodynamic equations for fluctuations and the resulting cubic dispersion relation reveals the existence of a range of densities and shear rates with growing flow heterogeneity. In this regime, after an initial transient, the velocity and density fields monotonically reach a spatially inhomogeneous stationary profile, where regions of high shear rate and low density coexist with regions of low shear rate and high density. The steady state is thus maintained by a competition between shear-induced enhancement of density inhomogeneities and relaxation via overdamped sound waves. An analysis of the mechanical equilibrium condition provides a criterion for the existence of steady state solutions. The dynamical evolution of the system is discussed in detail for various boundary conditions, imposing either a constant velocity, shear rate, or stress at the walls.

Effects of polydispersity on the glass transition dynamics of aqueous suspensions of soft spherical colloidal particles

Thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) particles of a nearly constant swelling ratio and with polydispersity indices (PDIs) varying over a wide range (7.4% - 48.9%) are synthesized to study the effects of polydispersity on the dynamics of suspensions of soft PNIPAM colloidal particles. The PNIPAM particles are characterized using dynamic light scattering (DLS) and scanning electron microscopy (SEM). The zero shear viscosity ($\eta_{0}$) data of these colloidal suspensions, estimated from rheometric experiments as a function of the effective volume fraction $\phi_{eff}$ of the suspensions, increases with increase in $\phi_{eff}$ and shows a dramatic increase at $\phi_{eff}=\phi_{0}$. The data for $\eta_{0}$ as a function of $\phi_{eff}$ fits well to the Vogel-Fulcher-Tammann (VFT) equation. It is observed that increasing PDIs results in increasingly fragile supercooled liquid-like behavior, with the parameter $\phi_{0}$, extracted from the fits to the VFT equation, shifting towards higher $\phi_{eff}$. The observed increase in fragility is attributed to the prevalence of dynamical heterogeneities (DHs) in these polydisperse suspensions, while the simultaneous shift in $\phi_{0}$ is ascribed to the decoupling of the dynamics of the smallest and largest particles. Finally, it is observed that the intrinsic nonlinearity of these suspensions, estimated at the third harmonic near $\phi_{0}$ in Fourier transform oscillatory rheological experiments, increases with increase in PDIs. Our results are in agreement with theoretical predictions and simulation results for polydisperse hard sphere colloidal glasses and clearly demonstrate that jammed suspensions of polydisperse colloidal particles can be effectively fluidized with increasing PDIs.

Many facets of intermittent dynamics in colloidal and molecular glasses

A popular picture of the intermittent dynamics of glassy materials depicts each particle as localized in a temporary cage formed by its neighbors, and seldom jumping to another cage. Drawing on experiments on hard sphere colloidal glasses and molecular dynamic simulations of supercooled liquids, here we show how this simplified scenario leads to quantitative relations between single particle motion and macroscopic properties, within a Continuous Time Random Walk (CTRW) framework. For example, the diffusivity and the relaxation time at different length scales can be directly predicted from the jump properties. In the accessible range of temperatures and volume fractions, these predictions work well, although the CTRW formalism neglects the spatially heterogeneous dynamics of glassy systems. In this respect, we show how these dynamic heterogeneities can be highlighted from a study of the correlations between jumps. Finally, the intermittent motion is exploited to infer correlations between local structure and dynamics.

Accelerated crystallization of colloidal glass by mechanical oscillation

Crystallization of a hard-sphere colloidal glass by mechanical oscillation is investigated, and accelerated crystallization is found at a specific frequency. The crystallization frequency increases as attractive force between particles increases, indicating that interparticle interaction affects the crystallization frequency. Time scale of the mechanical oscillation is different from that of the slow relaxation, and notable relationship with the low-frequency mode is not observed. The experimental results are not explained by the previously proposed model for crystallization by oscillatory shear. Conversely, we speculate that activations of the fast relaxation and particle motion in crystal-like clusters are possible causes of the observations.

Differential Variance Analysis: a direct method to quantify and visualize dynamic heterogeneities

Many amorphous materials show spatially heterogenous dynamics, as different regions of the same system relax at different rates. Such a signature, known as Dynamic Heterogeneity, has been crucial to understand the nature of the jamming transition in simple model systems and is currently considered very promising to characterize more complex fluids of industrial and biological relevance. Unfortunately, measurements of dynamic heterogeneities typically require sophisticated experimental set-ups and are performed by few specialized groups. It is now possible to quantitatively characterize the relaxation process and the emergence of dynamic heterogeneities using a straightforward method, here validated on video microscopy data of hard-sphere colloidal glasses. We call this method Differential Variance Analysis (DVA), since it focuses on the variance of the differential frames, obtained subtracting images at different time-lags. Moreover, direct visualization of dynamic heterogeneities naturally appears in the differential frames, when the time-lag is set to the one corresponding to the maximum dynamic susceptibility. This approach opens the way to effectively characterize and tailor a wide variety of soft materials, from complex formulated products to biological tissues.

Scaling for hard-sphere colloidal glasses near jamming

Hard-sphere colloids are model systems in which to study the glass transition and universal properties of amorphous solids. Using covariance matrix analysis to determine the vibrational modes, we experimentally measure here the scaling behavior of the density of states, shear modulus, and mean-squared displacement (MSD) in a hard-sphere colloidal glass. Scaling the frequency with the boson-peak frequency, we find that the density of states at different volume fractions all collapse on a single master curve, which obeys a power law in terms of the scaled frequency. Below the boson peak, the exponent is consistent with theoretical results obtained by real-space and phase-space approaches to understanding amorphous solids. We find that the shear modulus and the MSD are nearly inversely proportional, and show a singular power-law dependence on the distance from random close packing. Our results are in very good agreement with the theoretical predictions.

Structure beyond pair correlations: X-ray cross-correlation from colloidal crystals.

The results of an X-ray cross-correlation analysis (XCCA) study on hard-sphere colloidal crystals and glasses are presented. The article shows that cross-correlation functions can be used to extract structural information beyond the static structure factor in such systems. In particular, the powder average can be overcome by accessing the crystals' unit-cell structure. In this case, the results suggest that the crystal is of face-centered cubic type. It is demonstrated that XCCA is a valuable tool for X-ray crystallography, in particular for studies on colloidal systems. These are typically characterized by a rather poor crystalline quality due to size polydispersity and limitations in experimental resolution because of the small q values probed. Furthermore, nontrivial correlations are observed that allow a more detailed insight into crystal structures beyond conventional crystallography, especially to extend knowledge in structure formation processes and phase transitions.

Convective Cage Release in Model Colloidal Glasses.

The mechanism of flow in glassy materials is interrogated using mechanical spectroscopy applied to model nearly hard sphere colloidal glasses during flow. Superimposing a small amplitude oscillatory motion orthogonal onto steady shear flow makes it possible to directly evaluate the effect of a steady state flow on the out-of-cage (α) relaxation as well as the in-cage motions. To this end, the crossover frequency deduced from the viscoelastic spectra is used as a direct measure of the inverse microstructural relaxation time, during flow. The latter is found to scale linearly with the rate of deformation. The microscopic mechanism of flow can then be identified as a convective cage release. Further insights are provided when the viscoelastic spectra at different shear rates are shifted to scale the alpha relaxation and produce a strain rate-orthogonal frequency superposition, the colloidal analogue of time temperature superposition in polymers with the flow strength playing the role of temperature. Whereas the scaling works well for the α relaxation, deviations are observed both at low and high frequencies. Brownian dynamics simulations point to the origins of these deviations; at high frequencies these are due to the deformation of the cages which slows down the short-time diffusion, while at low frequency, deviations are most probably caused by some mild hydroclustering.

Local shear transformations in deformed and quiescent hard-sphere colloidal glasses.

We perform a series of deformation experiments on a monodisperse, hard-sphere colloidal glass while simultaneously following the three-dimensional trajectories of roughly 50,000 individual particles with a confocal microscope. In each experiment, we deform the glass in pure shear at a constant strain rate [(1-5)×10(-5) s(-1)] to maximum macroscopic strains (5%-10%) and then reverse the deformation at the same rate to return to zero macroscopic strain. We also measure three-dimensional particle trajectories in an identically prepared quiescent glass in which the macroscopic strain is always zero. We find that shear transformation zones exist and are active in both sheared and quiescent colloidal glasses, revealed by a distinctive fourfold signature in spatial autocorrelations of the local shear strain. With increasing shear, the population of local shear transformations develops more quickly than in a quiescent glass and many of these transformations are irreversible. When the macroscopic strain is reversed, we observe partial elastic recovery, followed by plastic deformation of the opposite sign, required to compensate for the irreversibly transformed regions. The average diameter of the shear transformation zones in both strained and quiescent glasses is slightly more than two particle diameters.

Direct Measurement of the Free Energy of Aging Hard Sphere Colloidal Glasses

The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however, so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements similar to the Gutenberg-Richter law in seismology.

Shear-induced anisotropic decay of correlations in hard-sphere colloidal glasses

Spatial correlations of microscopic fluctuations are investigated via real-space experiments and computer simulations of colloidal glasses under steady shear. It is shown that while the distribution of one-particle fluctuations is always isotropic regardless of the relative importance of shear as compared to thermal fluctuations, their spatial correlations show a marked sensitivity to the competition between shear-induced and thermally activated relaxation. Correlations are isotropic in the thermally dominated regime, but develop strong anisotropy as shear dominates the dynamics of microscopic fluctuations. We discuss the relevance of this observation for a better understanding of flow heterogeneity in sheared amorphous solids.

Schematic mode coupling theory of glass rheology: single and double step strains

Mode coupling theory (MCT) has had notable successes in addressing the rheology of hard-sphere colloidal glasses, and also soft colloidal glasses such as star-polymers. Here, we explore the properties of a recently developed MCT-based schematic constitutive equation under idealized experimental protocols involving single and then double step strains. We find strong deviations from expectations based on factorable, BKZ-type constitutive models. Specifically, a nonvanishing stress remains long after the application of two equal and opposite step strains; this residual stress is a signature of plastic deformation. We also discuss the distinction between hypothetically instantaneous step strains and fast ramps. These are not generally equivalent in our MCT approach, with the latter more likely to capture the physics of experimental `step' strains. The distinction points to the different role played by reversible anelastic, and irreversible plastic rearrangements.

Connecting Structural Relaxation with the Low Frequency Modes in a Hard-Sphere Colloidal Glass

Structural relaxation in hard-sphere colloidal glasses has been studied using confocal microscopy. The motion of individual particles is followed over long time scales to detect the rearranging regions in the system. We have used normal mode analysis to understand the origin of the rearranging regions. The low-frequency modes, obtained over short time scales, show strong spatial correlation with the rearrangements that happen on long time scales.

Shear Banding and Flow-Concentration Coupling in Colloidal Glasses

We report experiments on hard-sphere colloidal glasses that show a type of shear banding hitherto unobserved in soft glasses. We present a scenario that relates this to an instability due to shear-concentration coupling, a mechanism previously thought unimportant in these materials. Below a characteristic shear rate γ(c) we observe increasingly nonlinear and localized velocity profiles. We attribute this to very slight concentration gradients in the unstable flow regime. A simple model accounts for both the observed increase of γ(c) with concentration, and the fluctuations in the flow.

Slip and Flow of Hard-Sphere Colloidal Glasses

We study the flow of concentrated hard-sphere colloidal suspensions along smooth, nonstick walls using cone-plate rheometry and simultaneous confocal microscopy. In the glass regime, the global flow shows a transition from Herschel-Bulkley behavior at large shear rate to a characteristic Bingham slip response at small rates, absent for ergodic colloidal fluids. Imaging reveals both the "solid" microstructure during full slip and the local nature of the "slip to shear" transition. Both the local and global flow are described by a phenomenological model, and the associated Bingham slip parameters exhibit characteristic scaling with size and concentration of the hard spheres.