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.

Manipulating the kinetics and mechanism of phase separation in dynamically asymmetric LCST blends by nanoparticles.

The addition of nanoparticles in dynamically asymmetric LCST blends is used to induce preferred phase-separating morphology by tuning the dynamic asymmetry, and to control the kinetics of phase separation by slowing down (or even arresting) the domain growth. For this purpose, we used hydrophobic and hydrophilic fumed silica, which self-assemble during phase separation into the bulk of the slow (PS-rich) and fast (PVME-rich) dynamic phases, respectively. Both types of nanoparticles slow down considerably nucleation and growth (NG), spinodal decomposition (SD), and viscoelastic phase separation (VPS) at volume fractions as low as 0.5%. Remarkably, beyond a critical volume fraction of hydrophobic nanosilica thermodynamically controlled phase separation mechanisms (NG and SD) change to the VPS mechanism due to enhanced dynamic asymmetry. However, in the presence of hydrophilic nanosilica dynamic asymmetry decreases and beyond a critical particle volume fraction a transition from the VPS to the SD mechanism is observed. Phase separation is arrested at 2% nanoparticle loading, and VPS percolating networks as well as co-continuous SD structures are completely stabilized by hydrophobic silica or hydrophilic silica, respectively. Electron microscopy images confirm that double percolated structures are induced in the presence of 2 vol% of either hydrophobic or hydrophilic nanoparticles.

Anisotropic diffusion of concentrated hard-sphere colloids near a hard wall studied by evanescent wave dynamic light scattering.

Evanescent wave dynamic light scattering and Stokesian dynamics simulations were employed to study the dynamics of hard-sphere colloidal particles near a hard wall in concentrated suspensions. The evanescent wave averaged short-time diffusion coefficients were determined from experimental correlation functions over a range of scattering wave vectors and penetration depths. Stokesian dynamics simulations performed for similar conditions allow a direct comparison of both the short-time self- and collective diffusivity. As seen earlier [V. N. Michailidou, G. Petekidis, J. W. Swan, and J. F. Brady, Phys. Rev. Lett. 102, 068302 (2009)] while the near wall dynamics in the dilute regime slow down compared to the free bulk diffusion, the reduction is negligible at higher volume fractions due to an interplay between the particle-wall and particle-particle hydrodynamic interactions. Here, we provide a comprehensive comparison between experiments and simulations and discuss the interplay of particle-wall and particle-particle hydrodynamics in the self- and cooperative dynamics determined at different scattering wave vectors and penetration depths.

Residual stresses in glasses.

The history dependence of glasses formed from flow-melted steady states by a sudden cessation of the shear rate γ[over ˙] is studied in colloidal suspensions, by molecular dynamics simulations and by mode-coupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function of γ[over ˙]t, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this history dependence of glasses sharing the same thermodynamic state variables but differing static properties.

Complex oscillatory yielding of model hard-sphere glasses.

The yielding behavior of hard sphere glasses under large-amplitude oscillatory shear has been studied by probing the interplay of Brownian motion and shear-induced diffusion at varying oscillation frequencies. Stress, structure and dynamics are followed by experimental rheology and Browian dynamics simulations. Brownian-motion-assisted cage escape dominates at low frequencies while escape through shear-induced collisions at high ones, both related with a yielding peak in G''. At intermediate frequencies a novel, for hard sphere glasses, double peak in G'' is revealed reflecting both mechanisms. At high frequencies and strain amplitudes a persistent structural anisotropy causes a stress drop within the cycle after strain reversal, while higher stress harmonics are minimized at certain strain amplitudes indicating an apparent harmonic response.

Transient dynamics in dense colloidal suspensions under shear: shear rate dependence.

A combination of confocal microscopy and rheology experiments, Brownian dynamics (BD) and molecular dynamics (MD) simulations and mode coupling theory (MCT) have been applied in order to investigate the effect of shear rate on the transient dynamics and stress-strain relations in supercooled and glassy systems under shear. Immediately after shear is switched on, the microscopic dynamics display super-diffusion and the macroscopic rheology a stress overshoot, which become more pronounced with increasing shear rate. MCT relates both to negative sections of the generalized shear modulus, which grow with increasing shear rate. When the inverse shear rate becomes much smaller than the structural relaxation time of the quiescent system, relaxation through Brownian motion becomes less important. In this regime, larger stresses are accumulated before the system yields and the transition from localization to flow occurs earlier and more abruptly.

Yielding of hard-sphere glasses during start-up shear.

Concentrated hard-sphere suspensions and glasses are investigated with rheometry, confocal microscopy, and Brownian dynamics simulations during start-up shear, providing a link between microstructure, dynamics, and rheology. The microstructural anisotropy is manifested in the extension axis where the maximum of the pair-distribution function exhibits a minimum at the stress overshoot. The interplay between Brownian relaxation and shear advection as well as the available free volume determine the structural anisotropy and the magnitude of the stress overshoot. Shear-induced cage deformation induces local constriction, reducing in-cage diffusion. Finally, a superdiffusive response at the steady state, with a minimum of the time-dependent effective diffusivity, reflects a continuous cage breakup and reformation.

Osmotic shrinkage in star/linear polymer mixtures.

Multiarm star polymers were used as model grafted colloidal particles with long hairs, to study their size variation due to osmotic forces arising from added linear homopolymers of smaller size. This is the origin of the depletion phenomenon that has been exploited in the past as a means to melt soft colloidal glasses by adding linear chains and analyzed using dynamic light scattering experiments and an effective interactions analysis yielding the depletion potential. Shrinkage is a generic phenomenon for hairy particles, which affects macroscopic properties and state transitions at high concentrations. In this work we present a small-angle neutron scattering study of star/linear polymer mixtures with different size ratios (varying the linear polymer molar mass) and confirm the depletion picture, i.e., osmotic star shrinkage. Moreover, we find that as the linear/star polymer size ratio increases for the same effective linear volume fraction (c/c* with c* the overlapping concentration), the star shrinkage is reduced whereas the onset of shrinkage appears to take place at higher linear polymer volume fractions. A theoretical description of the force balance on a star polymer in solution, accounting for the classic Flory contributions, i.e. elastic and excluded volume, as well as the osmotic force due to the linear chains, accurately predicts the experimental findings of reduced star size as a function of linear polymer concentration. This is done in a parameter-free fashion, in which the size of the cavity created by the star, and from which the chains are excluded, is related to the radius of the former from first principles.

Slow dynamics, aging, and crystallization of multiarm star glasses.

Multiarm star polymers are model systems with tunable intermediate colloid to polymerlike character, exhibiting rich phase behavior, internal relaxations, and flow properties. An important puzzle for several years has been the lack of clear experimental proof of crystalline states despite strong theoretical predictions. We present unambiguous evidence via multispeckle dynamic light scattering (MSDLS) and small-angle neutron scattering (SANS) for such crystallization in a solvent of intermediate quality. An unexpected speed up of the short-time star diffusion observed in MSDLS was attributed by SANS to crystallization, via aging, of the multiam star glass. This delayed glass to crystal transition establishes a pathway for star crystallization that might be generic in colloidal glasses.

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.

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.

Structure, dynamics, and rheology of colloid-polymer mixtures: from liquids to gels.

We investigate the structural, dynamical, and viscoelastic properties of colloid-polymer mixtures at intermediate colloid volume fraction and varying polymer concentrations, thereby tuning the attractive interactions. Within the examined range of polymer concentrations, the samples varied from fluids to gels. In the liquid phase, an increasing correlation length of the density fluctuations when approaching the gelation boundary was observed by static light scattering and microscopy, indicating clustering and formation of space-spanning networks. Simultaneously, the correlation function determined by dynamic light scattering decays completely, indicating the absence of dynamical arrest. Clustering and formation of transient networks when approaching the gelation boundary is supported by significant changes in the viscoelastic properties of the samples. Upon increasing the polymer concentration beyond the gelation boundary, the rheological properties changed qualitatively again, now they are consistent with the formation of colloidal gels. Our experimental results, namely, the location of the gelation boundary as well as the elastic (storage) and viscous (loss) moduli, are compared to different theoretical models. These include consideration of the escape time as well as predictions for the viscoelastic moduli based on scaling relations and mode coupling theories.

Dynamics of concentrated hard-sphere colloids near a wall.

We investigate the Brownian motion of hard-sphere colloids near a solid wall by Evanescent Wave Dynamic Light Scattering (EWDLS). We carried out measurements for various volume fractions of sterically stabilized poly(methyl methacrylate) (PMMA) particles over a range of scattering wave vectors, q. While in the dilute regime, the near wall short-time diffusion is significantly slowed down due to particle-wall hydrodynamic interactions (HI); as volume fraction increases, the wall effect is progressively diminished at all q's. We present a new analysis for the EWDLS short-time self- and collective diffusivities applicable to all volume fractions and a simple model for the self-diffusion describing the interplay between particle-wall and particle-particle HI. Moreover, a weaker decay of the near-wall self-diffusion coefficient with volume fraction is predicted by Stokesian dynamics simulations.

Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition.

We use dynamic light scattering and computer simulations to study equilibrium dynamics and dynamic heterogeneity in concentrated suspensions of colloidal hard spheres. Our study covers an unprecedented density range and spans seven decades in structural relaxation time, tau(alpha0, including equilibrium measurements above phi(c), the location of the glass transition deduced from fitting our data to mode-coupling theory. Instead of falling out of equilibrium, the system remains ergodic above phi(c) and enters a new dynamical regime where tau(alpha) increases with a functional form that was not anticipated by previous experiments, while the amplitude of dynamic heterogeneity grows slower than a power law with tau(alpha), as found in molecular glass formers close to the glass transition.

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.

Particle dynamics within a wetting layer in a colloid-polymer mixture.

The near-wall dynamics at the top and bottom phases of a phase-separated colloid-polymer mixture were measured by evanescent-wave dynamic light scattering. The short-time dynamics near the wall were found to be liquidlike in both phases, confirming the presence of a liquid wetting layer. The short-time diffusion within the wetting layer was slower than in the bulk liquid phase. Similarly, the near-wall dynamics in both phases of the colloid-polymer mixture were also slower compared to the near-wall colloidal dynamics in a pure concentrated suspension at the same volume fraction. These effects highlight the role of interparticle attractions and specific wall-induced hydrodynamic interactions in slowing down the colloidal motion in confinement.

Yielding and crystallization of colloidal gels under oscillatory shear.

We have studied the behavior of a colloidal gel under oscillatory shear. The quiescent gel was an arrested structure formed by a 40% volume fraction hard-sphere suspension in which a "depletion" interparticle attraction was induced by adding nonadsorbing polymer. We applied progressively larger amplitude oscillatory shear to the sample, and observed its behavior using conventional and confocal microscopy as well as dynamic light scattering echo spectroscopy. We find that, to within experimental uncertainties, the point at which irreversible particle rearrangements (or yielding) occur coincides with the observation of crystallization. We summarize our findings in a "shear state diagram." The strain amplitude required for yielding/crystallization increases with decreasing oscillation frequency. We can quantitatively account for our observations by estimating the effect of shear on the probability for a particle to escape from the attractive potential of its neighbor using a Kramers approach.

Hypersonic acoustic excitations in binary colloidal crystals: big versus small hard sphere control.

The phononic band structure of two binary colloidal crystals, at hypersonic frequencies, is studied by means of Brillouin light scattering and analyzed in conjunction with corresponding dispersion diagrams of the single colloidal crystals of the constituent particles. Besides the acoustic band of the average medium, the authors' results show the existence of narrow bands originating from resonant multipole modes of the individual particles as well as Bragg-type modes due to the (short-range) periodicity. Strong interaction, leading to the occurrence of hybridization gaps, is observed between the acoustic band and the band of quadrupole modes of the particles that occupy the largest fractional volume of the mixed crystal; the effective radius is either that of the large (in the symmetric NaCl-type crystalline phase) or the small (in the asymmetric NaZn(13)-type crystalline phase) particles. The possibility to reveal a universal behavior of the phononic band structure for different single and binary colloidal crystalline suspensions, by representing in the dispersion diagrams reduced quantities using an appropriate length scale, is discussed.

Phonons in suspensions of hard sphere colloids: volume fraction dependence.

The propagation of sound waves in suspensions of hard sphere colloids is studied as a function of their volume fraction up to random close packing using Brillouin light scattering. The rich experimental phonon spectra of up to five phonon modes are successfully described by theoretical calculations based on the multiple scattering method. Two main types of phonon modes are revealed: Type A modes are acoustic excitations which set up deformations in both the solid (particles) and the liquid (solvent) phases; for type B modes the stress and strain are predominantly localized near the interface between the solid particles and the surrounding liquid (interface waves). While the former become harder (increase their effective sound velocity) as the particle volume fraction increases the latter become softer (the corresponding sound velocity decreases).

Dynamics of core-shell particles in concentrated suspensions.

The dynamics of soft colloidal particles in a concentrated suspension was studied by two color dynamic light scattering. The short-time diffusion coefficient, D(s)(q), revealed a weak slowing down around the peak of S(q) in contrast to the much stronger dependence observed in hard sphere systems, and the absence of any slowing down in ultrasoft diblock micelles. The low-q limit of the diffusion coefficient, D(s)(q=0), reflecting the cooperative nature of the dynamics was found to decrease from its dilute limit value in contrast to the weak increase observed in hard sphere systems. The behavior of D(s)(q) reflects distinct polymer-layer-induced hydrodynamic effects present in concentrated suspensions of core-shell particles.