Particle dynamics in supercooled liquids are often dominated by string-like motions in which lines of particles perform activated hops cooperatively. The structural features triggering these motions, crucial in understanding glassy dynamics, remain highly controversial. We experimentally study microscopic particle dynamics in colloidal glass formers at high packing fractions. With a small polydispersity leading to glass-crystal coexistence, a void in the form of a vacancy in the crystal can diffuse reversibly into the glass and further induces string-like motions. In the glass, a void takes the form of a quasi-void consisting of a few neighboring free volumes and is transported by the string-like motions it induces. In fully glassy systems with a large polydispersity, similar quasi-void actions are observed. The mobile particles cluster into string-like or compact geometries, but the compact ones can further be broken down into connected sequences of strings, establishing their general importance.
Using a carefully justified development of Debye-Huckel theory for highly asymmetric electrolytes, one finds that a region of expanded phase instability, or miscibility gap, can appear for charge-stabilised colloidal suspensions at high charges and low ionic strengths. It is argued that this is offers a straightforward explanation for the observations of void structures and other anomalies in such suspensions in this region. The nature of the interface between coexisting phases, and general arguments that many-body attractions form a key part of the underlying physical picture, are also examin…
We study a colloidal suspension confined between two quasi-parallel walls as a model system for glass transitions in confined geometries. The suspension is a mixture of two particle sizes to prevent wall-induced crystallization. We use confocal microscopy to directly observe the motion of colloidal particles. This motion is slower in confinement, thus producing glassy behavior in a sample which is a liquid in an unconfined geometry. For higher volume fraction samples (closer to the glass transition), the onset of confinement effects occurs at larger length scales.
We image local structural rearrangements in soft colloidal glasses under small periodic perturbations induced by thermal cycling. Local structural entropy $S_{2}$ positively correlates with observed rearrangements in colloidal glasses. The high $S_{2}$ values of the rearranging clusters in glasses indicate that fragile regions in glasses are structurally less correlated, similar to structural defects in crystalline solids. Slow-evolving high $S_{2}$ spots are capable of predicting local rearrangements long before the relaxations occur, while fluctuation-created high $S_{2}$ spots best correlat…
We use confocal microscopy to directly visualize the dynamics of aging colloidal glasses. We prepare a colloidal suspension at high density, a simple model system which shares many properties with other glasses, and initiate experiments by stirring the sample. We follow the motion of several thousand colloidal particles after the stirring and observe that their motion significantly slows as the sample ages. The aging is both spatially and temporally heterogeneous. Furthermore, while the characteristic relaxation time scale grows with the age of the sample, nontrivial particle motions continue …
We analyse structure and dynamics in simulated high-concentration hard sphere colloidal suspensions by means of calculations based on the void space. We show that remoteness, a quantity measuring the scale of spaces, is useful in studying crystallization, since ordering of the particles involves a change in the way empty space is distributed. Calculation of remoteness also allows breakdown of the system into mesoscopic neighbor sets: statistics of mean remoteness and local volume fraction in these neighbor sets reveal that nuclei are formed at locally higher concentration, i.e. nucleation invo…
The dynamics of a glass-forming material slow greatly near the glass transition, and molecular motion becomes inhibited. We use confocal microscopy to investigate the motion of colloidal particles near the colloidal glass transition. As the concentration in a dense colloidal suspension is increased, particles become confined in transient cages formed by their neighbors. This prevents them from diffusing freely throughout the sample. We quantify the properties of these cages by measuring temporal anticorrelations of the particles' displacements. The local cage properties are related to the subd…
We study a lattice model of attractive colloids. It is exactly solvable on sparse random graphs. As the pressure and temperature are varied it reproduces many characteristic phenomena of liquids, glasses and colloidal systems such as ideal gel formation, liquid-glass phase coexistence, jamming, or the reentrance of the glass transition.
Using video microscopy, we measure local spatial constraints in disordered binary colloidal samples, ranging from dilute fluids to jammed glasses, and probe their spatial and temporal correlations to local dynamics during the glass transition. We observe the emergence of significant correlations between constraints and local dynamics within the Lindemann criterion, which coincides with the onset of glassy dynamics in supercooled liquids. Rigid domains in fluids are identified based on local constraints, and demonstrate a percolation transition near glass transition, accompanied by the emergenc…
Colloids are suspensions of small solid particles in a liquid, and exhibit glassy behavior when the particle concentration is high. In these samples, the particles are roughly analogous to individual molecules in a traditional glass. This model system has been used to study the glass transition since the 1980's. In this Viewpoint we summarize some of the intriguing behaviors of the glass transition in colloids, and discuss open questions.
A recently proposed schematic model for the non--linear rheology of dense colloidal dispersions is compared to flow curves measured in suspensions that consist of thermosensitive particles. The volume fraction of this purely repulsive model system can be adjusted by changing temperature. Hence, high volume fractions ($ϕ\leq 0.63$) can be achieved in a reproducible manner. The quantitative analysis of the flow curves suggests that the theoretical approach captures the increase of the low shear viscosity with increasing density, the shear thinning for increasing shear rate, and the yielding of a…
We examine the response of a dense colloidal suspension to a local force applied by a small magnetic bead. For small forces, we find a linear relationship between the force and the displacement, suggesting the medium is elastic, even though our colloidal samples macroscopically behave as fluids. We interpret this as a measure of the strength of colloidal caging, reflecting the proximity of the samples' volume fractions to the colloidal glass transition. The strain field of the colloidal particles surrounding the magnetic probe appears similar to that of an isotropic homogeneous elastic medium.…
We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing molecular-dynamics data for all systems studied onto a single curve as a function of $T/p$, the ratio of the temperature to the pressure. At higher pressures, there are deviations from this universal behavior that depend on the inter-particle potential, implying that additional physical processes must enter into the dynamics of glass-formation.
We study aging in a colloidal suspension consisting of micron-sized particles in a liquid. This system is made glassy by increasing the particle concentration. We observe samples composed of particles of two sizes, with a size ratio of 1:2.1 and a volume fraction ratio 1:6, using fast laser scanning confocal microscopy. This technique yields real-time, three-dimensional movies deep inside the colloidal glass. Specifically, we look at how the size, motion and structural organization of the particles relate to the overall aging of the glass. Particles move in spatially heterogeneous cooperative …
We use a confocal microscope to examine the motion of individual particles in a dense colloidal suspension. Close to the glass transition, particle motion is strongly spatially correlated. The correlations decay exponentially with particle separation, yielding a dynamic length scale of O(2-3 sigma) (in terms of particle diameter sigma). This length scale grows modestly as the glass transition is approached. Further, the correlated motion exhibits a strong spatial dependence on the pair correlation function g(r). Motion within glassy samples is weakly correlated, but with a larger spatial scale…
We rejuvenate well-aged quasi-2D binary colloidal glasses by thermal cycling, and systematically measure both the statistical responses and particle-level structural evolutions during rejuvenation. While the moduli and boson peak are continuously rejuvenated with increasing number of cycles, the mean square displacement (MSD) fluctuates significantly between different groups of thermal cycles. The decoupling between the thermodynamical and dynamical evolutions suggests different microscopic origins for different bulk properties of glasses. We find that a small fraction of structural rearrangem…
We use confocal microscopy to study the motions of particles in concentrated colloidal systems. Near the glass transition, diffusive motion is inhibited, as particles spend time trapped in transient ``cages'' formed by neighboring particles. We measure the cage sizes and lifetimes, which respectively shrink and grow as the glass transition approaches. Cage rearrangements are more prevalent in regions with lower local concentrations and higher disorder. Neighboring rearranging particles typically move in parallel directions, although a nontrivial fraction move in anti-parallel directions, usual…
Despite their technological relevance, a full microscopic understanding of glasses is still lacking. This applies even more to their surfaces whose properties largely differ from that of the bulk material. Here, we experimentally investigate the surface of a two-dimensional glass as a function of the effective temperature. To yield a free surface, we use an attractive colloidal suspension of micron-sized particles interacting via tunable critical Casimir forces. Similar to crystals, we observe surface melting of the glass, i.e., the formation of a liquid film at the surface well below the glas…
Using fast confocal microscopy we image the three-dimensional dynamics of particles in a yielded hard-sphere colloidal glass under steady shear. The structural relaxation, observed in regions with uniform shear, is nearly isotropic but is distinctly different from that of quiescent metastable colloidal fluids. The inverse relaxation time $τ_α^{-1}$ and diffusion constant $D$, as functions of the {\it local} shear rate $\dotγ$, show marked shear thinning with $τ_α^{-1} \propto D \propto \dotγ^{0.8}$ over more than two decades in $\dotγ$. In contrast, the {\it global} rheology of the system disp…
We report experimental measurements of particle dynamics in a colloidal glass in order to understand the dynamical heterogeneities associated with the cooperative motion of the particles in the glassy regime. We study the local and global fluctuation of correlation and response functions in an aging colloidal glass. The observables display universal scaling behavior following a modified power-law, with a plateau dominating the less heterogeneous short-time regime and a power-law tail dominating the highly heterogeneous long-time regime.
Exploring structural order in disordered systems including liquids and glasses is an intriguing but challenging issue in condensed matter physics. Here we construct a new parameter based on the angular distribution function of particles and show that this new orientational order has significantly higher correlation with dynamic heterogeneity compared to a translational parameter based on the radial distribution functions in colloidal glasses. The gradual development of orientational and translational order in supercooled liquids shows that the higher correlation between orientational order and…
Glasses behave as solids on experimental time scales due to their slow relaxation. Growing dynamic length scales due to cooperative motion of particles are believed to be central to this slow response. For quiescent glasses, however, the size of the cooperatively rearranging regions has never been observed to exceed a few particle diameters, and the observation of long-range correlations that are signatures of an elastic solid has remained elusive. Here, we provide direct experimental evidence of long-range correlations during the deformation of a dense colloidal glass. By imposing an external…
Motivated by the mean field prediction of a Gardner phase transition between a "normal glass" and a "marginally stable glass", we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for colloidal or granular glasses. Deep inside the glass phase, we find that a sharp crossover pressure $P_{\rm G}$ separates two distinct dynamical regimes. For pressure $P < P_{\rm G}$, the glass behaves as a normal solid, displaying fast dynamics that quickly equilibrates within the glass free energy basin. For $P>P_{\rm G}$, instead, the dynamics becomes stro…
The phase behavior of hard-sphere particles interacting with a short-ranged potential is studied in the limit of infinite space dimensionality via the Franz-Parisi approach and the replica method of disordered systems. For an attractive square-well potential the phase diagram exhibits reentrancy of the liquid-glass transition, multiple glass states and glass-glass transition. For a repulsive square shoulder potential no such special features are observed. Our results show that the Franz-Parisi approach can be consistently extended to deal with higher-order glass singularities and that interpar…
The nonlinear rheological properties of dense suspensions are discussed within simplified models, suggested by a recent first principles approach to the model of Brownian particles in a constant-velocity-gradient solvent flow. Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses arise from a competition between a slowing down of structural relaxation, because of particle interactions, and enhanced decorrelation of fluctuations, caused by the shear advection of density fluctuations. A mode coupling approach is developed to explore the shear-induced suppression of parti…
In a dense colloidal suspension at a volume fraction slightly lower than that of its glass transition, we follow the trajectories of an assembly of tracers over a large time window. We define a local activity, which quantifies the local tendency of the system to rearrange. We determine the statistics of the time and space integrated activity, and we argue that it develops a low activity tail that comes on a par with the onset of glassy behavior and heterogeneous dynamics. These rare events may be interpreted as the reflection of an underlying dynamic phase transition.
We observed a two-step glass transition in monolayers of colloidal ellipsoids by video microscopy. The glass transition in the rotational degree of freedom was at a lower density than that in the translational degree of freedom. Between the two transitions, ellipsoids formed an orientational glass. Approaching the respective glass transitions, the rotational and translational fastest-moving particles in the supercooled liquid moved cooperatively and formed clusters with power-law size distributions. The mean cluster sizes diverge in power law as approaching the glass transitions. The clusters …
As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. This kinetic arrest is the colloidal glass transition. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the curre…
We derive a microscopic theory of glassy dynamics based on the transport of voids by micro-string motions, each of which involves particles arranged in a line hopping simultaneously displacing one another. Disorder is modeled by a random energy landscape quenched in the configuration space of distinguishable particles, but transient in the physical space as expected for glassy fluids. We study the evolution of local regions with m coupled voids. At low temperature, energetically accessible local particle configurations can be organized into a random tree with nodes and edges denoting configura…
Glasses are structurally liquid-like, but mechanically solid-like. Most attempts to understand glasses start from liquid state theory. Here we take the opposite point of view, and use concepts from solid state physics. We determine the vibrational modes of a colloidal glass experimentally, and find soft low-frequency modes that are very different in nature from the usual acoustic vibrations of ordinary solids. These modes extend over surprisingly large length scales.
The dynamical heterogeneities (DH) in non-ergodic states of an attractive colloidal glass are studied, as a function of the waiting time. Whereas the fluid states close to vitrify showed strong DH, the distribution of squared displacements of the glassy states studied here only present a tail of particles with increased mobility for the lower attraction strength at short waiting times. These particles are in the surface of the percolating cluster that comprises all of the particles, reminiscent of the fastest particles in the fluid. The quench deeper into the attractive glass is dynamically mo…
Glasses have liquid-like structure, but exhibit solid-like properties. A central question concerns the relation between the structure and mechanical properties of glasses, but structural changes remain difficult to resolve. We use a novel combination of rheology and x-ray scattering to resolve structural changes in colloidal glasses and link them directly to their mechanical behavior. By combining stress and structure factor measurements, we resolve shear induced changes in the nearest neighbor configuration as a function of applied stress, allowing us to elucidate the structural origin of the…
We investigate correlations between low-frequency vibrational modes and rearrangements in two-dimensional colloidal glasses composed of thermosensitive microgel particles which readily permit variation of sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the "shadow" colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in packing fraction. The experimental res…
We report the modifications of the microscopic dynamics of a colloidal glass submitted to shear. We use multispeckle diffusing wave spectroscopy to monitor the evolution of the spontaneous slow relaxation processes after the sample have been submitted to various straining. We show that high shear rejuvenates the system and accelerates its dynamics whereas moderate shear overage the system. We analyze this phenomena within the frame of the Bouchaud's trap model.
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…
We use theory and simulations to investigate the existence of amorphous glassy states in ultrasoft colloids. We combine the hyper-netted chain approximation with mode-coupling theory to study the dynamic phase diagram of soft repulsive spheres interacting with a Hertzian potential, focusing on low temperatures and large densities. At constant temperature, we find that an amorphous glassy state is entered upon compression, as in colloidal hard spheres, but the glass unexpectedly melts when density increases further. We attribute this re-entrant fluid-glass transition to particle softness, and c…
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.
We study colloidal particle dynamics of a model glass system using confocal and fluorescence microscopy as the sample evolves from a hard-sphere glass to a liquid with attractive interparticle interactions. The transition from hard-sphere glass to attractive liquid is induced by short-range depletion forces. The development of liquid-like structure is indicated by particle dynamics. We identify particles which exhibit substantial motional events and characterize the transition using the properties of these motional events. As samples enter the attractive liquid region, particle speed during th…
We describe a model for the colloidal glass transition that is based on Feynman's theory for the $λ$-transition in liquid helium. Our model essentially counts the number of configurations of dynamic loops, strings or clusters of different sizes, and determines the glass transition volume fraction $ϕ_{g}$ from the distribution of these heterogeneities. Since confinement restricts the available number of configurations for these loops, strings and clusters, its effect on $ϕ_{g}$ can also be calculated in a relatively straightforward manner.
When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Due to the much larger size of the colloidal particles with respect to the atoms comprising an amorphous solid, colloidal glasses allow to obtain microscopic insight into the nature of the yielding transition, as we illustrate here combining experiments, atomistic simulations, and mesoscopic modeling. Our results unanimously show growing clusters of non-affine deformation percolating at yielding. In agreement with percol…
Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of liquid relaxation. The prediction, however, has yet to be verified in 3D experiments. Here, we design a colloidal system, where particles are confined inside spherical cavities with an amorphous layer of particles pinned at the boundary. Using this novel system, we capture the amorphous-order particle clusters and demonstrate the development of a static correlat…
We study concentrated binary colloidal suspensions, a model system which has a glass transition as the volume fraction $ϕ$ of particles is increased. We use confocal microscopy to directly observe particle motion within dense samples with $ϕ$ ranging from 0.4 to 0.7. Our binary mixtures have a particle diameter ratio $d_S/d_L=1/1.3$ and particle number ratio $N_S/N_L=1.56$, which are chosen to inhibit crystallization and enable long-time observations. Near the glass transition we find that particle dynamics are heterogeneous in both space and time. The most mobile particles occur in spatially …
A confined colloidal glass, under the imposition of a uniform shear stress, is investigated using numerical simulations. Both at macro- and microscales, the consequent dynamics during the onset of flow is studied. When the imposed stress is gradually decreased, the time scale for the onset of steady flow diverges, associated with long-lived spatial heterogeneities. Near this yield-stress regime, persistent creep in the form of shear-banded structures is observed.
Although glassy relaxation is typically associated with disorder, here we report on a new type of glassy dynamics relating to dislocations within 2-D crystals of colloidal dimers. Previous studies have demonstrated that dislocation motion in dimer crystals is restricted by certain particle orientations. Here, we drag an optically trapped particle through such dimer crystals, creating dislocations. We find a two-stage relaxation response where initially dislocations glide until encountering particles that cage their motion. Subsequent relaxation occurs logarithmically slowly through a second pr…
We use an analogue of nanoindentation on a colloidal glass to elucidate the incipient plastic deformation of glasses. By tracking the motion of the individual particles in three dimensions, we visualize the strain field and glass structure during the emerging deformation. At the onset of flow, we observe a power-law distribution of strain indicating strongly correlated deformation, and reflecting a critical state of the glass. At later stages, the strain acquires a Gaussian distribution, indicating that plastic events become uncorrelated. Investigation of the glass structure using both static …
We study concentrated colloidal suspensions, a model system which has a glass transition. The non-equilibrium nature of the glassy state is most clearly highlighted by aging -- the dependence of the system's properties on the time elapsed since vitrification. Fast laser scanning confocal microscopy allows us to image a colloidal glass and track the particles in three dimensions. We analyze the static structure in terms of tetrahedral packing. We find that while the aging of the suspension clearly affects its dynamics, none of the geometrical quantities associated with tetrahedra change with ag…
The translational dynamics in a repulsive colloidal glass-former is probed by time-resolved X-ray Photon Correlation Spectroscopy. In this dense dispersion of charge-stabilized and magnetic nanoparticles, the interaction potential can be tuned, from quasi-isotropic to anisotropic by applying an external magnetic field. Structural and dynamical anisotropies are reported on interparticle lengthscales associated with highly anisotropic cooperativity, almost two orders of magnitude larger in the field direction than in the perpendicular direction and in zero field.
We study experimentally the origin of heterogeneous dynamics in strongly driven glass-forming systems. Thereto, we apply a well-defined force with a laser line trap on individual colloidal polystyrene probe particles seeded in an emulsion glass composed of droplets of the same size. Fluid and glass states can be probed. We monitor the trajectories of the probe and measure displacements and their distributions. Our experiments reveal intermittent dynamics around a depinning transition at a threshold force. For smaller forces, linear response connects mean displacement and quiescent mean squared…
Colloidal gels formed from small attractive particles are commonly used in formulations to keep larger components in suspension. However, despite extensive work characterizing unfilled gels, little is known about how larger inclusions alter the phase behavior and microstructure of the colloidal system. Here we use numerical simulations to examine how larger `granular' particles can alter the gel transition phase boundaries. We find two distinct regimes depending on both the filler size and native gel structure: a `passive' regime where the filler fits into already-present voids, giving little …
We study the phase ordering dynamics of a two dimensional model colloidal solid using molecular dynamics simulations. The colloid particles interact with each other with a Hamaker potential modified by the presence of equatorial "patches" of attractive and negative regions. The total interaction potential between two such colloids is, therefore, strongly directional and has three-fold symmetry. Working in the canonical ensemble, we determine the tentative phase diagram in the density-temperature plane which features three distinct crystalline ground states viz, a low density honeycomb solid fo…
We use colloidal suspensions encapsulated in emulsion droplets to model confined glass-forming liquids with tunable boundary mobility. We show dynamics in these idealized systems are governed by physical interactions with the boundary. Gradients in dynamics are present for more mobile boundaries, whereas for less mobile boundaries gradients are almost entirely suppressed. Motions in a system are not isotropic, but have a strong directional dependence with respect to the boundary. These findings bring into question the ability of conventional quantities to adequately describe confined glasses.
We study the thermal fluctuations of an optically confined probe particle, suspended in an aging colloidal suspension, as the suspension transforms from a viscous liquid into an elastic glass. The micron-sized bead forms a harmonic oscillator. By monitoring the equal-time fluctuations of the tracer, at two different laser powers, we determine the temperature of the oscillator, $T_{\text{o}}$. In the ergodic liquid the temperatures of the oscillator and its environment are equal while, in contrast, in a nonequilibrium glassy phase we find that $T_{\text{o}}$ substantially exceeds the bath tempe…
The nonlinear rheological properties of dense colloidal suspensions under steady shear are discussed within a first principles approach. It starts from the Smoluchowski equation of interacting Brownian particles in a given shear flow, derives generalized Green-Kubo relations, which contain the transients dynamics formally exactly, and closes the equations using mode coupling approximations. Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses arise from a competition between a slowing down of structural relaxation, because of particle interactions, and enhanced decorr…
Glass-forming materials are characterized by an intermittent motion at the microscopic scale. Particles spend most of their time rattling within the cages formed by their neighbors, and seldom jump to a different cage. In molecular glass formers the temperature dependence of the jump features, such as the average caging time and jump length, characterizes the relaxation processes and allows for a short-time prediction of the diffusivity. Here we experimentally investigate the cage-jump motion of a two-dimensional hard-sphere-like colloidal suspension, where the volume fraction is the relevant …
Roughening the surface of spherical colloids can drastically change their translational and rotational dynamics in dense suspensions. Using 3D confocal microscopy, we show that roughness not only lowers the concentration of the translational colloidal glass transition, but also generates a broad concentration range in which the rotational Brownian motion changes signature from high-amplitude diffusive to low-amplitude rattling. This hitherto not reported second glass transition for rough spherical colloids emerges when the particle intersurface distance becomes comparable to the roughness leng…
