We consider a model dense colloidal dispersion at the glass transition, and investigate the connection between equilibrium stress fluctuations, seen in linear shear moduli, and the shear stresses under strong flow conditions far from equilibrium, viz. flow curves for finite shear rates. To this purpose thermosensitive core-shell particles consisting of a polystyrene core and a crosslinked poly(N-isopropylacrylamide)(PNIPAM) shell were synthesized. Data over an extended range in shear rates and frequencies are compared to theoretical results from integrations through transients and mode coupling approaches. The connection between non-linear rheology and glass transition is clarified. While the theoretical models semi-quantitatively fit the data taken in fluid states and the predominant elastic response of glass, a yet unaccounted dissipative mechanism is identified in glassy states.
I review recent progress in understanding the arrest and flow behaviour of colloidal glasses, based on mode coupling theory (MCT) and related approaches. MCT has had notable recent successes in predicting the re-entrant arrest behaviour of colloids with short range attractions. Developments based upon it offer important steps towards calculating, from rational foundations in statistical mechanics, nonlinear flow parameters such as the yield stress of a colloidal glass. An important open question is why MCT works so well.
We provide a detailed derivation of the mode-coupling equations for a colloidal liquid confined by two parallel smooth walls. We introduce irreducible memory kernels for the different relaxation channels thereby extending the projection operator technique to colloidal liquids in slit geometry. Investigating both the collective dynamics as well as the tagged-particle motion, we prove that the mode-coupling functional assumes the same form as in the Newtonian case corroborating the universality of the glass-transition singularity with respect to the microscopic dynamics.
The replica theory of glasses predicts that in the infinite dimensional mean field limit there exist two distinct glassy phases of matter: stable glass and marginal glass. We have developed a technique to experimentally probe these phases of matter using a colloidal glass. We avoid the difficulties inherent in measuring the long time behavior of glasses by instead focusing on the very short time dynamics of the ballistic to caged transition. We track a single tracer particle within a slowly densifying glass and measure the resulting mean squared displacement (MSD). By analyzing the MSD we find…
We study the Brownian motion of particles trapped by optical tweezers inside a colloidal glass (Laponite) during the sol-gel transition. We use two methods based on passive rheology to extract the effective temperature from the fluctuations of the Brownian particles. All of them give a temperature that, within experimental errors, is equal to the heat bath temperature. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition.
A new theory for dynamics of concentrated colloidal suspensions and the colloidal glass transition is proposed. The starting point is the memory function representation of the density correlation function. The memory function can be expressed in terms of a time-dependent pair-density correlation function. An exact, formal equation of motion for this function is derived and a factorization approximation is applied to its evolution operator. In this way a closed set of equations for the density correlation function and the memory function is obtained. The theory predicts an ergodicity breaking t…
The flow curves, viz. the curves of stationary stress under steady shearing, are obtained close to the glass transition in dense colloidal dispersions using asymptotic expansions in a schematic model of mode coupling theory. The shear thinning of the viscosity in fluid states and the yielding of glassy states is discussed. At the transition between fluid and shear-molten glass, simple and generalized Herschel-Bulkley laws are derived with power law exponents that can be computed for different particle interactions from the equilibrium structure factor.
The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding collo…
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.
We present a direct experimental measurement of an effective temperature in a colloidal glass of Laponite, using a micrometric bead as a thermometer. The nonequilibrium fluctuation-dissipation relation, in the particular form of a modified Einstein relation, is investigated with diffusion and mobility measurements of the bead embedded in the glass. We observe an unusual non-monotonic behavior of the effective temperature : starting from the bath temperature, it is found to increase up to a maximum value, and then decreases back, as the system ages. We show that the observed deviation from the …
We monitor the relaxation of internal stresses in a fractal colloidal gel on cessation of flow and find a weak power law decay, $σ_i \sim t^{-α}$ over 5 decades of time where $α\approx 0.07$. The system exhibits physical aging of the elastic modulus, $G' \sim t^β$, with $β\approx α$. Imposition of zero stress after waiting time $t_w$ results in strain recovery as the system relaxes without constraint. Remarkably, recoveries at different $t_w$ can be shifted to construct a master curve where data are scaled vertically by $1/σ_i(t_w)$ and plotted horizontally as $(t-t_w)/t_w^μ$ where $μ\approx 1…
We study the effect of shear on the aging dynamics of a colloidal suspension of synthetic clay particles. We find that a shear of amplitude $γ$ reduces the relaxation time measured just after the cessation of shear by a factor $\exp(-γ/γ_c)$, with $γ_c \sim 5%$, and is independent of the duration and the frequency of the shear. This simple law for the rejuvenation effect shows that the energy involved in colloidal rearrangements is proportional to the shear amplitude, $γ$, rather than $γ^2$, leading to an Eyring-like description of the dynamics of our system.
We provide a direct experimental test of the Stokes-Einstein relation as a special case of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this non-equilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequenci…
We discuss the nonlinear rheology of dense colloidal dispersions at the glass transition. A first principles approach starting with interacting Brownian particles in given arbitrary homogeneous (incompressible) flow neglecting hydrodynamic interactions is sketched. It e.g. explains steady state flow curves for finite shear rates measured in dense suspensions of thermosensitive core-shell particles consisting of a polystyrene core and a crosslinked poly(N-isopropylacrylamide)(PNIPAM) shell. The exponents of simple and generalized Herschel Bulkley laws are computed for hard spheres.
G. Brambilla et al. Reply to a Comment by J. Reinhardt et al. questioning the existence of equilibrium dynamics above the critical volume fraction of colloidal hard spheres predicted by mode coupling theory.
Colloidal dispersions of Laponite platelets are known to age slowly from viscous sols to colloidal glasses. We follow this aging process by monitoring the diffusion of probe particles embedded in the sample via dynamic light scattering. Our results show that the time-dependent diffusion of the probe particles scales with their size. This implies that the fluctuation-dissipation theorem can be generalized for this out-of-equilibrium system by replacing the bath temperature with an effective temperature. Simultaneous dynamic rheological measurements reveal that this effective temperature increas…
Colloidal gels consist of percolating networks of interconnected arms. Their mechanical properties depend on the individual arms, and on their collective behaviour. We use numerical simulations to pull on a single arm, built from a model colloidal gel-former with short-ranged attractive interactions. Under elongation, the arm breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole arm; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different measurements …
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.
A fresh approach to the data from experiments with hard sphere colloids yields seminal insights into the glass transition. The precise determination of the fraction of particles caged by their neighbours is unprecedented and provides cornerstone of our study. We show that the so-called "dramatic slowing" that accompanies super-packing is due to correlated cage fluctuations, rather than caging per se. Their statistics establish that the amorphous assemblies of caged particles are in states of self-organised criticality. The implied connection between the onset of caging and the thermodynamic 1s…
The consolidation of colloidal particles in drying colloidal dispersions is influenced by various factors such as particle size and shape, and inter-particle potential. The capillary pressure induced by the menisci, formed between the top layer of particles in the packed bed, compresses the bed of particles while the constraints enforced by the boundaries result in tensile stresses in the packing. Presence of flaws or defects in the bed determines its ultimate strength under such circumstances. In this study, we determine the asymptotic stress distribution around a flaw in a two dimensional co…
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…
Dilute Laponite suspensions in water at low salt concentration form repulsive colloidal glasses which display physical aging. This phenomenon is still not completely understood and in particular, little is known about the connection between the flow history, as a determinant of the initial state of the system, and the subsequent aging dynamics. Using a stress controlled rheometer, we perform stress jump experiments to observe the elastic component of the flow stress that remains on cessation of flow or flow quenching. We investigate the connection between the dynamics of these residual stresse…
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…
The complex behavior of confined fluids arising due to a competition between layering and local packing can be disentangled by considering quasi-confined liquids, where periodic boundary conditions along the confining direction restore translational invariance. This system provides a means to investigate the interplay of the relevant length scales of the confinement and the local order. We provide a mode-coupling theory of the glass transition (MCT) for quasi-confined liquids and elaborate an efficient method for the numerical implementation. The nonergodicity parameters in MCT are compared to…
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…
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.
There is mounting evidence indicating that relaxation dynamics in liquids approaching their glass transition not only becomes increasingly cooperative (1,2) but the relaxing regions also become more compact in shape(3-7). While the surface tension of the interface separating neighboring relaxing regions is thought to play a crucial role in deciding both their size and morphology(8-10), owing to the amorphous nature of these regions, even identifying these interfaces has not been possible in bulk liquids. Here, by devising a scheme to identify self-induced disorder sites in bulk colloidal liqui…
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…
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.
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…
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…
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…
The non-equilibrium self-consistent generalized Langevin equation theory of colloid dynamics is used to describe the non-stationary aging processes occurring in a suddenly quenched model colloidal liquid with hard-sphere plus short-ranged attractive interactions, whose static structure factor and van Hove function evolve irreversibly from the initial conditions before the quench to a final, dynamically arrested state. The comparison of our numerical results with available simulation data are highly encouraging.
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…
We report a numerical study of the shear viscosity and the frequency dependent elastic moduli close to dynamical arrest for a model of short-range attractive colloids, both for the repulsive and the attractive glass transition. Calculating the stress autocorrelation functions, we find that density fluctuations of wavevectors close to the first peak in the structure factor control the viscosity rise on approaching the repulsive glass, while fluctuations of larger wavevectors control the viscosity close to the attractive glass. On approaching the glass transition, the viscosity diverges with a p…
We present an experimental and theoretical investigation of the Generalized Einstein Relation (GER), a particular form of a fluctuation-dissipation relation, in an out-of-equilibrium visco-elastic fluid. Micrometer beads, used as thermometers, are immersed in an aging colloidal glass to provide both fluctuation and dissipation measurements. The deviations from the Generalized Einstein Relation are derived as a function of frequency and aging time. The observed deviations from GER are interpreted as directly related to the change in the glass relaxation times with aging time. In our scenario, d…
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 demonstrate that application of an increasing shear field on a glass leads to an intriguing dynamic first order transition in analogy to equilibrium transitions. By following the particle dynamics as a function of the driving field in a colloidal glass, we identify a critical shear rate upon which the diffusion time scale of the glass exhibits a sudden discontinuity. Using a new dynamic order parameter, we show that this discontinuity is analogous to a first order transition, in which the applied stress acts as the conjugate field on the system's dynamic evolution. These results offer new p…
In this chapter, a study of the glass transitions in colloidal systems is presented, in connection with gelation, mainly from theoretical and simulation results. Mode Coupling Theory, which anticipated the existence of attraction driven glasses, is reviewed, and its predictions concerning attractive glasses discussed. Results from computer simulations will be presented for different models and the predictions of the theory will be tested. Starting from high density, where reasonable agreement is found, the study will be extended to low density, where new modes for the decay of density correlat…
The drying of a colloidal dispersion can result in a gel phase defined as a porous matrix saturated in solvent. During the drying process, high mechanical stresses are generated. When these stresses exceed the strength of the material, they can be released in the formation of cracks. This process strongly depends on both the mechanical properties of the material and the way the gel consolidates. In this report, we give experimental evidences that the number of cracks formed in the consolidating film depend on the drying rate, the nature of the solvent and the mechanical properties of the collo…
We study the flow of concentrated hard-sphere colloidal suspensions along smooth, non-stick 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 paramete…
We study concentrated colloidal suspensions, a model system which has a glass transition. Samples in the glassy state show aging, in that the motion of the colloidal particles slows as the sample ages from an initial state. We study the relationship between the static structure and the slowing dynamics, using confocal microscopy to follow the three-dimensional motion of the particles. The structure is quantified by considering tetrahedra formed by quadruplets of neighboring particles. We find that while the sample clearly slows down during aging, the static properties as measured by tetrahedra…
