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.
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 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.
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 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 couplin…
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…
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.
We here discuss the results of 3d MonteCarlo simulations of a minimal lattice model for gelling systems. We focus on the dynamics, investigated by means of the time autocorrelation function of the density fluctuations and the particle mean square displacement. We start from the case of chemical gelation, i.e. with permanent bonds, we characterize the critical dynamics as determined by the formation of the percolating cluster, as actually observed in polymer gels. By opportunely introducing a finite bond life time $τ_b$ the dynamics displays relevant changes and eventually the onset of a glassy…
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…
By means of molecular dynamics, we study the structure and the dynamics of a microscopic model for colloidal gels at low volume fractions. The presence of directional interactions leads to the formation of a persistent interconnected network at temperatures where phase separation does not occur. We find that large scale spatial correlations strongly depend on the volume fraction and characterize the formation of the persistent network. We observe a pre-peak in the static structure factor and relate it to the network structure. The slow dynamics at gelation is characterized by the coexistence o…
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…
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…
We measure the fluctuations of the position of a silica bead trapped by an optical tweezers during the aging of a Laponite suspension. We find that the effective temperature is equal to the bath temperature.
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.
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…
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…
We use a recently derived diagrammatic formulation of the dynamics of interacting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)] to study a four-point dynamic density correlation function. We re-sum a class of diagrams which separate into two disconnected components upon cutting a single propagator. The resulting formula for the four-point correlation function can be expressed in terms of three-point functions closely related to the three-point susceptibility introduced by Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)] and the standard two-point correlation function. The…
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…
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 …
This model describes cluster aggregation in a stirred colloidal solution Interacting clusters compete for growth in this 'winner-takes-all' model; for finite assemblies, the largest cluster always wins, i.e. there is a uniform sediment. In mean-field, the model exhibits glassy dynamics, with two well-separated time scales, corresponding to individual and collective behaviour; the survival probability of a cluster eventually falls off according to a universal law $(\ln t)^{-1/2}$. In finite dimensions, the glassiness is enhanced: the dynamics manifests both {\it ageing} and metastability, where…
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…
This article discusses recent attempts to provide a deeper understanding of the thermoreversible "gel" state of colloidal matter and to unravel the analogies between gels at the colloidal level and gels at the molecular level, commonly known as network-forming strong liquids. The connection between gel-forming patchy colloids and strong liquids is provided by the limited valence of the inter-particle interactions, i.e. by the presence of a limit in the number of bonded nearest neighbors.
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…
We formulate a microscopic, force-level, activated dynamics-based statistical-mechanical theory for the continuous startup nonlinear shear-rheology of ultra-dense glass-forming hard-sphere fluids and colloidal suspensions in the context of the ECNLE approach. Activated structural relaxation is described as a coupled local-nonlocal event involving caging and longer-range collective elasticity which controls the characteristic stress relaxation time. Theoretical predictions for the deformation-induced mobility enhancement, onset of relaxation acceleration at low values of stress, strain, or shea…
The shear rheology of soft particles systems becomes complex at large density because crowding effects may induce a glass transition for Brownian particles, or a jamming transition for non-Brownian systems. Here we successfully explore the hypothesis that the shear stress contributions from glass and jamming physics are `additive'. We show that the experimental flow curves measured in a large variety of soft materials (colloidal hard spheres, microgel suspensions, emulsions, aqueous foams) as well as numerical flow curves obtained for soft repulsive particles in both thermal and athermal limit…
Glasses behave as solids due to their long relaxation time; however the origin of this slow response remains a puzzle. Growing dynamic length scales due to cooperative motion of particles are believed to be central to the understanding of both the slow dynamics and the emergence of rigidity. Here, we provide experimental evidence of a growing dynamical heterogeneity length scale that increases with increasing waiting time in an aging colloidal glass of Laponite. The signature of heterogeneity in the dynamics follows from dynamic light scattering measurements in which we study both the rotation…
Colloidal Janus spheres in water (one hemisphere attractive and the other repulsive) assemble into two-dimensional hexagonal crystals with orientational order controlled by anisotropic interactions. We exploit the decoupled translational and rotational order to quantify the orientational dynamics. Via imaging experiments and Monte Carlo simulations we demonstrate that the correlations in the orientation of individual Janus spheres exhibit glasslike dynamics that can be controlled via the ionic strength. Thus, these colloidal building blocks provide a particularly suitable model glass system fo…
