Dynamical correlation length and relaxation processes in a glass former

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

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

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

Scaling and universality in glass transition

Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field theory, for such systems by considering the behavior of the density correlator 〈q(t)〉 and the dynamical susceptibility 〈q(2)(t)〉 - 〈q(t)〉(2). Focusing on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe lattice, we extend a cluster approach that was previously developed for continuous glass transitions by Arenzon et al. (Phys. Rev. E 90, 020301(R) (2014)) to describe the decay to the plateau, and consider a damage spreading mechanism to describe the departure from the plateau. We predict scaling laws, which relate dynamical exponents to the static exponents of mean field bootstrap percolation. The dynamical behavior and the scaling laws for both density correlator and dynamical susceptibility coincide with those predicted by MCT. These results explain the origin of scaling laws and the universal behavior associated with the glass transition in mean field, which is characterized by the divergence of the static length of the bootstrap percolation model with an upper critical dimension dc = 8.

Particle jumps in structural glasses

Particles in structural glasses rattle around temporary equilibrium positions, that seldom change through a process which is much faster than the relaxation time, known as particle jump. Since the relaxation of the system is due to the accumulation of many such jumps, it could be possible to connect the single particle short time motion to the macroscopic relaxation by understanding the features of the jump dynamics. Here we review recent results in this research direction, clarifying the features of particle jumps that have been understood and those that are still under investigation, and examining the role of particle jumps in different theories of the glass transition.

Questioning the relationship between the χ4 susceptibility and the dynamical correlation length in a glass former

Clusters of fast and slow correlated particles, identified as dynamical heterogeneities (DHs), constitute a central aspect of glassy dynamics. A key factor of the glass transition scenario is a significant increase of the cluster size ξ4 as the transition is approached. In need of easy-to-compute tools to measure ξ4, the dynamical susceptibility χ4 was introduced recently, and used in various experimental studies to probe DHs. Here, we investigate DHs in dense microgel suspensions using image correlation analysis, and compute both χ4 and the four-point correlation function G4. The spatial decrease of G4 provides a direct access to ξ4, which is found to grow significantly with increasing volume fraction. However, this increase is not captured by χ4. We show that the assumptions that validate the connection between χ4 and ξ4 are not fulfilled in our experiments.

Dynamic phase coexistence in glass-forming liquids

One of the most controversial hypotheses for explaining the heterogeneous dynamics of glasses postulates the temporary coexistence of two phases characterized by a high and by a low diffusivity. In this scenario, two phases with different diffusivities coexist for a time of the order of the relaxation time and mix afterwards. Unfortunately, it is difficult to measure the single-particle diffusivities to test this hypothesis. Indeed, although the non-Gaussian shape of the van-Hove distribution suggests the transient existence of a diffusivity distribution, it is not possible to infer from this quantity whether two or more dynamical phases coexist. Here we provide the first direct observation of the dynamical coexistence of two phases with different diffusivities, by showing that in the deeply supercooled regime the distribution of the single-particle diffusivities acquires a transient bimodal shape. We relate this distribution to the heterogeneity of the dynamics and to the breakdown of the Stokes-Einstein relation, and we show that the coexistence of two dynamical phases occurs up to a timescale growing faster than the relaxation time on cooling, for some of the considered models. Our work offers a basis for rationalizing the dynamics of supercooled liquids and for relating their structural and dynamical properties.

Connecting short and long time dynamics in hard-sphere-like colloidal glasses

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 parameter controlling the slowing down of the dynamics. We characterize the volume fraction dependence of the cage-jump features and show that, as in molecular systems, they allow for a short time prediction of the diffusivity.

The freezing tendency towards 4-coordinated amorphous networks causes an increase in the heat capacity of supercooled Stillinger–Weber silicon

A heat-capacity increase near the liquid-amorphous (glass) transition temperature (1060 K) is caused by dynamical instability leading to the freezing of the 4-coordinated network.

Mesoscopic model of temporal and spatial heterogeneity in aging colloids

We develop a simple and effective description of the dynamics of dense hard sphere colloids in the aging regime deep in the glassy phase. Our description complements the many efforts to understand the onset of jamming in low density colloids, whose dynamics is still time-homogeneous. Based on a small set of principles, our model provides emergent dynamic heterogeneity, reproduces the known results for dense hard sphere colloids and makes detailed, experimentally-testable predictions for canonical observables in glassy dynamics. In particular, we reproduce the shape of the intermediate scattering function and particle mean-square displacements for jammed colloidal systems, and we predict a growth for the peak of the χ(4) mobility correlation function that is logarithmic in waiting-time. At the same time, our model suggests a novel unified description for the irreversible aging dynamics of structural and quenched glasses based on the dynamical properties of growing clusters of highly correlated degrees of freedom.

From cage-jump motion to macroscopic diffusion in supercooled liquids

The evaluation of the long term stability of a material requires the estimation of its long-time dynamics. For amorphous materials such as structural glasses, it has proven difficult to predict the long-time dynamics starting from static measurements. Here we consider how long one needs to monitor the dynamics of a structural glass to predict its long-time features. We present a detailed characterization of the statistical features of the single-particle intermittent motion, and show that single-particle jumps are the irreversible events leading to the relaxation of the system. This allows us to evaluate the diffusion constant on the time-scale of the jump duration, which is small and temperature independent, i.e. well before the system enters the diffusive regime. The prediction is obtained by analyzing the particle trajectories via a parameter-free algorithm.

Driving kinetically constrained models into nonequilibrium steady states: Structural and slow transport properties

Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at a theoretical level and by molecular dynamic simulations. To understand some of these features we study a schematic model of a highly viscous liquid, the two-dimensional Kob-Andersen kinetically constrained model, driven into nonequilibrium steady states by a uniform non-Hamiltonian force. We present a detailed numerical analysis of the microscopic behavior of the model, including transversal and longitudinal spatial correlations and dynamic heterogeneities. In particular, we show that at high particle density the transition from positive to negative resistance regimes in the current vs field relation can be explained via the emergence of nontrivial structures that intermittently trap the particles and slow down the dynamics. We relate such spatial structures to the current vs field relation in the different transport regimes.