Many facets of intermittent dynamics in colloidal and molecular glasses

Intermittent random walks under stochastic resetting

We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. We demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. We calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, we prove that the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. Moreover, we demonstrate the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition.

Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids

Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length λ growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law λ(t)∝tα, with α≃1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a "universal" evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.

Fickian Non-Gaussian Diffusion in Glass-Forming Liquids

Fickian yet non-Gaussian diffusion (FnGD), a most intriguing open issue in soft matter, is generically associated with some dynamical and/or structural heterogeneity of the environment. Here we investigate the features of FnGD in glass-forming liquids, the epitome of dynamical heterogeneity, drawing on experiments on hard-sphere colloidal suspensions and simulations of a simple model of molecular liquid. We demonstrate that FnGD strengthens on approaching the glass transition, by identifying distinct timescales for Fickianity, τ_{F}, and for restoring of Gaussianity, τ_{G}>τ_{F}, as well as their associated length scales, ξ_{F} and ξ_{G}. We find τ_{G}∝τ_{F}^{γ} with γ≃1.8 for both systems. In the deep FnGD regime, the displacement distributions display exponential tails. We show that, in simulations, the time-dependent decay lengths l(t) at different temperatures all collapse onto a power-law master curve [l(t)/(ξ_{G})]∝(t/τ_{G})^{α}, with α=0.33. A similar collapse, if less sharp, is also found in experiments, seemingly with the same exponent α. We further discuss the connections of the timescales and length scales characterizing FnGD with structural relaxation and dynamic heterogeneity.

Multiscale heterogeneous dynamics in two-dimensional glassy colloids

On approaching the glass transition, a dense colloid exhibits a dramatic slowdown with minute structural changes. Most microscopy experiments directly follow the motion of individual particles in real space, whereas scattering experiments typically probe the collective dynamics in reciprocal space, at variable wavevector q. Multiscale studies of glassy dynamics are experimentally demanding and thus seldom performed. By using two-dimensional hard-sphere colloids at various area fractions φ, we show here that Differential Dynamic Microscopy (DDM) can be effectively used to measure the collective dynamics of a glassy colloid in a range of q within a single experiment. As φ is increased, the single decay of the intermediate scattering functions is progressively replaced by a more complex relaxation that we fit to a sum of two stretched-exponential decays. The slowest process, corresponding to the long-time particle escapes from caging, has a characteristic time τs = 1/(DLq2 ) with diffusion coefficient DL ∼ (φc −φ)2.8 , and φc ≈ 0.81. The fast process exhibits, instead, a non-Brownian scaling of the characteristic time τf(q) and a relative amplitude a(q) that monotonically increases with q. Despite the non-Brownian nature of τf(q), we succeed in estimating the short-time diffusion coefficient Dcage, whose φ-dependence is practically negligible compared to the one of DL. Finally, we extend DDM to measure the q-dependent dynamical susceptibility χ4(q,t), a powerful yet hard-to-access multiscale indicator of dynamical heterogeneities. Our results show that DDM is a convenient tool to study the dynamics of colloidal glasses over a broad range of time and length-scales.

A model-system of Fickian yet non-Gaussian diffusion: light patterns in place of complex matter

Fickian yet non-Gaussian Diffusion (FnGD), widely observed for colloidal particles in a variety of complex and biological fluids, emerges as a most intriguing open issue in Soft Matter. To fully monitor FnGD and advance its understanding, recording many trajectories over a large time range is crucial, which makes experiments challenging. Here we exploit a recently introduced experimental model of finely tunable FnGD: a quasi-2d system of Brownian beads in water moving in a heterogeneous energy landscape generated by a static and spatially random optical force field (speckle pattern). By performing experiments at different optical power, we succeed in monitoring the evolution as well as the precursors of FnGD. Fickian scaling of the mean square displacement is always attained after a subdiffusive regime while the displacement distributions keep on being non-Gaussian, which allows for measuring a characteristic length- and time-scale for the onset of FnGD, ξ_f and t_f. We find that ξ_f stays constant, whereas t_f grows as the inverse of the long-time diffusion coefficient t_f ∝ D^-1 for increasing the optical power. Deviations from the standard Gaussian shape of the displacement distribution are neatly characterized on a broad range of times, focusing on the excess probability at small displacements and on the decay-length of the distinctive exponential tails. Such deviations are fully built in the subdiffusive regime and, at the FnGD onset, grow with the optical power. As time goes on, the small-displacement probability narrows and the exponential tails progressively break up, with a tendency to recover the Gaussian behaviour. Overall, both subdiffusion and FnGD become more marked and persistent on increasing the optical power, suggesting a strict relation between these two regimes. As clearly demonstrated by our results, the adopted model-system represents a privileged stage for in-depth study of FnGD and opens the way to unveil the nature of this phenomenon through finely tuned and well-controlled experiments.

Breakdown of the Stokes-Einstein relation in supercooled liquids: A cage-jump perspective

The breakdown of the Stokes-Einstein relation in supercooled liquids, which is the increase in the ratio τ_ατ_D between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that τ_ατ_D∝⟨t_p⟩⟨t_c⟩, where ⟨t_p⟩ and ⟨t_c⟩ are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations τ_α∝⟨t_p⟩⟨Δr_J ²⟩ and τ_D∝⟨t_c⟩⟨Δr_J ²⟩ effectively connect the macroscopic and microscopic timescales, with the mean square jump length ⟨Δr_J ²⟩ shrinking on cooling. Our work provides a microscopic perspective on the Stokes-Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.

Understanding charged vesicle suspensions as Wigner glasses: dynamical aspects

Suspensions of charged vesicles in water with added salt are widespread in nature and industrial production. Here we investigate, via Brownian dynamics simulations, a model that grasps the key features of these systems, with bidisperse colloidal beads interacting via a hard-core and an electrostatic double layer potential. Our goal is to focus on a set of interaction parameters that is not generic but measured in recent experiments, and relevant for a class of consumer products, such as liquid fabric softeners. On increasing the volume fraction in a range relevant to real formulation, we show that the dynamics become progressively slower and heterogeneous, displaying the typical signatures of an approaching glass transition. On lowering the salt concentration, which corresponds to increasing the strength and range of the electrostatic repulsion, the emergence of glassy dynamics becomes significantly steeper, and, remarkably, occurs at volume fractions well below the hard-sphere glass transition. The volume fraction dependence of the structural relaxation time at different salt concentration is well described through a functional law inspired by a recently proposed model (Krausser et al 2015 Proc. Natl Acad. Sci. USA 112 13762). According to our results, the investigated system may be thought of as a Wigner glass, i.e. a low-density glassy state stabilized by long-range repulsive interactions. Overall, our study suggests that glassy dynamics plays an important role in controlling the stability of these suspensions.

Emergence and percolation of rigid domains during the colloidal 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 the glass transition, accompanied by the emergence of dynamical heterogeneities. Our results show that spatial constraint instead of the geometry of amorphous structures is the key that connects the complex spatial-temporal correlations in disordered materials.

Effects of chemically heterogeneous nanoparticles on polymer dynamics: insights from molecular dynamics simulations

The dispersion of solid nanoparticles within polymeric materials is widely used to enhance their performance. Many scientific and technological aspects of the resulting polymer nanocomposites have been studied, but the role of the structural and chemical heterogeneity of the nanoparticles has just started to be appreciated. For example, simulations of polymer films on planar heterogeneous surfaces revealed unexpected, non-monotonic activation energy to diffusion on varying the surface composition. Motivated by these intriguing results, here we simulate via molecular dynamics a different, fully three-dimensional system, in which the heterogeneous nanoparticles are incorporated in a polymer melt. The nanoparticles are roughly spherical assemblies of strongly and weakly attractive sites, in fractions of f and 1 - f, respectively. We show that the polymer diffusion is still characterized by a non-monotonic dependence of the activation energy on f. The comparison with the case of homogeneous nanoparticles clarifies that the effect of the heterogeneity increases on approaching the polymer glass transition.