Pinaki Chaudhuri

Universal Nature of Particle Displacements close to Glass and Jamming Transitions

We examine the structure of the distribution of single particle displacements (van Hove function) in a broad class of materials close to glass and jamming transitions. In a wide time window comprising structural relaxation, van Hove functions reflect the coexistence of slow and fast particles (dynamic heterogeneity). The tails of the distributions exhibit exponential, rather than Gaussian, decay. We argue that this behavior is universal in glassy materials and should be considered the analog, in space, of the stretched exponential decay of time correlation functions. We introduce a dynamical model that describes quantitatively numerical and experimental data in supercooled liquids, colloidal hard spheres, and granular materials. The tails of the distributions directly explain the decoupling between translational diffusion and structural relaxation observed in glassy materials.

Jamming transitions in amorphous packings of frictionless spheres occur over a continuous range of volume fractions

We numerically produce fully amorphous assemblies of frictionless spheres in three dimensions and study the jamming transition these packings undergo at large volume fractions. We specify four protocols yielding a critical value for the jamming volume fraction which is sharply defined in the limit of large system size, but is different for each protocol. Thus, we directly establish the existence of a continuous range of volume fractions where nonequilibrium jamming transitions occur. However, these jamming transitions share the same critical behavior. Our results suggest that, even in the absence of partial crystalline ordering, a unique location of a random close packing does not exist.

Creep and flow of glasses: strain response linked to the spatial distribution of dynamical heterogeneities.

Mechanical properties are of central importance to materials sciences, in particular if they depend on external stimuli. Here we investigate the rheological response of amorphous solids, namely colloidal glasses, to external forces. Using confocal microscopy and computer simulations, we establish a quantitative link between the macroscopic creep response and the microscopic single-particle dynamics. We observe dynamical heterogeneities, namely regions of enhanced mobility, which remain localized in the creep regime, but grow for applied stresses leading to steady flow. These different behaviors are also reflected in the average particle dynamics, quantified by the mean squared displacement of the individual particles, and the fraction of active regions. Both microscopic quantities are found to be proportional to the macroscopic strain, despite the non-equilibrium and non-linear conditions during creep and the transient regime prior to steady flow.

Inhomogeneous shear flows in soft jammed materials with tunable attractive forces.

We perform molecular dynamics simulations to characterize the occurrence of inhomogeneous shear flows in soft jammed materials. We use rough walls to impose a simple shear flow and study the athermal motion of jammed assemblies of soft particles in two spatial dimensions, both for purely repulsive interactions and in the presence of an additional short-range attraction of varying strength. In steady state, pronounced flow inhomogeneities emerge for all systems when the shear rate becomes small. Deviations from linear flow are stronger in magnitude and become very long lived when the strength of the attraction increases, but differ from permanent shear bands. Flow inhomogeneities occur in a stress window bounded by the dynamic and static yield stress values. Attractive forces enhance the flow heterogeneities because they accelerate stress relaxation, thus effectively moving the system closer to the yield stress regime where inhomogeneities are most pronounced. The present scenario for understanding the effect of particle adhesion on shear localization, which is based on detailed molecular dynamics simulations with realistic particle interactions, differs qualitatively from previous qualitative explanations and ad hoc theoretical modeling.

Suppressed compressibility at large scale in jammed packings of size-disperse spheres.

We analyze the large-scale structure and fluctuations of jammed packings of size-disperse spheres, produced in a granular experiment as well as numerically. While the structure factor of the packings reveals no unusual behavior for small wave vectors, the compressibility displays an anomalous linear dependence at low wave vectors and vanishes when q→0. We show that such behavior occurs because jammed packings of size-disperse spheres have no bulk fluctuations of the volume fraction and are thus hyperuniform, a property not observed experimentally before. Our results apply to arbitrary particle size distributions. For continuous distributions, we derive a perturbative expression for the compressibility that is accurate for polydispersity up to about 30%.

A random walk description of the heterogeneous glassy dynamics of attracting colloids

We study the heterogeneous dynamics of attractive colloidal particles close to the gel transition using confocal microscopy experiments combined with a theoretical statistical analysis. We focus on single particle dynamics and show that the self-part of the van Hove distribution function is not the Gaussian expected for a Fickian process, but that it reflects instead the existence, at any given time, of colloids with widely different mobilities. Our confocal microscopy measurements can be described well by a simple analytical model based on a conventional continuous time random walk picture, as already found for several other glassy materials. In particular, the theory successfully accounts for the presence of broad tails in the van Hove distributions that exhibit exponential, rather than Gaussian, decay at large distance.

Tracking heterogeneous dynamics during the alpha relaxation of a simple glass former.

We study the relaxation process in a simple glass former--the Kob-Andersen lattice gas model. We show that, for this model, structural relaxation is due to slow percolation of regions of cooperatively moving particles, which leads to heterogeneous dynamics of the system. We find that the size distribution of these regions is given by a power law and that their formation is encoded in the initial structure of the particles, with the memory of initial configuration increasingly retained with increasing density.

Yielding of glass under shear: A directed percolation transition precedes shear-band formation

The response of glasses to mechanical loading often leads to the formation of inhomogeneous flow patterns. Among them, shear bands, associated with strain localization in form of band-like structures, are ubiquitous in a wide variety of materials, ranging from soft matter systems to metallic alloys. They can be precursors to catastrophic failure, implying that a better understanding of the underlying mechanisms of shear banding could lead to the design of smarter materials. Here, molecular dynamics simulations are used to reveal the formation of shear bands in a binary Lennard-Jones glass, subject to a constant strain rate. At a critical strain, this system exhibits for all considered strain rates a transition towards the formation of a percolating cluster of mobile regions. We give evidence that this transition belongs to the universality class of directed percolation. Only at low shear rates, the percolating cluster evolves into a transient (but long-lived) shear band with a diffusive growth of its width.

Impact of attractive interactions on the rheology of dense athermal particles.

Using numerical simulations, the rheological response of an athermal assembly of soft particles with tunable attractive interactions is studied in the vicinity of jamming. At small attractions, a fragile solid develops and a finite yield stress is measured. Moreover, the measured flow curves have unstable regimes, which lead to persistent shear banding. These features are rationalized by establishing a link between the rheology and the interparticle connectivity, which also provides a minimal model to describe the flow curves.

A molecular dynamics study of non-local effects in the flow of soft jammed particles

In this paper, we used numerical simulations to investigate the flow properties of soft glassy materials. These systems display a mixed fluid–solid behavior whose theoretical description remains a challenging task. The molecular dynamic simulations exhibit non-local rheological behavior, in direct line with previous experimental results. The inverse viscosity of the material at a given point, denoted as fluidity, is not a local function of the local stress, but also depends on the state of the system in the neighborhood, with a spatial correlation length typically equal to a few particles. The fluidity is furthermore related directly to the velocity fluctuations and rate of plastic events in the form of a scaling function. Correlations are the signature of a cooperative process at the origin of the flow and of the non-local effects. We compare the obtained results with a scalar fluidity model and emphasize the similarities between the two approaches.