Dependence of the Glass Transition and Jamming Densities on Spatial Dimension.

We investigate the dynamics of soft sphere liquids through computer simulations for spatial dimensions from d=3 to 8, over a wide range of temperatures and densities. Employing a scaling of density-temperature-dependent relaxation times, we precisely identify the density ϕ_{0}, which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between ϕ_{0} and the athermal jamming density ϕ_{J}, small in 3 and 4 dimensions, increases with dimension, with ϕ_{0}>ϕ_{J} for d>4. We compare our results with recent theoretical calculations.

Discontinuous rigidity transition associated with shear jamming in granular simulations.

We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition under quasi-static shear is discontinuous, with an instantaneous emergence of a system spanning rigid clusters at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transition associated with shear jamming is discontinuous, as demonstrated in the past for isotropic jamming of frictionless particles, and therefore a unifying feature of the jamming transition in general.

Analysis of Structural Change across the Liquid-Liquid Transition and the Widom Line in Supercooled Stillinger-Weber Silicon.

We consider the changes in the structure of supercooled Stillinger-Weber silicon at pressures at which the studied range of temperatures traverses the liquid-liquid transition or the "Widom line" (at which the isothermal compressibility or the specific heat exhibits a maximum). In addition to the conventional characterizations in terms of the pair-correlation function and bond orientational order, we analyze the statistics of rings in the bond network as well as the statistics of clusters of low density liquid (LDL)- and high density liquid (HDL)-like atoms. We investigate the nature of the change in these structural characterizations when the liquid-liquid transition line or the Widom line is crossed. We find that the isobaric temperature variation of these structural features reveals clear indications of maximal structural heterogeneity or frustration upon crossing the liquid-liquid transition or the Widom line, as in the case of water, but with some differences in detail, which we discuss.

Kinetic reconstruction of free energies as a function of multiple order parameters.

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

Protein as evolvable functionally constrained amorphous matter.

We explore current ideas around the representation of a protein as an amorphous material, in turn represented by an abstract graph G with edges weighted by elastic stiffnesses. By embedding this graph in physical space, we can map every graph to a spectrum of conformational fluctuations and responses (as a result of, say, ligandbinding). This sets up a 'genotype-phenotype' map, which we use to evolve the amorphous material to select for fitness. Using this, we study the emergence of allosteric interaction, hinge joint, crack formation and a slide bolt in functional proteins such as adenylate kinase, HSP90, calmodulin and GPCR proteins. We find that these emergent features are associated with specific geometries and mode spectra of floppy or liquid-like regions. Our analysis provides insight into understanding the architectural demands on a protein that enable a prescribed function and its stability to mutations.

Annealing glasses by cyclic shear deformation.

A major challenge in simulating glassy systems is the ability to generate configurations that may be found in equilibrium at sufficiently low temperatures, in order to probe static and dynamic behavior close to the glass transition. A variety of approaches have recently explored ways of surmounting this obstacle. Here, we explore the possibility of employing mechanical agitation, in the form of cyclic shear deformation, to generate low energy configurations in a model glass former. We perform shear deformation simulations over a range of temperatures, shear rates, and strain amplitudes. We find that shear deformation induces faster relaxation toward low energy configurations, or overaging, in simulations at sufficiently low temperatures, consistently with previous results for athermal shear. However, for temperatures at which simulations can be run until a steady state is reached with or without shear deformation, we find that the inclusion of shear deformation does not result in any speed up of the relaxation toward low energy configurations. Although we find the configurations from shear simulations to have properties indistinguishable from an equilibrium ensemble, the cyclic shear procedure does not guarantee that we generate an equilibrium ensemble at a desired temperature. In order to ensure equilibrium sampling, we develop a hybrid Monte Carlo algorithm that employs cyclic shear as a trial generation step and has acceptance probabilities that depend not only on the change in internal energy but also on the heat dissipated (equivalently, work done). We show that such an algorithm, indeed, generates an equilibrium ensemble.

Criticality and marginal stability of the shear jamming transition of frictionless soft spheres.

We study numerically the critical behavior and marginal stability of the shear jamming transition for frictionless soft spheres, observed to occur over a finite range of densities, associated with isotropic jamming for densities above the minimum jamming (J-point) density. Several quantities are shown to scale near the shear jamming point in the same way as the isotropic jamming point. We compute the exponents associated with the small force distribution and the interparticle gap distribution and show that the corresponding exponents are consistent with the marginal stability condition observed for isotropic jamming and with predictions of the mean-field theory of jamming in hard spheres.

Mean-Field Theory of Yielding under Oscillatory Shear.

We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behavior of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a nontrivial, nonmonotonic approach to the yielded state. The timescale diverges as one approaches the yielding point from above, which we identify with the fatigue limit. We finally discuss the connections to brittle yielding under uniform shear.

Avalanches, Clusters, and Structural Change in Cyclically Sheared Silica Glass.

We investigate avalanches and clusters associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. We perform a detailed analysis of avalanches, and of spatially disconnected clusters that constitute them, for a wide range of system sizes. Although qualitative aspects of yielding in silica are similar to other glasses, the statistics of clusters exhibits significant differences, which we associate with differences in local structure. Across the yielding transition, anomalous structural change and densification, associated with a suppression of tetrahedral order, is observed to accompany strain localization.

Yielding transition of a two dimensional glass former under athermal cyclic shear deformation.

We study numerically the yielding transition of a two dimensional model glass subjected to athermal quasi-static cyclic shear deformation, with the aim of investigating the effect on the yielding behavior of the degree of annealing, which in turn depends on the preparation protocol. We find two distinct regimes of annealing separated by a threshold energy. Poorly annealed glasses progressively evolve toward the threshold energy as the strain amplitude is increased toward the yielding value. Well annealed glasses with initial energies below the threshold energy exhibit stable behavior, with a negligible change in energy with increasing strain amplitude, until they yield. Discontinuities in energy and stress at yielding increase with the degree of annealing, consistent with recent results found in three dimensions. We observe a significant structural change with strain amplitude that closely mirrors the changes in energy and stresses. We investigate groups of particles that are involved in plastic rearrangements. We analyze the distributions of avalanche sizes, of clusters of connected rearranging particles, and related quantities, employing finite size scaling analysis. We verify previously investigated relations between exponents characterizing these distributions.

Temperature protocols to guide selective self-assembly of competing structures.

Multicomponent self-assembly mixtures offer the possibility of encoding multiple target structures with the same set of interacting components. Selective retrieval of one of the stored structures has been attempted by preparing an initial state that favors the assembly of the required target, through seeding, concentration patterning, or specific choices of interaction strengths. This may not be possible in an experiment where on-the-fly reconfiguration of the building blocks to switch functionality may be required. In this paper, we explore principles of inverse design of a multicomponent, self-assembly mixture capable of encoding two competing structures that can be selected through simple temperature protocols. We design the target structures to realize the generic situation in which one of the targets has the lower nucleation barrier, while the other is globally more stable. We observe that, to avoid the formation of spurious or chimeric aggregates, the number of neighboring component pairs that occur in both structures should be minimal. Our design also requires the inclusion of components that are part of only one of the target structures. We observe, however, that to maximize the selectivity of retrieval, the component library itself should be maximally shared by the two targets, within such a constraint. We demonstrate that temperature protocols can be designed that lead to the formation of either one of the target structures with high selectivity. We discuss the important role played by secondary aggregation products in improving selectivity, which we term "vestigial aggregates."

Correlation between plastic rearrangements and local structure in a cyclically driven glass.

The correlation between the local structure and the propensity for structural rearrangements has been widely investigated in glass forming liquids and glasses. In this paper, we use the excess two-body entropy S2 and tetrahedrality ntet as the per-particle local structural order parameters to explore such correlations in a three-dimensional model glass subjected to cyclic shear deformation. We first show that for both liquid configurations and the corresponding inherent structures, local ordering increases upon lowering temperature, signaled by a decrease in the two-body entropy and an increase in tetrahedrality. When the inherent structures, or glasses, are periodically sheared athermally, they eventually reach absorbing states for small shear amplitudes, which do not change from one cycle to the next. Large strain amplitudes result in the formation of shear bands, within which particle motion is diffusive. We show that in the steady state, there is a clear difference in the local structural environment of particles that will be part of plastic rearrangements during the next shear cycle and that of particles that are immobile. In particular, particles with higher S2 and lower ntet are more likely to go through rearrangements irrespective of the average energies of the configurations and strain amplitude. For high shear, we find very distinctive local order outside the mobile shear band region, where almost 30% of the particles are involved in icosahedral clusters, contrasting strongly with the fraction of <5% found inside the shear band.

Liquid-liquid phase transition in deeply supercooled Stillinger-Weber silicon.

The existence of a phase transition between two distinct liquid phases in single-component network-forming liquids (e.g. water, silica, silicon) has elicited considerable scientific interest. The challenge, both for experiments and simulations, is that the liquid-liquid phase transition (LLPT) occurs under deeply supercooled conditions, where crystallization occurs very rapidly. Thus, early evidence from numerical equation of state studies was challenged with the argument that slow spontaneous crystallization had been misinterpreted as evidence of a second liquid state. Rigorous free-energy calculations have subsequently confirmed the existence of a LLPT in some models of water, and exciting new experimental evidence has since supported these computational results. Similar results have so far not been found for silicon. Here, we present results from free-energy calculations performed for silicon modeled with the classical, empirical Stillinger-Weber-potential. Through a careful study employing state-of-the-art constrained simulation protocols and numerous checks for thermodynamic consistency, we find that there are two distinct metastable liquid states and a phase transition. Our results resolve a long-standing debate concerning the existence of a liquid-liquid transition in supercooled liquid silicon and address key questions regarding the nature of the phase transition and the associated critical point.

Metastability as a Mechanism for Yielding in Amorphous Solids under Cyclic Shear.

We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a threshold energy and yield strain, suggesting thereby an appealing approach to understanding fatigue failure.

Thermodynamics and kinetics of crystallization in deeply supercooled Stillinger-Weber silicon.

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three-body potential. The free energy barriers to crystallization are computed using umbrella sampling Monte Carlo simulations and from unconstrained molecular dynamics simulations using a mean first passage time formulation. We focus on state points that have been described in earlier work [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)] as straddling a liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys. 117, 3254 (2019)] that the apparent transition is due to the loss of metastability of the liquid state with respect to the crystalline state. The presence of a barrier to crystallization for these state points is therefore of importance to ascertain, which we investigate, with due attention to ambiguities that may arise from the choice of order parameters. We find a well-defined free energy barrier to crystallization and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallization, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallization at other state points over a broad range of temperatures and pressures and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

Spatial Dimensionality Dependence of Heterogeneity, Breakdown of the Stokes-Einstein Relation, and Fragility of a Model Glass-Forming Liquid.

We investigate the heterogeneity of dynamics, the breakdown of the Stokes-Einstein relation and fragility in a model glass forming liquid, a binary mixture of soft spheres with a harmonic interaction potential for spatial dimensions from 3 to 8. The dynamical heterogeneity is quantified through the dynamical susceptibility χ4 and the non-Gaussian parameter α2. We find that the fragility, the degree of breakdown of the Stokes-Einstein relation, and the heterogeneity of the dynamics decrease with increasing spatial dimensionality. We briefly describe the dependence of fragility on the density and use it to resolve an apparent inconsistency with previous results.

Topology of the energy landscape of sheared amorphous solids and the irreversibility transition.

Recent experiments and simulations of amorphous solids plastically deformed by an oscillatory drive have found a surprising behavior-for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit cycles in which plastic events repeat indefinitely under the oscillatory drive. It was also found that reaching reversible limit cycles can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again and are thus irreversible. Using a graph representation of the stable configurations of the system and the plastic events connecting them, we show that the notion of reversibility in these systems is more subtle. We find that reversible plastic events are abundant and that a large portion of the plastic events encountered during the transient period are actually reversible in the sense that they can be part of a reversible deformation path. More specifically, we observe that the transition graph can be decomposed into clusters of configurations that are connected by reversible transitions. These clusters are the strongly connected components of the transition graph and their sizes turn out to be power-law distributed. The largest of these are grouped in regions of reversibility, which in turn are confined by regions of irreversibility whose number proliferates at larger strains. Our results provide an explanation for the irreversibility transition-the divergence of the transient period at a critical forcing amplitude. The long transients result from transition between clusters of reversibility in a search for a cluster large enough to contain a limit cycle of a specific amplitude. For large enough amplitudes, the search time becomes very large, since the sizes of the limit cycles become incompatible with the sizes of the regions of reversibility.

Models for the Yielding Behavior of Amorphous Solids.

Investigations of plastic deformation and yielding of amorphous solids reveal a strong dependence of their yielding behavior on the degree of annealing. Above a threshold degree of annealing, the nature of yielding changes qualitatively, becoming progressively more discontinuous. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on uniform deformation, but cyclic deformation reveals intriguing features that remain uninvestigated. Focusing on athermal cyclic deformation, I investigate a family of models, which reproduce key features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.

Dimensionality dependence of the Kauzmann temperature: A case study using bulk and confined water.

The Kauzmann temperature (TK) of a supercooled liquid is defined as the temperature at which the liquid entropy becomes equal to that of the crystal. The excess entropy, the difference between liquid and crystal entropies, is routinely used as a measure of the configurational entropy, whose vanishing signals the thermodynamic glass transition. The existence of the thermodynamic glass transition is a widely studied subject, and of particular recent interest is the role of dimensionality in determining the presence of a glass transition at a finite temperature. The glass transition in water has been investigated intensely and is challenging as the experimental glass transition appears to occur at a temperature where the metastable liquid is strongly prone to crystallization and is not stable. To understand the dimensionality dependence of the Kauzmann temperature in water, we study computationally bulk water (three-dimensions), water confined in the slit pore of the graphene sheet (two-dimensions), and water confined in the pore of the carbon nanotube of chirality (11,11) having a diameter of 14.9 Å (one-dimension), which is the lowest diameter where amorphous water does not always crystallize into nanotube ice in the supercooled region. Using molecular dynamics simulations, we compute the entropy of water in bulk and under reduced dimensional nanoscale confinement to investigate the variation of the Kauzmann temperature with dimension. We obtain a value of TK (133 K) for bulk water in good agreement with experiments [136 K (C. A. Angell, Science 319, 582-587 (2008) and K. Amann-Winkel et al., Proc. Natl. Acad. Sci. U. S. A. 110, 17720-17725 (2013)]. However, for confined water, in two-dimensions and one-dimension, we find that there is no finite temperature Kauzmann point (in other words, the Kauzmann temperature is 0 K). Analysis of the fluidicity factor, a measure of anharmonicity in the oscillation of normal modes, reveals that the Kauzmann temperature can also be computed from the difference in the fluidicity factor between amorphous and ice phases.