Local Dynamical Heterogeneity in Simple Glass Formers.

We study the local dynamical fluctuations in glass-forming models of particles embedded in d-dimensional space, in the mean-field limit of d→∞. Our analytical calculation reveals that single-particle observables, such as squared particle displacements, display divergent fluctuations around the dynamical (or mode-coupling) transition, due to the emergence of nontrivial correlations between displacements along different directions. This effect notably gives rise to a divergent non-Gaussian parameter, α_{2}. The d→∞ local dynamics therefore becomes quite rich upon approaching the glass transition. The finite-d remnant of this phenomenon further provides a long sought-after, first-principle explanation for the growth of α_{2} around the glass transition that is not based on multiparticle correlations.

Communication: Weakening the critical dynamical slowing down of models with SALR interactions.

In systems with frustration, the critical slowing down of the dynamics severely impedes the numerical study of phase transitions for even the simplest of lattice models. In order to help sidestep the gelation-like sluggishness, a clearer understanding of the underlying physics is needed. Here, we first obtain generic insight into that phenomenon by studying one-dimensional and Bethe lattice versions of a schematic frustrated model, the axial next-nearest neighbor Ising (ANNNI) model. Based on these findings, we formulate two cluster algorithms that speed up the simulations of the ANNNI model on a 2D square lattice. Although these schemes do not eliminate the critical slowing own, speed-ups of factors up to 40 are achieved in some regimes.

The dimensional evolution of structure and dynamics in hard sphere liquids.

The formulation of the mean-field infinite-dimensional solution of hard sphere glasses is a significant milestone for theoretical physics. How relevant this description might be for understanding low-dimensional glass-forming liquids, however, remains unclear. These liquids indeed exhibit a complex interplay between structure and dynamics, and the importance of this interplay might only slowly diminish as dimension d increases. A careful numerical assessment of the matter has long been hindered by the exponential increase in computational costs with d. By revisiting a once common simulation technique involving the use of periodic boundary conditions modeled on Dd lattices, we here partly sidestep this difficulty, thus allowing the study of hard sphere liquids up to d = 13. Parallel efforts by Mangeat and Zamponi [Phys. Rev. E 93, 012609 (2016)] have expanded the mean-field description of glasses to finite d by leveraging the standard liquid-state theory and, thus, help bridge the gap from the other direction. The relatively smooth evolution of both the structure and dynamics across the d gap allows us to relate the two approaches and to identify some of the missing features that a finite-d theory of glasses might hope to include to achieve near quantitative agreement.

Memory Formation in Jammed Hard Spheres.

Liquids equilibrated below an onset condition share similar inherent states, while those above that onset have inherent states that markedly differ. Although this type of materials memory was first reported in simulations over 20 years ago, its physical origin remains controversial. Its absence from mean-field descriptions, in particular, has long cast doubt on its thermodynamic relevance. Motivated by a recent theoretical proposal, we reassess the onset phenomenology in simulations using a fast hard sphere jamming algorithm and find it to be both thermodynamically and dimensionally robust. Remarkably, we also uncover a second type of memory associated with a Gardner-like regime of the jamming algorithm.

Thermodynamic stability of hard sphere crystals in dimensions 3 through 10.

Although much is known about the metastable liquid branch of hard spheres-from low dimension d up to [Formula: see text]-its crystal counterpart remains largely unexplored for [Formula: see text]. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to [Formula: see text], and the dimensional trends suggest that crystal stability likely persists well beyond that point.

Solution of disordered microphases in the Bethe approximation.

The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive (SALR) interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features. Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, and between glassiness and microphase ordering.

Characterization and efficient Monte Carlo sampling of disordered microphases.

The disordered microphases that develop in the high-temperature phase of systems with competing short-range attractive and long-range repulsive (SALR) interactions result in a rich array of distinct morphologies, such as cluster, void cluster, and percolated (gel-like) fluids. These different structural regimes exhibit complex relaxation dynamics with marked heterogeneity and slowdown. The overall relationship between these structures and configurational sampling schemes, however, remains largely uncharted. Here, the disordered microphases of a schematic SALR model are thoroughly characterized, and structural relaxation functions adapted to each regime are devised. The sampling efficiency of various advanced Monte Carlo sampling schemes-Virtual-Move (VMMC), Aggregation-Volume-Bias (AVBMC), and Event-Chain (ECMC)-is then assessed. A combination of VMMC and AVBMC is found to be computationally most efficient for cluster fluids and ECMC to become relatively more efficient as density increases. These results offer a complete description of the equilibrium disordered phase of a simple microphase former as well as dynamical benchmarks for other sampling schemes.

Finite Dimensional Vestige of Spinodal Criticality above the Dynamical Glass Transition.

Finite dimensional signatures of spinodal criticality are notoriously difficult to come by. The dynamical transition of glass-forming liquids, first described by mode-coupling theory, is a spinodal instability preempted by thermally activated processes that also limit how close the instability can be approached. We combine numerical tools to directly observe vestiges of the spinodal criticality in finite dimensional glass formers. We use the swap Monte Carlo algorithm to efficiently thermalize configurations beyond the mode-coupling crossover, and analyze their dynamics using a scheme to screen out activated processes, in spatial dimensions ranging from d=3 to d=10. We observe a strong softening of the mean-field square-root singularity in d=3 that is progressively restored as d increases above d=8, in surprisingly good agreement with perturbation theory.

Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling.

Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, because of the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally relevant timescales. In this work, we not only close the colossal gap between experiments and simulations but manage to create in silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.

Temperature-Dependent Interactions Explain Normal and Inverted Solubility in a γD-Crystallin Mutant.

Protein crystal production is a major bottleneck in the structural characterization of proteins. To advance beyond large-scale screening, rational strategies for protein crystallization are crucial. Understanding how chemical anisotropy (or patchiness) of the protein surface, due to the variety of amino-acid side chains in contact with solvent, contributes to protein-protein contact formation in the crystal lattice is a major obstacle to predicting and optimizing crystallization. The relative scarcity of sophisticated theoretical models that include sufficient detail to link collective behavior, captured in protein phase diagrams, and molecular-level details, determined from high-resolution structural information, is a further barrier. Here, we present two crystal structures for the P23T + R36S mutant of γD-crystallin, each with opposite solubility behavior: one melts when heated, the other when cooled. When combined with the protein phase diagram and a tailored patchy particle model, we show that a single temperature-dependent interaction is sufficient to stabilize the inverted solubility crystal. This contact, at the P23T substitution site, relates to a genetic cataract and reveals at a molecular level the origin of the lowered and retrograde solubility of the protein. Our results show that the approach employed here may present a productive strategy for the rationalization of protein crystallization.

Front-Mediated Melting of Isotropic Ultrastable Glasses.

Ultrastable vapor-deposited glasses display uncommon material properties. Most remarkably, upon heating they are believed to melt via a liquid front that originates at the free surface and propagates over a mesoscopic crossover length, before crossing over to bulk melting. We combine swap Monte Carlo with molecular dynamics simulations to prepare and melt isotropic amorphous films of unprecedendtly high kinetic stability. We are able to directly observe both bulk and front melting, and the crossover between them. We measure the front velocity over a broad range of conditions, and a crossover length scale that grows to nearly 400 particle diameters in the regime accessible to simulations. Our results disentangle the relative roles of kinetic stability and vapor deposition in the physical properties of stable glasses.

Gardner physics in amorphous solids and beyond.

One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain mean-field spin glass models, its materials relevance was only realized when a systematic effort to relate glass formation and jamming was undertaken. A number of nontrivial physical signatures associated with the Gardner transition have since been considered in various areas, from models of structural glasses to constraint satisfaction problems. This perspective surveys these recent advances and discusses the novel research opportunities that arise from them.

Growing timescales and lengthscales characterizing vibrations of amorphous solids.

Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye's theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions, displaying enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (i.e., a boson peak), and complex irreversible responses to small mechanical deformations. These experimental observations indirectly suggest that the dynamics of amorphous solids becomes anomalous at low temperatures. Here, we present direct numerical evidence that vibrations change nature at a well-defined location deep inside the glass phase of a simple glass former. We provide a real-space description of this transition and of the rapidly growing time- and lengthscales that accompany it. Our results provide the seed for a universal understanding of low-temperature glass anomalies within the theoretical framework of the recently discovered Gardner phase transition.

Clustering and assembly dynamics of a one-dimensional microphase former.

Both ordered and disordered microphases ubiquitously form in suspensions of particles that interact through competing short-range attraction and long-range repulsion (SALR). While ordered microphases are more appealing materials targets, understanding the rich structural and dynamical properties of their disordered counterparts is essential to controlling their mesoscale assembly. Here, we study the disordered regime of a one-dimensional (1D) SALR model, whose simplicity enables detailed analysis by transfer matrices and Monte Carlo simulations. We first characterize the signature of the clustering process on macroscopic observables, and then assess the equilibration dynamics of various simulation algorithms. We notably find that cluster moves markedly accelerate the mixing time, but that event chains are of limited help in the clustering regime. These insights will inspire further study of three-dimensional microphase formers.

A microscopic model of the Stokes-Einstein relation in arbitrary dimension.

The Stokes-Einstein relation (SER) is one of the most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for self-solvation, which cannot be explained by the standard hydrodynamic derivation. Here, we revisit the work of Masters and Madden [J. Chem. Phys. 74, 2450-2459 (1981)], who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents, we identify a potential microscopic origin of some of these deviations. We also reproduce the SER-like result from the exact dynamics of infinite-dimensional fluids.

Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions.

The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon-the Gardner transition-has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_{u}=6. Here, we obtain evidence for the existence of these transitions in d

Origin of Ultrastability in Vapor-Deposited Glasses.

Glass films created by vapor-depositing molecules onto a substrate can exhibit properties similar to those of ordinary glasses aged for thousands of years. It is believed that enhanced surface mobility is the mechanism that allows vapor deposition to create such exceptional glasses, but it is unclear how this effect is related to the final state of the film. Here we use molecular dynamics simulations to model vapor deposition and an efficient Monte Carlo algorithm to determine the deposition rate needed to create ultrastable glassy films. We obtain a scaling relation that quantitatively captures the efficiency gain of vapor deposition over bulk annealing, and demonstrates that surface relaxation plays the same role in the formation of vapor-deposited glasses as bulk relaxation does in ordinary glass formation.

Assembly of hard spheres in a cylinder: a computational and experimental study.

Hard spheres are an important benchmark of our understanding of natural and synthetic systems. In this work, colloidal experiments and Monte Carlo simulations examine the equilibrium and out-of-equilibrium assembly of hard spheres of diameter σ within cylinders of diameter σ≤D≤ 2.82σ. Although phase transitions formally do not exist in such systems, marked structural crossovers can nonetheless be observed. Over this range of D, we find in simulations that structural crossovers echo the structural changes in the sequence of densest packings. We also observe that the out-of-equilibrium self-assembly depends on the compression rate. Slow compression approximates equilibrium results, while fast compression can skip intermediate structures. Crossovers for which no continuous line-slip exists are found to be dynamically unfavorable, which is the main source of this difference. Results from colloidal sedimentation experiments at low diffusion rate are found to be consistent with the results of fast compressions, as long as appropriate boundary conditions are used.

Communication: Microphase equilibrium and assembly dynamics.

Despite many attempts, ordered equilibrium microphases have yet to be obtained in experimental colloidal suspensions. The recent computation of the equilibrium phase diagram of a microscopic, particle-based microphase former [Zhuang et al., Phys. Rev. Lett. 116, 098301 (2016)] has nonetheless found such mesoscale assemblies to be thermodynamically stable. Here, we consider their equilibrium and assembly dynamics. At intermediate densities above the order-disorder transition, we identify four different dynamical regimes and the structural changes that underlie the dynamical crossovers from one disordered regime to the next. Below the order-disorder transition, we also find that periodic lamellae are the most dynamically accessible of the periodic microphases. Our analysis thus offers a comprehensive view of the dynamics of disordered microphases and a route to the assembly of periodic microphases in a putative well-controlled, experimental system.