Local order and crystallization of dense polydisperse hard spheres

Emerging exotic compositional order on approaching low-temperature equilibrium glasses

The ultimate fate of a glass former upon cooling has been a fundamental problem in condensed matter physics and materials science since Kauzmann. Recently, this problem has been challenged by a model with an extraordinary glass-forming ability effectively free from crystallisation and phase separation, two well-known fates of most glass formers, combined with a particle-size swap method. Thus, this system is expected to approach the ideal glass state if it exists. However, we discover exotic compositional order as the coexistence of space-spanning network-like structures formed by small-large particle connections and patches formed by medium-size particles at low temperatures. Therefore, the glass transition is accompanied unexpectedly by exotic compositional ordering inaccessible through ordinary structural or thermodynamic characterisations. Such exotic compositional ordering is found to have an unusual impact on structural relaxation dynamics. Our study thus raises fundamental questions concerning the role of unconventional structural ordering in understanding glass transition.

Dynamic heterogeneity in polydisperse systems: A comparative study of the role of local structural order parameter and particle size

In polydisperse systems, describing the structure and any structural order parameter (SOP) is not trivial as it varies with the number of species we use to describe the system, M. Depending on the degree of polydispersity, there is an optimum value of M = M0 where we show that the mutual information of the system increases. However, surprisingly, the correlation between a recently proposed SOP and the dynamics is highest for M = 1. This effect increases with polydispersity. We find that the SOP at M = 1 is coupled with the particle size, σ, and this coupling increases with polydispersity and decreases with an increase in M. Careful analysis shows that at lower polydispersities, the SOP is a good predictor of the dynamics. However, at higher polydispersity, the dynamics is strongly dependent on σ. Since the coupling between the SOP and σ is higher for M = 1, it appears to be a better predictor of the dynamics. We also study the Vibrality, an order parameter independent of structural information. Compared to SOP, at high polydispersity, we find Vibrality to be a marginally better predictor of the dynamics. However, this high predictive power of Vibrality, which is not there at lower polydispersity, appears to be due to its stronger coupling with σ. Therefore, our study suggests that for systems with high polydispersity, the correlation of any order parameter and σ will affect the correlation between the order parameter and dynamics and need not project a generic predictive power of the order parameter.

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote-and, in some cases, may be necessary for-the self-assembly of a binary cocrystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of nearly hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.

Glassy Behavior of Sticky Spheres: What Lies beyond Experimental Timescales?

We use the swap Monte Carlo algorithm to analyze the glassy behavior of sticky spheres in equilibrium conditions at densities where conventional simulations and experiments fail to reach equilibrium, beyond predicted phase transitions and dynamic singularities. We demonstrate the existence of a unique ergodic region comprising all the distinct phases previously reported, except for a phase-separated region at strong adhesion. All structural and dynamic observables evolve gradually within this ergodic region, the physics evolving smoothly from well-known hard sphere glassy behavior at small adhesions and large densities, to a more complex glassy regime characterized by unusually broad distributions of relaxation timescales and length scales at large adhesions.

Spontaneous Crystallization in Systems of Binary Hard Sphere Colloids

Computer simulations of the fluid-to-solid phase transition in the hard sphere system were instrumental for our understanding of crystallization processes. But while colloid experiments and theory have been predicting the stability of several binary hard sphere crystals for many years, simulations were not successful to confirm this phenomenon. Here, we report the growth of binary hard sphere crystals isostructural to Laves phases, AlB_{2}, and NaZn_{13} in simulation directly from the fluid. We analyze particle kinetics during Laves phase growth using event-driven molecular dynamics simulations with and without swap moves that speed up diffusion. The crystallization process transitions from nucleation and growth to spinodal decomposition already deep within the fluid-solid coexistence regime. Finally, we present packing fraction-size ratio state diagrams in the vicinity of the stability regions of three binary crystals.

Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters

Monte Carlo simulations, fully constrained by experimental parameters, are found to agree well with a measured phase diagram of aqueous dispersions of nanoparticles with a moderate size polydispersity over a broad range of salt concentrations, c_{s}, and volume fractions, ϕ. Upon increasing ϕ, the colloids freeze first into coexisting compact solids then into a body centered cubic phase (bcc) before they melt into a glass forming liquid. The surprising stability of the bcc solid at high ϕ and c_{s} is explained by the interaction (charge) polydispersity and vibrational entropy.

Configurational entropy of glass-forming liquids

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraught with difficulties, misconceptions, and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, nonambiguous, and experimentally relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.

Complex Crystals from Size-Disperse Spheres

Colloids are rarely perfectly uniform but follow a distribution of sizes, shapes, and charges. This dispersity can be inherent (static) or develop and change over time (dynamic). Despite a long history of research, the conditions under which nonuniform particles crystallize and which crystal forms is still not well understood. Here, we demonstrate that hard spheres with Gaussian radius distribution and dispersity up to 19% always crystallize if compressed slowly enough, and they do so in surprisingly complex ways. This result is obtained by accelerating event-driven simulations with particle swap moves for static dispersity and particle resize moves for dynamic dispersity. Above 6% dispersity, AB_{2} Laves, AB_{13}, and a region of Frank-Kasper phases are found. The Frank-Kasper region includes a quasicrystal approximant with Pearson symbol oS276. Our findings are relevant for ordering phenomena in soft matter and alloys.

Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions

The recent implementation of a swap Monte Carlo algorithm (SWAP) for polydisperse glass forming mixtures bypasses computational sluggishness and closes the gap between experimental and simulation timescales in physical dimensions d=2 and 3. Here, we consider suitably optimized systems in d=2,3,⋯,8 to obtain insights into the performance and underlying physics of SWAP. We show that the speedup obtained decays rapidly with increasing the dimension. SWAP nonetheless delays systematically the onset of the activated dynamics by an amount that remains seemingly finite in the limit d→∞. This shows that the glassy dynamics in high dimensions d>3 is now computationally accessible using SWAP, thus opening the door for the systematic consideration of finite-dimensional deviations from the mean-field description.

Morphometric Approach to Many-Body Correlations in Hard Spheres

We model the thermodynamics of local structures within the hard sphere liquid at arbitrary volume fractions through the morphometric calculation of n-body correlations. We calculate absolute free energies of local geometric motifs in excellent quantitative agreement with molecular dynamics simulations across the liquid and supercooled liquid regimes. We find a bimodality in the density library of states where fivefold symmetric structures appear lower in free energy than fourfold symmetric structures and from a single reaction path predict a dynamical barrier which scales linearly in the compressibility factor. The method provides a new route to assess changes in the free energy landscape at volume fractions dynamically inaccessible to conventional techniques.