Structural origin of dynamic heterogeneity in three-dimensional colloidal glass formers and its link to crystal nucleation

Is icosahedral short-range order presented in supercooled transition metals?

Supercooled transition metals are characterized by the absence of long-range order and the presence of a specific short-range order in the arrangement of atoms. So, the presence of shoulders and broadenings at the second maximum in the experimentally measured quantity-in the static structure factorS(k)-is usually interpreted as a manifestation of the icosahedral (ideal or distorted) short-range order (ISRO-Icosahedral Short-Range Order). Icosahedral short-range order is a structure with fivefold symmetry in the arrangement of atoms, which can lead to the possibility of achieving deep supercooling. In this work, we study the local structural features of equilibrium and supercooled nickel melts under various cooling protocols (γ∈1010,1014 K s^-1) in order to clarify the mechanism of formation of the icosahedral short-range order in pure transition metals. Comprehensive studies of the properties of nickel melts were carried out using experiments on x-ray diffraction, large-scale molecular dynamics (MD) simulations with subsequent structural and cluster analysis. A good agreement was found between the results of x-ray diffraction data and the MD simulations results for an equilibrium nickel melt. It was found that the nickel melt is characterized by a short-range order, formed by fragments of icosahedra and distorted icosahedral clusters. It was revealed that the 'liquid-crystal' phase transition in nickel is accompanied by the transformation of distorted icosahedral clusters into clusters with thefcc/hcp-symmetry. It is shown that, in contrast to the Voronoi tessellation method, the cluster analysis method based on the (q4,q6) rotational invariants does not allow sufficiently correct identification of the distorted icosahedral short-range order in metal melts.

Translation-rotation decoupling of tracers reflects medium-range crystalline order in two-dimensional colloid glasses

The dynamic heterogeneity and the translation-rotation decoupling are the dynamic signatures of glasses and supercooled liquids. Whether and how the dynamic heterogeneity would relate to the local structure of glasses has been a puzzle for decades. In this work we perform molecular dynamics simulations for tracers in both two-dimensional polydisperse colloids (2DPC) and two-dimensional binary colloids (2DBC). In 2DPC glasses, hexatic local structures develop at low enough temperatures and grow quickly along with the dynamic correlation length of the 2DPC, which is well known as the medium-range crystalline order (MRCO). In 2DBC glasses, on the other hand, any explicit local structure has not been reported to grow significantly with the dynamic correlation length at low temperatures. We introduce two different types of tracers into colloidal systems: A diamond tracer that resembles the MRCO of 2DPC glasses and a square tracer that is dissimilar to any local structure of glasses. The translation-rotation decoupling of the diamond tracer in 2DPC glasses is much more significant than that of the square tracer in the same 2DPC glasses. On the other hand, such a tracer shape-dependence of the decoupling is not observed in 2DBC glasses where the local hexatic structure does not develop significantly. We introduce a shape-dependency parameter of the decoupling and find that the shape-dependency parameter grows along with the dynamic correlation length in 2DPC glasses but not in 2DBC glasses. This illustrates that the dynamic heterogeneity and the translation-rotation decoupling of tracers could reveal the local structure that develops in glasses.

Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is vital for the prediction and characterization of yield and the study of how memory is stored in disordered materials. Here, we investigate the evolution of local structural homogeneity on an individual particle level in amorphous jammed two-dimensional (athermal) systems under oscillatory shear and relate this evolution to rearrangement, memory, and macroscale rheological measurements. We define the structural metric crystalline shielding, and show that it is predictive of rearrangement propensity and structural volatility of individual particles under shear. We use this metric to identify localized regions of the system in which the material's memory of its preparation is preserved. Our results contribute to a growing understanding of how local structure relates to dynamic response and memory in disordered systems.

Connecting relaxation time to a dynamical length scale in athermal active glass formers

Supercooled liquids display dynamics that are inherently heterogeneous in space. This essentially means that at temperatures below the melting point, particle dynamics in certain regions of the liquid can be orders of magnitude faster than other regions. Often dubbed dynamical heterogeneity, this behavior has fascinated researchers involved in the study of glass transition for over two decades. A fundamentally important question in all glass transition studies is whether one can connect the growing relaxation time to a concomitantly growing length scale. In this paper, we go beyond the realm of ordinary glass forming liquids and study the origin of a growing dynamical length scale ξ in a self-propelled "active" glass former. This length scale, which is constructed using structural correlations, agrees well with the average size of the clusters of slow-moving particles that are formed as the liquid becomes spatially heterogeneous. We further report that the concomitantly growing α-relaxation time exhibits a simple scaling law, τ_{α}∼exp(μξ/T_{eff}), with μ as an effective chemical potential, T_{eff} as the effective temperature, and μξ as the growing free energy barrier for cluster rearrangements. The findings of our study are valid over four decades of persistence times, and hence they could be very useful in understanding the slow dynamics of a generic active liquid such as an active colloidal suspension, or a self-propelled granular medium.

Pathway of orientational symmetry breaking in crystallization of short n-alkane droplets: A molecular dynamics study

We carry out molecular dynamics simulations by using an all-atom model to study the nucleation and crystallization of n-alkane droplets under three-dimensional and quasi-two-dimensional conditions. We focus on the development of orientational order of chains from a random state to a neatly ordered one. Two new methods, the map of symmetry breaking and the information entropy of chain orientations, are introduced to characterize the emerge and remelting phenomena of a primary nucleus at the early stage of crystallization. Stepwise nucleation, as well as the surface induced nucleation, of large droplets is observed. We elucidate the kinetic process of the formation of a primary nucleus and the rearrangement of every single molecule involved in a primary nucleus. We found that density fluctuation and orientational preordering are coupled together and occur simultaneously in nucleation. Our results show the pathway of orientational symmetry breaking in the crystallization of n-alkane droplets that are heuristic for the deeper understanding of the crystallization in more complex molecules such as polymers.

Influence of Hydrodynamic Interactions on Colloidal Crystallization

One of the biggest unresolved problems in crystallization phenomena is the significant discrepancy in the nucleation rate between experiments and simulations even for the simplest liquid, i.e., the hard-sphere system. A popular explanation for this discrepancy is the neglect of hydrodynamic interactions (HI) in simulation studies. By comparing simulations with and without HI, we show that the long-time diffusive dynamics of the colloids is slowed down more rapidly by hydrodynamic lubrication effects with increasing volume fraction. We find that the kinetics of both nucleation and growth are controlled by this long-time diffusion and that it is possible to account for most of the effects of HI by rescaling with this timescale. Therefore, we conclude that HI is not the primary cause of the accelerated nucleation rates observed in experiments.

Identity crisis in alchemical space drives the entropic colloidal glass transition

A universally accepted explanation for why liquids sometimes vitrify rather than crystallize remains hotly pursued, despite the ubiquity of glass in our everyday lives, the utilization of the glass transition in innumerable modern technologies, and nearly a century of theoretical and experimental investigation. Among the most compelling hypothesized mechanisms underlying glass formation is the development in the fluid phase of local structures that somehow prevent crystallization. Here, we explore that mechanism in the case of hard particle glasses by examining the glass transition in an extended alchemical (here, shape) space; that is, a space where particle shape is treated as a thermodynamic variable. We investigate simple systems of hard polyhedra, with no interactions aside from volume exclusion, and show via Monte Carlo simulation that glass formation in these systems arises from a multiplicity of competing local motifs, each of which is prevalent in-and predictable from-nearby ordered structures in alchemical space.

Apparent strength versus universality in glasses of soft compressible colloids

Microgel colloids, solvent swollen hydrogel particles of microscopic size, are in osmotic equilibrium with their surroundings. This has a profound effect on the behaviour of dense solutions of these polymeric colloids, most notably their ability to swell and deswell depending on the osmotic pressure of the system as a whole. Here we develop a minimal simulation model to treat this intrinsic volume regulation in order to explore the effects this has on the properties of dense solutions close to a liquid-solid transition. We demonstrate how the softness dependent volume regulation of particles gives rise to an apparent change in the fragility of the colloidal glass transition, which can be scaled out through the use of an adjusted volume fraction that accounts for changes in particle size. Moreover, we show how the same model can be used to explain the selective deswelling of soft microgels in a crystalline matrix of harder particles leading to robust crystals free of defects. Our results not only highlight the non-trivial effects of osmotic regulation in governing the apparent physics of microgel suspensions, but also provides a platform to efficiently account for particle deswelling in simulations.

The race to the bottom: approaching the ideal glass?

Key to resolving the scientific challenge of the glass transition is to understand the origin of the massive increase in viscosity of liquids cooled below their melting temperature (avoiding crystallisation). A number of competing and often mutually exclusive theoretical approaches have been advanced to describe this phenomenon. Some posit a bona fide thermodynamic phase to an 'ideal glass', an amorphous state with exceptionally low entropy. Other approaches are built around the concept of the glass transition as a primarily dynamic phenomenon. These fundamentally different interpretations give equally good descriptions of the data available, so it is hard to determine which-if any-is correct. Recently however this situation has begun to change. A consensus has emerged that one powerful means to resolve this longstanding question is to approach the putative thermodynamic transition sufficiently closely, and a number of techniques have emerged to meet this challenge. Here we review the results of some of these new techniques and discuss the implications for the existence-or otherwise-of the thermodynamic transition to an ideal glass.

Glass forming phase diagram and local structure of Kob-Andersen binary Lennard-Jones nanoparticles

Molecular dynamics simulation is used to study glass formation in Kob-Andersen binary Lennard-Jones nanoparticles and determine the glass forming phase diagram for the system as a function of composition. The radial distribution function, a Steinhardt bond-orientational order parameter, and favored local structure analysis are used to distinguish between glassy and ordered systems. We find that surface enrichment of the large atoms alters the nanoparticle core composition, leading to an overall shift of the glass forming region to lower small atom mole fractions, relative to the bulk system. At small atom mole fraction, x_B = 0.1, the nanoparticles form a solid with an amorphous core, enriched with the small atoms, surrounded by a partially ordered surface region, enriched with the large atom component. The most disordered glass nanoparticles occur at x_B ≈ 0.3, but the surface-core enrichment leads to the crystallization of the nanoparticle to the CsCl crystal above x_B ≈ 0.35, which is lower than observed in the bulk. The glass transition temperatures of the nanoparticles are also significantly reduced. This allows the liquid to remain dynamic to low temperatures and sample the low energy inherent structure minima on the potential energy surface containing a high abundance of favoured local structures.

Glass Transition in Supercooled Liquids with Medium-Range Crystalline Order

The origin of the rapid dynamical slowdown in glass forming liquids in the growth of static length scales, possibly associated with identifiable structural ordering, is a much debated issue. Growth of medium range crystalline order (MRCO) has been observed in various model systems to be associated with glassy behavior. Such observations raise the question of whether molecular mechanisms for the glass transition in liquids with and without MRCO are the same. In this study we perform extensive molecular dynamics simulations of a number of glass forming liquids and show that the static and dynamic properties of glasses with MRCO are different from those of other glass forming liquids with no predominant local order. We also resolve an important issue regarding the so-called point-to-set method for determining static length scales, and demonstrate it to be a robust method for determining static correlation lengths in glass formers.

Universal glass-forming behavior of in vitro and living cytoplasm

Physiological processes in cells are performed efficiently without getting jammed although cytoplasm is highly crowded with various macromolecules. Elucidating the physical machinery is challenging because the interior of a cell is so complex and driven far from equilibrium by metabolic activities. Here, we studied the mechanics of in vitro and living cytoplasm using the particle-tracking and manipulation technique. The molecular crowding effect on cytoplasmic mechanics was selectively studied by preparing simple in vitro models of cytoplasm from which both the metabolism and cytoskeletons were removed. We obtained direct evidence of the cytoplasmic glass transition; a dramatic increase in viscosity upon crowding quantitatively conformed to the super-Arrhenius formula, which is typical for fragile colloidal suspensions close to jamming. Furthermore, the glass-forming behaviors were found to be universally conserved in all the cytoplasm samples that originated from different species and developmental stages; they showed the same tendency for diverging at the macromolecule concentrations relevant for living cells. Notably, such fragile behavior disappeared in metabolically active living cells whose viscosity showed a genuine Arrhenius increase as in typical strong glass formers. Being actively driven by metabolism, the living cytoplasm forms glass that is fundamentally different from that of its non-living counterpart.

Common mechanism of thermodynamic and mechanical origin for ageing and crystallization of glasses

The glassy state is known to undergo slow structural relaxation, where the system progressively explores lower free-energy minima which are either amorphous (ageing) or crystalline (devitrification). Recently, there is growing interest in the unusual intermittent collective displacements of a large number of particles known as ‘avalanches’. However, their structural origin and dynamics are yet to be fully addressed. Here, we study hard-sphere glasses which either crystallize or age depending on the degree of size polydispersity, and show that a small number of particles are thermodynamically driven to rearrange in regions of low density and bond orientational order. This causes a transient loss of mechanical equilibrium which facilitates a large cascade of motion. Combined with previously identified phenomenology, we have a complete kinetic pathway for structural change which is common to both ageing and crystallization. Furthermore, this suggests that transient force balance is what distinguishes glasses from supercooled liquids.

Glass is characterized by stochastic and slow structural relaxation dynamics, whose details remain elusive due to its complicated kinetic processes. Here, the authors show that avalanche-like dynamics in both ageing and devitrifying glasses are governed by thermodynamic initiation and a transient loss in mechanical stability.

Seeding approach to crystal nucleation

We present a study of homogeneous crystal nucleation from metastable fluids via the seeding technique for four different systems: mW water, Tosi-Fumi NaCl, Lennard-Jones, and Hard Spheres. Combining simulations of spherical crystal seeds embedded in the metastable fluid with classical nucleation theory, we are able to successfully describe the nucleation rate for all systems in a wide range of metastability. The crystal-fluid interfacial free energy extrapolated to coexistence conditions is also in good agreement with direct calculations of such parameter. Our results show that seeding is a powerful technique to investigate crystal nucleation.

Structures and Dynamics of Glass-Forming Colloidal Liquids under Spherical Confinement

Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of liquid relaxation. The prediction, however, has yet to be verified in 3D experiments. Here, we design a colloidal system, where particles are confined inside spherical cavities with an amorphous layer of particles pinned at the boundary. Using this novel system, we capture the amorphous-order particle clusters and demonstrate the development of a static correlation. Moreover, by investigating the dynamics of spherically confined samples, we reveal a profound influence of the static correlation on the relaxation of colloidal liquids. In analogy to glass-forming liquids with randomly pinned particles, we propose a simple relation for the change of the configurational entropy of confined colloidal liquids, which quantitatively explains our experimental findings and illustrates a divergent static length scale during the colloidal glass transition.

Chiral Ordering in Supercooled Liquid Water and Amorphous Ice

The emergence of homochiral domains in supercooled liquid water is presented using molecular dynamics simulations. An individual water molecule possesses neither a chiral center nor a twisted conformation that can cause spontaneous chiral resolution. However, an aggregation of water molecules will naturally give rise to a collective chirality. Such homochiral domains possess obvious topological and geometrical orders and are energetically more stable than the average. However, homochiral domains cannot grow into macroscopic homogeneous structures due to geometrical frustrations arising from their icosahedral local order. Homochiral domains are the major constituent of supercooled liquid water and the origin of heterogeneity in that substance, and are expected to be enhanced in low-density amorphous ice at lower temperatures.

Collisional statistics and dynamics of two-dimensional hard-disk systems: From fluid to solid

We perform extensive MD simulations of two-dimensional systems of hard disks, focusing on the collisional statistical properties. We analyze the distribution functions of velocity, free flight time, and free path length for packing fractions ranging from the fluid to the solid phase. The behaviors of the mean free flight time and path length between subsequent collisions are found to drastically change in the coexistence phase. We show that single-particle dynamical properties behave analogously in collisional and continuous-time representations, exhibiting apparent crossovers between the fluid and the solid phases. We find that, both in collisional and continuous-time representation, the mean-squared displacement, velocity autocorrelation functions, intermediate scattering functions, and self-part of the van Hove function (propagator) closely reproduce the same behavior exhibited by the corresponding quantities in granular media, colloids, and supercooled liquids close to the glass or jamming transition.

Chromatic patchy particles: Effects of specific interactions on liquid structure

We study the structural and thermodynamic properties of patchy particle liquids, with a special focus on the role of "color," i.e., specific interactions between individual patches. A possible experimental realization of such "chromatic" interactions is by decorating the particle patches with single-stranded DNA linkers. The complementarity of the linkers can promote selective bond formation between predetermined pairs of patches. By using MD simulations, we compare the local connectivity, the bond orientation order, and other structural properties of the aggregates formed by the "colored" and "colorless" systems. The analysis is done for spherical particles with two different patch arrangements (tetrahedral and cubic). It is found that the aggregated (liquid) phase of the "colorless" patchy particles is better connected, denser and typically has stronger local order than the corresponding "colored" one. This, in turn, makes the colored liquid less stable thermodynamically. Specifically, we predict that in a typical case the chromatic interactions should increase the relative stability of the crystalline phase with respect to the disordered liquid, thus expanding its region in the phase diagram.

Correlation between crystalline order and vitrification in colloidal monolayers

We investigate experimentally the relationship between local structure and dynamical arrest in a quasi-2d colloidal model system which approximates hard discs. We introduce polydispersity to the system to suppress crystallisation. Upon compression, the increase in structural relaxation time is accompanied by the emergence of local hexagonal symmetry. Examining the dynamical heterogeneity of the system, we identify three types of motion: 'zero-dimensional' corresponding to β-relaxation, 'one-dimensional' or stringlike motion and '2D' motion. The dynamic heterogeneity is correlated with the local order, that is to say locally hexagonal regions are more likely to be dynamically slow. However, we find that lengthscales corresponding to dynamic heterogeneity and local structure do not appear to scale together approaching the glass transition.

String model for the dynamics of glass-forming liquids

We test the applicability of a living polymerization theory to describe cooperative string-like particle rearrangement clusters (strings) observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combining this theory with the Adam-Gibbs model allows us to predict the relaxation time τ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann "entropy crisis."

Correlated heterogeneous dynamics in glass-forming polymers

We report x-ray photon correlation spectroscopy experiments on the dynamics of the glass-former polypropylene glycol covering a temperature range from room temperature to the glass transition at T(g)=205 K using silica tracer particles. Three temperature regimes are identified: At high temperatures, Brownian motion of the tracer particles is observed. Near T(g), the dynamics is hyperdiffusive and ballistic. Around 1.12T(g), we observe an intermediate regime. Here the stretching exponent of the Kohlrausch-Williams-Watts function becomes q dependent. By analyzing higher-order correlations in the scattering data, we find that dynamical heterogeneities dramatically increase in this intermediate-temperature regime. This leads to two effects: increasing heterogeneous dynamics and correlated motion at temperatures close to and below 1.12T(g).

Mutual information reveals multiple structural relaxation mechanisms in a model glass former

Among the key challenges to our understanding of solidification in the glass transition is that it is accompanied by little apparent change in structure. Recently, geometric motifs have been identified in glassy liquids, but a causal link between these motifs and solidification remains elusive. One 'smoking gun' for such a link would be identical scaling of structural and dynamic lengthscales on approaching the glass transition, but this is highly controversial. Here we introduce an information theoretic approach to determine correlations in displacement for particle relaxation encoded in the initial configuration of a glass-forming liquid. We uncover two populations of particles, one inclined to relax quickly, the other slowly. Each population is correlated with local density and geometric motifs. Our analysis further reveals a dynamic lengthscale similar to that associated with structural properties, which may resolve the discrepancy between structural and dynamic lengthscales.

Detecting orientational order in model systems by X-ray cross-correlation methods

The results of a computational X-ray cross-correlation analysis (XCCA) study on two-dimensional polygonal model structures are presented. This article shows how to detect and identify the orientational order of such systems, demonstrates how to eliminate the influence of the `computational box' on the XCCA results and develops new correlation functions that reflect the sample's orientational order only. For this purpose, the dependence of the correlation functions on the number of polygonal clusters and scattering vector magnitudeqis studied for various types of polygons, including mixtures of polygons and randomly placed particles. An order parameter that describes the orientational order within the sample is defined. Finally, the influence of detector noise and nonplanar wavefronts on the XCCA data is determined, both of which appear to affect the results significantly and have thus to be considered in real experiments.

Structural evolution in the aging process of supercooled colloidal liquids

When a liquid is rapidly quenched to a temperature below the glass-transition point, it is driven out of equilibrium; it then slowly relaxes to a (quasi)equilibrium state. This slow relaxation process is called aging. By definition, any glasses are inevitably in the process of aging and actually slowly evolving with time. Thus the study of aging phenomena is of fundamental importance for understanding not only the nonequilibrium nature of the glass transition, but also the stability of glassy materials. Here we consider aging after a rather shallow quench, for which a system is still able to reach (metastable) equilibrium. By using polydisperse colloidal liquids as a model, we show the validity of dynamical scaling that there is only one relevant length scale not only for a quasiequilibrium supercooled state but also for a nonequilibrium process of aging, which is reminiscent of dynamical critical phenomena. Our finding indicates that the aging toward (metastable) equilibrium may be regarded as the growth process of critical-like fluctuations of static order associated with low-free-energy configurations, further suggesting that this ordering is the origin of cooperative slow dynamics in the systems studied. The generality of this statement for other glass-forming systems remains for a future study.

Avalanches mediate crystallization in a hard-sphere glass

By molecular-dynamics simulations, we have studied the devitrification (or crystallization) of aged hard-sphere glasses. First, we find that the dynamics of the particles are intermittent: Quiescent periods, when the particles simply "rattle" in their nearest-neighbor cages, are interrupted by abrupt "avalanches," where a subset of particles undergo large rearrangements. Second, we find that crystallization is associated with these avalanches but that the connection is not straightforward. The amount of crystal in the system increases during an avalanche, but most of the particles that become crystalline are different from those involved in the avalanche. Third, the occurrence of the avalanches is a largely stochastic process. Randomizing the velocities of the particles at any time during the simulation leads to a different subsequent series of avalanches. The spatial distribution of avalanching particles appears random, although correlations are found among avalanche initiation events. By contrast, we find that crystallization tends to take place in regions that already show incipient local order.

Direct measurement of the free energy of aging hard sphere colloidal glasses

The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however, so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements similar to the Gutenberg-Richter law in seismology.

Generalized bond order parameters to characterize transient crystals

Higher order parameters in the hard disk fluid are computed to investigate the number, the lifetime, and size of transient crystal nuclei in the pre-freezing phase. The methodology introduces further neighbor shells bond orientational order parameters and coarse-grains the correlation functions needed for the evaluation of the stress autocorrelation function for the viscosity. We successfully reproduce results by the previous collision method for the pair orientational correlation function, but some two orders of magnitude faster. This speed-up allows calculating the time dependent four body orientational correlation between two different pairs of particles as a function of their separation, needed to characterize the size of the transient crystals. The result is that the slow decay of the stress autocorrelation function near freezing is due to a large number of rather small crystal nuclei lasting long enough to lead to the molasses tail.

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

The microscopic pathway to crystallization in supercooled liquids

Despite its fundamental and technological importance, a microscopic understanding of the crystallization process is still elusive. By computer simulations of the hard-sphere model we reveal the mechanism by which thermal fluctuations drive the transition from the supercooled liquid state to the crystal state. In particular we show that fluctuations in bond orientational order trigger the nucleation process, contrary to the common belief that the transition is initiated by density fluctuations. Moreover, the analysis of bond orientational fluctuations shows that these not only act as seeds of the nucleation process, but also i) determine the particular polymorph which is to be nucleated from them and ii) at high density favour the formation of fivefold structures which can frustrate the formation of crystals. These results can shed new light on our understanding of the relationship between crystallization and vitrification.

Roles of bond orientational ordering in glass transition and crystallization

It is widely believed that crystallization in three dimensions is primarily controlled by positional ordering, and not by bond orientational ordering. In other words, bond orientational ordering is usually considered to be merely a consequence of positional ordering and thus has often been ignored. This one-order-parameter (density) description may be reasonable when we consider an equilibrium liquid-solid transition, but may not be enough to describe a metastable state and the kinetics of the transition. Here we propose that bond orientational ordering can play a key role in (i) crystallization, (ii) the ordering to quasi-crystal and (iii) vitrification, which occurs under rather weak frustration against crystallization. In a metastable supercooled state before crystallization, a system generally tends to have bond orientational order at least locally as a result of a constraint of dense packing. For a system interacting with hard-core repulsions, the constraint is intrinsically of geometrical origin and thus the basic physics is the same as nematic ordering of rod-like particles upon densification. Furthermore, positional ordering is easily destroyed even by weak frustration such as polydispersity and anisotropic interactions which favour a symmetry not consistent with that of the equilibrium crystal. Thus we may say that vitrification can be achieved by disturbing and prohibiting long-range positional ordering. Even in such a situation, bond orientational ordering still survives, accompanying its critical-like fluctuations, which are the origin of dynamic heterogeneity for this case. This scenario naturally explains both the absence of positional order and the development of bond orientational order upon cooling in a supercooled state. Although our argument is speculative in nature, we emphasize that this physical picture can coherently explain crystallization, vitrification, quasi-crystallization and their relationship in a natural manner. For a strongly frustrated system, even bond orientational order can be destroyed. Even in such a case there may still appear a structural signature of dense packing, which is linked to slow dynamics.

Structural origin of enhanced slow dynamics near a wall in glass-forming systems

Spatial confinement is known to induce a drastic change in the viscosity, relaxation times, and flow profile of liquids near the glass (or jamming) transition point. The essential underlying question is how a wall affects the dynamics of densely packed systems. Here we study this fundamental problem, using experiments on a driven granular hard-sphere liquid and numerical simulations of polydisperse and bidisperse colloidal liquids. The nearly hard-core nature of the particle-wall interaction provides an ideal opportunity to study purely geometrical confinement effects. We reveal that the slower dynamics near a wall is induced by wall-induced enhancement of 'glassy structural order', which is a manifestation of strong interparticle correlations. By generalizing the structure-dynamics relation for bulk systems, we find a quantitative relation between the structural relaxation time at a certain distance from a wall and the correlation length of glassy structural order there. Our finding suggests that glassy structural ordering may be the origin of the slow glassy dynamics of a supercooled liquid.

Crystallization mechanism of hard sphere glasses

In supercooled liquids, vitrification generally suppresses crystallization. Yet some glasses can still crystallize despite the arrest of diffusive motion. This ill-understood process may limit the stability of glasses, but its microscopic mechanism is not yet known. Here we present extensive computer simulations addressing the crystallization of monodisperse hard-sphere glasses at constant volume (as in a colloid experiment). Multiple crystalline patches appear without particles having to diffuse more than one diameter. As these patches grow, the mobility in neighboring areas is enhanced, creating dynamic heterogeneity with positive feedback. The future crystallization pattern cannot be predicted from the coordinates alone: Crystallization proceeds by a sequence of stochastic micronucleation events, correlated in space by emergent dynamic heterogeneity.

Crystallization in suspensions of hard spheres: a Monte Carlo and molecular dynamics simulation study

The crystallization of a metastable melt is one of the most important non-equilibrium phenomena in condensed matter physics, and hard sphere colloidal model systems have been used for several decades to investigate this process by experimental observation and computer simulation. Nevertheless, there is still an unexplained discrepancy between the simulation data and experimental nucleation rate densities. In this paper we examine the nucleation process in hard spheres using molecular dynamics and Monte Carlo simulation. We show that the crystallization process is mediated by precursors of low orientational bond-order and that our simulation data fairly match the experimental data sets.

Structural signature of slow dynamics and dynamic heterogeneity in two-dimensional colloidal liquids: glassy structural order

Glassy states are formed if crystallization is avoided upon cooling or increasing density. However, the physical factors controlling the ease of vitrification and the nature of glass transition remain elusive. Among various glass-forming systems, colloidal liquids are one of the most ideal glass-forming systems because of the simplicity and controllability of the interactions. We use numerical simulations of two-dimensional polydisperse and binary hard discs to tackle both of these longstanding questions. For polydisperse systems, we systematically control the polydispersity, which can be regarded as the strength of frustration effects on crystallization. We reveal that crystal-like hexatic order grows in size and lifetime with an increase in the colloid volume fraction or with a decrease in polydispersity (or frustration). We stress that hexatic ordering in hard disc systems is a direct consequence of dense packing and a manifestation of low configurational entropy. Our study suggests an intriguing scenario that the strength of frustration controls both the ease of vitrification and the nature of the glass transition. Vitrification may be a process of hidden crystal-like ordering under frustration for this system. This may provide not only a physical basis for glass formation, but also an answer to another longstanding question on the structure of amorphous materials: 'order in disorder' may be an intrinsic feature of a glassy state of many materials. For binary mixtures, on the other hand, the relevant structural feature linked to slow dynamics is not hexatic order, but an amorphous structure of low structural entropy. These results suggest that slow dynamics is associated with bond orientational order linked to the crystal for a weakly frustrated system, whereas to amorphous structures of low configurational entropy for a strongly frustrated system. This suggests an intrinsic link between structure and dynamics in glass-forming materials: slow dynamics is linked to structuring ('glassy ordering') towards low configurational entropy. We discuss the nature of 'glassy order' responsible for slow dynamics.