Global Orientational Order Research Articles

Disordering two-dimensional magnet-particle configurations using bidispersity.

In various types of many-particle systems, bidispersity is frequently used to avoid spontaneous ordering in particle configurations. In this study, the relation between bidispersity and disorder degree of particle configurations is investigated. By using magnetic dipole-dipole interaction, magnet particles are dispersed in a two-dimensional cell without any physical contact between them. In this magnetic system, bidispersity is introduced by mixing large and small magnets. Then, the particle system is compressed to produce a uniform particle configuration. The compressed particle configuration is analyzed by using Voronoi tessellation for evaluating the disorder degree, which strongly depends on bidispersity. Specifically, the standard deviation and skewness of the Voronoi cell area distribution are measured. As a result, we find that the peak of standard deviation is observed when the numbers of large and small particles are almost identical. Although the skewness shows a non-monotonic behavior, a zero skewness state (symmetric distribution) can be achieved when the numbers of large and small particles are identical. In this ideally random (disordered) state, the ratio between pentagonal, hexagonal, and heptagonal Voronoi cells becomes roughly identical, while hexagons are dominant under monodisperse (ordered) conditions. The relation between Voronoi cell analysis and the global bond orientational order parameter is also discussed.

Active cell divisions generate fourfold orientationally ordered phase in living tissue

Morphogenesis, the process through which genes generate form, establishes tissue-scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fuelled by cell proliferation, which, naively, should destroy order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order—rather than annihilate it—remains an outstanding question in animal development. We show that cell divisions are the primary drivers of tissue flow, leading to a fourfold orientationally ordered phase. Waves of anisotropic cell proliferation propagate across the embryo with precise patterning. Defects introduced into the nascent lattice by cell divisions are moved out of the tissue bulk towards the boundary by subsequent divisions. Specific cell proliferation rates and orientations enable cell divisions to organize rather than fluidize the tissue. We observe this using live imaging and tissue cartography to analyse the dynamics of fourfold tissue ordering in the trunk segmental ectoderm of the crustacean Parhyale hawaiensis beginning 72 h after egg lay. The result is a robust, active mechanism for generating global orientational order in a non-equilibrium system that sets the stage for the subsequent development of shape and form.

How Far Is "Bulk Water" from Interfaces? Depends on the Nature of the Surface and What We Measure.

Using systematic molecular dynamics (MD) simulations, we revisit the question: At what distance from an interface do the properties of "bulk water" get recovered? We have considered three different kinds of interfaces: nonpolar (hydrophobic; isooctane-water interface), charged (negative; AOT bilayer), and polar (zwitterionic; POPC bilayer). In order to interrogate the extent of perturbation of the interfacial water molecules as a function of the distance from the interface, we utilize a diverse range of structural and dynamical parameters. To capture the structural perturbations, we look into local density (translational order), local tetrahedral order parameter, and dipolar orientation of the water molecules. We also explore the anisotropic diffusion of the water molecules in the direction perpendicular to the interface as well as the planar diffusion parallel to the interface in a distance dependent manner. In addition, the orientational time correlation functions have been computed to understand the extent of slowdown in the rotational dynamics. As expected, the electrostatic field emanating from the charged AOT interface seems to have the highest long-range effect on the orientational order and dynamics of the water molecules, whereas specific interactions like hydrogen bonding and electrostatic interaction lead to significant trapping and kinetic slowdown for both AOT and POPC (zwitterionic) very close to the interface. Our analysis highlights that not only the length-scale of perturbation depends on the nature of the interfaces and specific interactions but also the type of water property that we measure/calculate. Different water properties seem to have widely different length-scale of perturbation. Orientational order parameters seem to be perturbed to a much longer length-scale as compared to translational order parameters. The global orientational order of water can be perturbed even up to ∼4-5 nm near the negatively charged AOT surface in the absence of any extra electrolyte. This observation has significant implication toward the interpretation of experimental measurements as well since different spectroscopic techniques would probe different parameters or water properties with possible mutual disagreement and inconsistency between different types of measurements. Thus, our study provides a broader and unifying perspective toward the aspect of "context dependent" structural and dynamical perturbation of "interfacial water".

Tuning Hierarchical Order and Plasmonic Coupling of Large-Area, Polymer-Grafted Gold Nanorod Assemblies via Flow-Coating.

Solution-based printing of anisotropic nanostructures is foundational to many emerging technologies, such as energy storage devices, photonic elements, and sensors. Methods to rapidly (>mm/s) manufacture large area assemblies (≫cm2) with simultaneous control of thickness (<10 nm), nanoparticle spacing (<5 nm), surface roughness (<5 nm), and global and local orientational order are still lacking. Herein, we demonstrate such capability using flow-coating to fabricate robust, self-supporting mono- and bilayer films of polystyrene-grafted gold nanorods (PS-AuNRs) onto solid substrates. The relationship among solvent evaporation, deposition speed, substrate surface energy, concentration, and film thickness for solutions of such hairy hybrid nanoparticles spans the Landau-Levich and evaporative film formation regimes. In the Landau-Levich regime, solvent evaporation rapidly concentrates the PS-AuNRs, leading to the formation of thin films with distinct, randomized side-by-side domains. Alternatively, processing at slower velocities in the evaporative regime results in the global alignment of PS-AuNRs. Processing speed and substrate surface energy afford tuning of the film's optical extinction of a given PS-AuNR via fine control of inter-rod distance and subsequent plasmonic coupling between neighboring nanorods. Because the concept of the polymer-grafted nanorod can be expanded to a variety of different polymer canopies, shapes, and core materials, the processing-structure relationships established in this work will have important implications on the future development of anisotropic nanostructure-based applications.

Gliding filament system giving both global orientational order and clusters in collective motion.

Emergence and collapse of coherent motions of self-propelled particles are affected more by particle motions and interactions than by their material or biological details. In the reconstructed systems of biofilaments and molecular motors, several types of collective motion including a global-order pattern emerge due to the alignment interaction. Meanwhile, earlier studies show that the alignment interaction of a binary collision of biofilaments is too weak to form the global order. The multiple collision is revealed to be important to achieve global order, but it is still unclear what kind of multifilament collision is actually involved. In this study, we demonstrate that not only alignment but also crossing of two filaments is essential to produce an effective multiple-particle interaction and the global order. We design the reconstructed system of biofilaments and molecular motors to vary a probability of the crossing of biofilaments on a collision and thus control the effect of volume exclusion. In this system, biofilaments glide along their polar strands on the turf of molecular motors and can align themselves nematically when they collide with each other. Our experiments show the counterintuitive result, in which the global order is achieved only when the crossing is allowed. When the crossing is prohibited, the cluster pattern emerges instead. We also investigate the numerical model in which we can change the strength of the volume exclusion effect and find that the global orientational order and clusters emerge with weak and strong volume exclusion effects, respectively. With those results and simple theory, we conclude that not only alignment but also finite crossing probability are necessary for the effective multiple-particles interaction forming the global order. Additionally, we describe the chiral symmetry breaking of a microtubule motion which causes a rotation of global alignment.

Multi-species dynamical density functional theory for microswimmers: Derivation, orientational ordering, trapping potentials, and shear cells

Microswimmers typically operate in complex environments. In biological systems, often diverse species are simultaneously present and interact with each other. Here, we derive a (time-dependent) particle-scale statistical description, namely, a dynamical density functional theory, for such multispecies systems, extending existing works on one-component microswimmer suspensions. In particular, our theory incorporates not only the effect of external potentials but also steric and hydrodynamic interactions between swimmers. For the latter, a previously introduced force-dipole-based minimal (pusher or puller) microswimmer model is used. As a limiting case of our theory, mixtures of hydrodynamically interacting active and passive particles are captured as well. After deriving the theory, we apply it to different planar swimmer configurations. First, these are binary pusher–puller mixtures in external traps. In the considered situations, we find that the majority species imposes its behavior on the minority species. Second, for unconfined binary pusher–puller mixtures, the linear stability of an orientationally disordered state against the emergence of global polar orientational order (and thus emergent collective motion) is tested analytically. Our statistical approach predicts, qualitatively in line with previous particle-based computer simulations, a threshold for the fraction of pullers and for their propulsion strength that lets overall collective motion arise. Third, we let driven passive colloidal particles form the boundaries of a shear cell, with confined active microswimmers on their inside. Driving the passive particles then effectively imposes shear flows, which persistently acts on the inside microswimmers. Their resulting behavior reminds of the one of circle swimmers although with varying swimming radii.

DEM study on the packing density and randomness for packing of ellipsoids

This paper presents a numerical study on the packing density and bed orderness in packing and vibration of ellipsoids by discrete element method (DEM). The shapes considered are oblate and prolate spheroids, with aspect ratio varying from 0.15 to 4.0. It is shown that under the poured packing conditions of coarse ellipsoids, flat or elongate particles show strong orientation preference on the horizontal direction. For packing with different particle sizes, when increasing particle size, packing density increases, global orientational order increases. For the cases of packing under one-dimensional vibration with periodic boundary condition and cylindrical wall conditions, after vibration, packing density increases, but global orientational order decreases. Boundary condition affects packing structure under both poured packing and vibration conditions. Under the cylindrical wall condition, considerable part of oblate particles have the symmetry axis pointing to the horizontal direction and quite a number of prolate particles have the symmetry axis pointing to the vertical direction after vibration. For spheres, denser packing leads to more (positional) ordered structure. For ellipsoids, denser packing can either be more (global and local orientational) ordered or random packing, which implies it does not necessarily be ordered packed to obtain higher packing density.

Topological description of the solidification of undercooled fluids and the temperature dependence of the thermal conductivity of crystalline and glassy solids above approximately 50 K

Topological origins of the thermal transport properties of crystalline and non-crystalline solid states are considered herein, by the adoption of a quaternion orientational order parameter to describe solidification. Global orientational order, achieved by spontaneous symmetry breaking, is prevented at finite temperatures for systems that exist in restricted dimensions (Mermin–Wagner theorem). Just as complex ordered systems exist in restricted dimensions in 2D and 1D, owing to the dimensionality of the order parameter, quaternion ordered systems in 4D and 3D exist in restricted dimensions. Just below the melting temperature, misorientational fluctuations in the form of spontaneously generated topological defects prevent the development of the solid state. Such solidifying systems are well-described using O(4) quantum rotor models, and a defect-driven Berezinskii–Kosterlitz–Thouless transition is anticipated to separate an undercooled fluid from a crystalline solid state. In restricted dimensions, in addition to orientationally-ordered ground states, orientationally-disordered ground states may be realized by tuning a non-thermal parameter in the relevant O(n) quantum rotor model Hamiltonian. Thus, glassy solid states are anticipated to exist as distinct ground states of O(4) quantum rotor models. Within this topological framework for solidification, the finite Kauzmann temperature marks a first-order transition between crystalline and glassy solid states at a ‘self-dual’ critical point that belongs to O(4) quantum rotor models. This transition is a higher-dimensional analogue to the quantum phase transition that belongs to O(2) Josephson junction arrays (JJAs). The thermal transport properties of crystalline and glassy solid states, above approximately 50 K, are considered alongside the electrical transport properties of JJAs across the superconductor-to-superinsulator transition.

Chiral Plasmonic Fields Probe Structural Order of Biointerfaces.

The structural order of biopolymers, such as proteins, at interfaces defines the physical and chemical interactions of biological systems with their surroundings and is hence a critical parameter in a range of biological problems. Known spectroscopic methods for routine rapid monitoring of structural order in biolayers are generally only applied to model single-component systems that possess a spectral fingerprint which is highly sensitive to orientation. This spectroscopic behavior is not a generic property and may require the addition of a label. Importantly, such techniques cannot readily be applied to real multicomponent biolayers, have ill-defined or unknown compositions, and have complex spectroscopic signatures with many overlapping bands. Here, we demonstrate the sensitivity of plasmonic fields with enhanced chirality, a property referred to as superchirality, to global orientational order within both simple model and “real” complex protein layers. The sensitivity to structural order is derived from the capability of superchiral fields to detect the anisotropic nature of electric dipole–magnetic dipole response of the layer; this is validated by numerical simulations. As a model study, the evolution of orientational order with increasing surface density in layers of the antibody immunoglobulin G was monitored. As an exemplar of greater complexity, superchiral fields are demonstrated, without knowledge of exact composition, to be able to monitor how qualitative changes in composition alter the structural order of protein layers formed from blood serum, thereby establishing the efficacy of the phenomenon as a tool for studying complex biological interfaces.

Molecular simulation of flow-enhanced nucleation in n-eicosane melts under steady shear and uniaxial extension.

Non-equilibrium molecular dynamics is used to study crystal nucleation of n-eicosane under planar shear and, for the first time, uniaxial extension. A method of analysis based on the mean first-passage time is applied to the simulation results in order to determine the effect of the applied flow field type and strain rate on the steady-state nucleation rate and a characteristic growth rate, as well as the effects on kinetic parameters associated with nucleation: the free energy barrier, critical nucleus size, and monomer attachment pre-factor. The onset of flow-enhanced nucleation (FEN) occurs at a smaller critical strain rate in extension as compared to shear. For strain rates larger than the critical rate, a rapid increase in the nucleation rate is accompanied by decreases in the free energy barrier and critical nucleus size, as well as an increase in chain extension. These observations accord with a mechanism in which FEN is caused by an increase in the driving force for crystallization due to flow-induced entropy reduction. At high applied strain rates, the free energy barrier, critical nucleus size, and degree of stretching saturate, while the monomer attachment pre-factor and degree of orientational order increase steadily. This trend is indicative of a significant diffusive contribution to the nucleation rate under intense flows that is correlated with the degree of global orientational order in a nucleating system. Both flow fields give similar results for all kinetic quantities with respect to the reduced strain rate, which we define as the ratio of the applied strain rate to the critical rate. The characteristic growth rate increases with increasing strain rate, and shows a correspondence with the nucleation rate that does not depend on the type of flow field applied. Additionally, a structural analysis of the crystalline clusters indicates that the flow field suppresses the compaction and crystalline ordering of clusters, leading to the formation of large articulated clusters under strong flow fields, and compact well-ordered clusters under weak flow fields.

Search for microscopic and macroscopic biaxiality in the cybotactic nematic phase of new oxadiazole bent-core mesogens

The possibility of biaxial orientational order in nematic liquid crystals is a subject of intense current interest. We explore the tendencies toward local and global biaxial ordering in the recently synthesized trimethylated oxadiazole-based bent-core mesogens with a pronounced asymmetric (bow-type) shape of molecules. The combination of x-ray diffraction and optical studies suggests that the biaxial order is expressed differently at the short- and long-range scales. Locally, at the scale of a few molecules, x-ray-diffraction data demonstrate biaxial packing. However, above the mesoscopic scale, the global orientational order in all three compounds is uniaxial, as evidenced by uniform homeotropic alignment of the nematic phase which is optically tested over the entire temperature range and by the observations of topological defects induced by individual and aggregated colloidal spheres in the nematic bulk.

Homogeneous alignment of liquid crystalline dendrimers confined in a slit-pore. A simulation study

In this work we present results from isobaric-isothermal (NPT) Monte Carlo simulation studies of model liquid crystalline dendrimer (LCDr) systems confined in a slit-pore made of two parallel flat walls. The dendrimers are modelled as a collection of spherical and ellipsoidal particles corresponding to the junction points of the dendritic core and to the mesogenic units respectively. Assuming planar uniform (unidirectional) soft anchoring of the mesogenic units on the substrates we investigate the conformational and alignment properties of the LCDr system at different thermodynamic state points. Tractable coarse grained force fields have been used from our previous work. At low pressures the interior of the pore is almost empty, since almost all LCDrs are anchored to the substrates forming two-dimensional smectic-like structures with the mesogens aligned along the aligning direction of the substrates. As the pressure grows the LCDrs occupy the whole pore. However, even at low temperatures, the smectic organization does not transmit in the interior of the pore and is preserved for distances of 2–3 mesogenic diameters from the walls. For this reason, the global orientational order decreases with increasing pressure (density). In the vicinity (2–3 mesogenic diameters) of the pore walls, mesogenic units preserve the smectic structure whose layers are separated by layers of spherical beads. In this region individual LCDrs possess a rod like shape.

Maximally dense random packings of spherocylinders

A spherocylinder, a convex 3D object consisting of a cylinder with two hemispherical ends, can possess a wide range of aspect ratios and is one of the most studied non-spherical particle shapes. Previous investigations on disordered spherocylinder packings yielded inconsistent packing characteristics, especially the packing density φ, indicating that density alone is not sufficient to uniquely characterize a packing. In this paper, we delineate in the density–order–metric diagram (i.e. order map) the border curve that separates geometrically feasible and infeasible packings of congruent spherocylinders via the geometric-structure approach, i.e., by generating and analyzing a large number of packing configurations with a diversity of densities and degrees of order generated via a relaxation algorithm. We find that the border curve possesses a sharp transition as the packing density increases, i.e., the initial increase of φ is not associated with any notable increase of the degree of order, while beyond a threshold φ value, the increase of density is strongly positively correlated with the increase of order. This allows us to propose the concept of maximally dense random packing (MDRP) state for spherocylinders, which corresponds to the transition point in the boarder curve and characterizes the on-set of nontrivial spatial correlations among the particles. It can also be considered as the maximally dense packing arrangement of spherocylinders without nontrivial spatial correlations. The degree of order of a spherocylinder packing is quantified via the nematic order parameter (S) and the local order metric (SLocal), which respectively characterize the level of global orientational order and local order in particle clusters. The latter metric SLocal, which measures the average order in the neighborhoods of particles with the second Legendre polynomial, is a new order metric for spherocylinder systems. We find that the packing density of the MDRPs initially increases with the increase of the aspect ratio w from 0, and reaches the maximal value of 0.725 when w=0.5, then drops with further increase of w. The MDRP at w=0.5 is verified to be jammed via a Monte Carlo jamming-testing algorithm and thus, should also represent the maximally random jammed (MRJ) packing state as well.

Strong orientational coordinates and orientational order parameters for symmetric objects

Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in self-assembly and in inducing complex order. The problem of identifying different types of order that can emerge in such systems can, however, be challenging. Here, we revisit the problem of quantifying orientational order in systems of building blocks with non-trivial rotational symmetries. We first propose a systematic way of constructing orientational coordinates for such symmetric building blocks. We call the arising tensorial coordinates strong orientational coordinates (SOCs) as they fully and exclusively specify the orientation of a symmetric object. We then use SOCs to describe and quantify local and global orientational order, and spatiotemporal orientational correlations in systems of symmetric building blocks. The SOCs and the orientational order parameters developed in this work are not only useful in performing and analyzing computer simulations of symmetric molecules or particles, but can also be utilized for the efficient storage of rotational information in long trajectories of evolving many-body systems.

Use of polydispersity index as control parameter to study melting/freezing of Lennard-Jones system: Comparison among predictions of bifurcation theory with Lindemann criterion, inherent structure analysis and Hansen-Verlet rule

Using polydispersity index as an additional order parameter we investigate freezing/melting transition of Lennard-Jones polydisperse systems (with Gaussian polydispersity in size), especially to gain insight into the origin of the terminal polydispersity. The average inherent structure (IS) energy and root mean square displacement (RMSD) of the solid before melting both exhibit quite similar polydispersity dependence including a discontinuity at solid-liquid transition point. Lindemann ratio, obtained from RMSD, is found to be dependent on temperature. At a given number density, there exists a value of polydispersity index (δ P) above which no crystalline solid is stable. This transition value of polydispersity(termed as transition polydispersity, δ P ) is found to depend strongly on temperature, a feature missed in hard sphere model systems. Additionally, for a particular temperature when number density is increased, δ P shifts to higher values. This temperature and number density dependent value of δ P saturates surprisingly to a value which is found to be nearly the same for all temperatures, known as terminal polydispersity (δ TP). This value (δ TP∼ 0.11) is in excellent agreement with the experimental value of 0.12, but differs from hard sphere transition where this limiting value is only 0.048. Terminal polydispersity (δ TP) thus has a quasiuniversal character. Interestingly, the bifurcation diagram obtained from non-linear integral equation theories of freezing seems to provide an explanation of the existence of unique terminal polydispersity in polydisperse systems. Global bond orientational order parameter is calculated to obtain further insights into mechanism for melting.

Self-propelled rods exhibit a phase-separated state characterized by the presence of active stresses and the ejection of polar clusters.

We study collections of self-propelled rods (SPR) moving in two dimensions for packing fractions less than or equal to 0.3. We find that in the thermodynamical limit the SPR undergo a phase transition between a disordered gas and a novel phase-separated system state. Interestingly, (global) orientational order patterns-contrary to what has been suggested-vanish in this limit. In the found novel state, the SPR self-organize into a highly dynamical, high-density, compact region-which we call aggregate-which is surrounded by a disordered gas. Active stresses build inside aggregates as a result of the combined effect of local orientational order and active forces. This leads to the most distinctive feature of these aggregates: constant ejection of polar clusters of SPR. This novel phase-separated state represents a novel state of matter characterized by large fluctuations in volume and shape, related to mass ejection, and exhibits positional as well as orientational local order. SPR systems display new physics unseen in other active matter systems.

Molecular dynamics simulation of melting and crystallization processes of polyethylene clusters confined in armchair single-walled carbon nanotubes.

The confined interaction is important to understand the melting and crystallization of polymers within single-wall carbon tube (SWNT). However, it is difficult for us to observe this interaction. In the current work, the structures and behaviors of melting and crystallization for polyethylene (PE) clusters confined in armchair single-walled carbon nanotubes ((n,n)-SWNTs) are investigated and examined based on molecular dynamics (MD) simulations. The nonbonded energies, structures, Lindemman indices, radial density distributions, and diffusion coefficients are used to demonstrate the features of melting phase transition for PE clusters confined in (n,n)-SWNTs. The chain end-to-end distance (R(n)) and chain end-to-end distribution are used to examine the flexibility of the PE chain confined in SWNT. The global orientational order parameter (P2) is employed to reveal the order degree of whole PE polymer. The effect of polymerization degree on melting temperature and the influence of SWNT chirality on structure of PE cluster are examined and discussed. Results demonstrate that within the confined environment of SWNT, PE clusters adopt novel co-axial crystalline layer structure, in which parallel chains of each layer are approximately vertical to tube axis. The disordered-ordered transformation of PE chains in each layer is an important structural feature for crystallization of confined PE clusters. SWNTs have a considerable effect on the structures and stabilities of the confined PE clusters.

Periodic ordering of clusters and stripes in a two-dimensional lattice model. II. Results of Monte Carlo simulation.

The triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion, introduced by Pȩkalski, Ciach, and Almarza [J. Chem. Phys. 140, 114701 (2014)] is studied by Monte Carlo simulation. Introduction of appropriate order parameters allowed us to construct a phase diagram, where different phases with patterns made of clusters, bubbles or stripes are thermodynamically stable. We observe, in particular, two distinct lamellar phases-the less ordered one with global orientational order and the more ordered one with both orientational and translational order. Our results concern spontaneous pattern formation on solid surfaces, fluid interfaces or membranes that is driven by competing interactions between adsorbing particles or molecules.

Conformational Properties of Semiflexible Chains at Nematic Ordering Transitions in Thin Films: A Monte Carlo Simulation

Athermal solutions of semiflexible macromolecules with excluded volume interactions and with varying concentration (dilute, semidilute, and concentrated solutions) in a film of thickness D between two hard walls have been studied by means of grand canonical Monte Carlo simulation using the bond fluctuation lattice model. In earlier work, we have reported on the phase diagram of this model system, which exhibits a continuous quasi-two-dimensional order–disorder transition at rather small concentration and (for thick enough films) a “capillary nematization”-type first-order phase transition. In the “semi-infinite” case (i.e., macroscopically thick films) the onset of nematic order is triggered by the walls (surface-induced ordering). While the focus of this previous work was on the order parameters of these phase transitions and associated surface effects, in the present paper we focus on the interplay between the conformational statistics of the semiflexible chains and these orientational ordering phenomena. In particular, we study how characteristic lengths of the chains (persistence length, end-to-end distance) depend on the local and global orientational order in the system. We show that there is a strong coupling between single-chain properties and long-range orientational order. The relation between mean-square end-to-end distance of short semiflexible chains and their persistence length predicted by the Kratky–Porod model is found to be applicable (within 10% errors) in the dilute limit, while it fails as soon as nematic short- or long-range order is present.

Crystallization time scales for polydisperse hard-sphere fluids

We study the evolution of crystallization in dense mono- and polydisperse hard sphere fluids, initially quenched to an amorphous configuration. We use as signatures of crystallization both the decay of the reduced pressure Z and the increase in the local and global orientational order parameters Q[over ¯](6). For a given realization of the crystallization process these parameters show sudden changes, both large and small, separated by long periods of quiescence. However, averaging over a large number of realizations, a well-defined scenario for their evolution appears. We find an initial fast relaxation to a disordered state, followed by a period of slow variation, associated to the presence of nucleation events, followed by a fast change, composed of the growth of a few crystals with different orientations, and a final and slow coarsening in a domain-growth process. No clear scaling for this whole process was found. We also find that the transition to an stable glassy fluid is quite sharp as the polydispersity is increased, showing a probable first-order phase transition behavior. A well-defined boundary between crystallizing and permanently amorphous fluids should exist, at least for a region in packing fractions. We looked for segregation at large values of polydispersity, but no effects of this type were found.