Local Orientational Order Research Articles

Phase behavior and crystal nucleation of hard triangular prisms.

The interplay between densification and positional ordering during the process of crystal nucleation is a greatly investigated topic. Even for the simplest colloidal model-hard spheres-there has been much debate regarding the potential foreshadowing of nucleation by significant fluctuations in either local density or local structure. Considering anisotropic particles instead of spheres adds a third degree of freedom to the self-organization process of crystal nucleation: orientational ordering. Here, we investigate the crystal nucleation of hard triangular prisms. Using Monte Carlo simulations, we first carefully determine the crystal-fluid coexistence values and calculate the nucleation barriers for two degrees of supersaturation. Next, we use brute force simulations to obtain a large set of spontaneous nucleation events. By studying the time evolution of the local density, positional ordering, and orientational ordering in the region in which the nucleus first arises, we demonstrate that all local order parameters increase simultaneously from the very start of the nucleation process. We thus conclude that we observe no precursor for the crystal nucleation of hard triangular prisms.

Hole statistics of equilibrium 2D and 3D hard-sphere crystals.

The probability of finding a spherical "hole" of a given radius r contains crucial structural information about many-body systems. Such hole statistics, including the void conditional nearest-neighbor probability functions GV(r), have been well studied for hard-sphere fluids in d-dimensional Euclidean space Rd. However, little is known about these functions for hard-sphere crystals for values of r beyond the hard-sphere diameter, as large holes are extremely rare in crystal phases. To overcome these computational challenges, we introduce a biased-sampling scheme that accurately determines hole statistics for equilibrium hard spheres on ranges of r that far extend those that could be previously explored. We discover that GV(r) in crystal and hexatic states exhibits oscillations whose amplitudes increase rapidly with the packing fraction, which stands in contrast to GV(r) that monotonically increases with r for fluid states. The oscillations in GV(r) for 2D crystals are strongly correlated with the local orientational order metric in the vicinity of the holes, and variations in GV(r) for 3D states indicate a transition between tetrahedral and octahedral holes, demonstrating the power of GV(r) as a probe of local coordination geometry. To further study the statistics of interparticle spacing in hard-sphere systems, we compute the local packing fraction distribution f(ϕl) of Delaunay cells and find that, for d ≤ 3, the excess kurtosis of f(ϕl) switches signat a certain transitional global packing fraction. Our accurate methods to access hole statistics in hard-sphere crystals at the challenging intermediate length scales reported here can be applied to understand the important problem of solvation and hydrophobicity in water at such length scales.

Statistics of a granular cluster ensemble at a liquid-solid-like phase transition.

We report on the construction of a granular network of particles to study the formation, evolution, and statistical properties of clusters of particles developing at the vicinity of a liquid-solid-like phase transition within a vertically vibrated quasi-two-dimensional granular system. Using the data of particle positions and local order from Castillo etal. [G. Castillo, N. Mujica, and R. Soto, Phys. Rev. Lett. 109, 095701 (2012)0031-900710.1103/PhysRevLett.109.095701], we extract granular clusters taken as communities of the granular network via modularity optimization. Each one of these communities is a patch of particles with a very well defined local orientational order embedded within an array of other patches forming a complex cluster network. The distributions of cluster sizes and lifespans for the cluster network depend on the distance to the liquid-solid-like phase transition of the quasi-two-dimensional granular system. Specifically, the cluster size distribution displays a scale-invariant behavior for at least a decade in cluster sizes, while cluster lifespans grow monotonically with each cluster size. We believe this systematic community analysis for clustering in granular systems can help to study and understand the spatiotemporal evolution of mesoscale structures in systems displaying out-of-equilibrium phase transitions.

Study of phase transition and local order in equiatomic and nonequiatomic mixtures of HfNbTaTi under uniaxial loading from molecular dynamics simulations

We simulate an alloy of HfNbTaTi mixed in six different proportions and also of the equiatomic system under uniaxial tensile loading at 300 K. Molecular dynamics simulation trajectories are analyzed using radial distribution functions, OVITO, bond-orientational order parameters, and coordination numbers. Equiatomic and the two other alloys (Hf0.31Nb0.23Ta0.23Ti0.23 and Hf0.23Nb0.31Ta0.23Ti0.23) containing comparable fraction of elements deform similarly through the formation of an amorphous state. Two alloys rich in Nb (Hf0.17Nb0.50Ta0.16Ti0.17) and Ta (Hf0.17Nb0.16Ta0.50Ti0.17) deform similarly resulting in the formation of bcc atoms, which transform to fcc at higher loading. Finally, alloys rich in Hf (Hf0.50Nb0.16Ta0.17Ti0.17) and Ti (Hf0.17Nb0.16Ta0.17Ti0.50) deform resulting in high dislocation densities and hcp atoms. These two hcp-rich alloys also undergo strain hardening. In each mixture during loading, local orientational order of all the different elements changes similarly. Atoms prefer to pair with other atoms than to themselves during tensile loading.

Geometrical impacts of platonic particles on nematic liquid crystal dynamics.

Platonic-solid-like particles in liquid crystals offer intriguing opportunities for engineering complex materials with tailored properties. Inspired by platonic solids' geometric simplicity and symmetry, these particles possess well-defined shapes such as cubes, tetrahedra, octahedra, dodecahedra, and icosahedra. When dispersed within nematic liquid-crystalline media, these particles interact with the surrounding medium in intricate ways, influencing the local orientational order of liquid crystal molecules. In this work, we implement continuum simulations to study how the combination of particle shape and surface anchoring gives rise to line defects that follow the edges of the particles and how they are affected by the presence of a Poiseuille flow. Platonic-solid-like particles in liquid crystals have shown promise in diverse applications ranging from photonics and metamaterials to colloidal self-assembly and responsive soft materials.

Orientational Order in Dense Colloidal Liquids and Glasses.

We construct structural order parameters based on local angular and radial distribution functions in dense colloidal suspensions. All the order parameters show significant correlations to local dynamics in the supercooled and glass regime. In particular, the correlations between the orientational order and dynamical heterogeneity are consistently higher than those between the conventional two-body structural entropy and local dynamics. The structure-dynamics correlations can be explained by a excitation model with the energy barrier depending on local structural order. Our results suggest that in dense disordered packings, local orientational order is higher than translational order, and plays a more important role in determining the dynamics in glassy systems.

Molecular dynamics simulation of polymorphic transformation between ε-CL-20 and β-CL-20 by short range order and orientational order parameter

Phase transition simulation of molecular crystals is a challenge. In order to clarify the polymorphic transformation mechanism of molecular crystal, a molecular dynamics (MD) simulation of the transformation between ε-CL-20 and β-CL-20 was carried out by the short range order g(r) and local orientational order parameter (OPs) P2(cosθ) as well as the spatial orientation correlation function. The effects of the temperature on them were performed. The results indicate that the g(r), orientational OPs and spatial orientation correlation function, composed of the structural parameters from three CL-20 molecules in three different single crystal, could be used to simulate the process of the polymorphic transformation between ε-CL-20 and β-CL-20. Only at a high temperature, could two kinds of the CL-20 supercells realize the transformation of crystal form. Furthermore, there were local and global minimum energy points, indicating that there could be the metastable or stable crystal forms in the process of the transformation from β-CL-20 to ε-CL-20. The values of P2(cosθ) were well related to results of the surface electrostatic potentials (ESPs), suggesting that the ESPs have an influence on polymorphic transformation.

A neural network potential with self-trained atomic fingerprints: A test with the mW water potential.

We present a neural network (NN) potential based on a new set of atomic fingerprints built upon two- and three-body contributions that probe distances and local orientational order, respectively. Compared with the existing NN potentials, the atomic fingerprints depend on a small set of tunable parameters that are trained together with the NN weights. In addition to simplifying the selection of the atomic fingerprints, this strategy can also considerably increase the overall accuracy of the network representation. To tackle the simultaneous training of the atomic fingerprint parameters and NN weights, we adopt an annealing protocol that progressively cycles the learning rate, significantly improving the accuracy of the NN potential. We test the performance of the network potential against the mW model of water, which is a classical three-body potential that well captures the anomalies of the liquid phase. Trained on just three state points, the NN potential is able to reproduce the mW model in a very wide range of densities and temperatures, from negative pressures to several GPa, capturing the transition from an open random tetrahedral network to a dense interpenetrated network. The NN potential also reproduces very well properties for which it was not explicitly trained, such as dynamical properties and the structure of the stable crystalline phases of mW.

New Liquid Crystalline Elastomeric Films Containing a Smectic Crosslinker: Chemical and Physical Properties

Side-chain liquid crystal elastomers (SC-LCEs) have been designed by using a new smectic crosslinker. Two types of monodomain films were prepared based on polysiloxane chains, with a different relative concentration of both crosslinker and mesogenic comonomers. The mesomorphic behavior of the two SC-LCE systems was investigated by differential scanning calorimetry and polarized optical microscopy showing a different mesomorphic behavior: in one case, we obtained a nematic SC-LCE film, in the other case, a Smectic A SC-LCE film. In both systems, the mesophases were stable in a wide temperature range. Moreover, the SC-LCE films possess a relatively high orientation at room temperature. The physical-chemical properties, such as the local orientational ordering, structural organization, and dynamics of SC-LCEs’ constituents were studied by means of static and dynamic 2H NMR experiments, small-angle X-ray, and wide-angle X-ray diffractions. The relevant physical properties, such as the thermo-elastic and thermo-mechanic behaviors, are reported and discussed in view of the practical applications.

Vorticity phase separation and defect lattices in the isotropic phase of active liquid crystals.

We use numerical simulations and linear stability analysis to study the dynamics of an active liquid crystal film on a substrate in the regime where the passive system would be isotropic. Extensile activity builds up local orientational order and destabilizes the quiescent isotropic state above a critical activity, eventually resulting in spatiotemporal chaotic dynamics akin to the one observed ubiquitously in the nematic state. Here we show that tuning substrate friction yields a variety of emergent structures at intermediate activity, including lattices of flow vortices with associated regular arrangements of topological defects and a new state where flow vortices trap pairs of +1/2 defect that chase each other's tail. These chiral units spontaneously pick the sense of rotation and organize in a hexagonal lattice, surrounded by a diffuse flow of opposite rotation to maintain zero net vorticity. The length scale of these emergent structures is set by the screening length of the flow, controlled by the shear viscosity η and the substrate friction Γ, and can be captured by simple mode selection of the vortical flows. We demonstrate that the emergence of coherent structures can be interpreted as a phase separation of vorticity, where friction plays a role akin to that of birth/death processes in breaking conservation of the phase separating species and selecting a characteristic scale for the patterns. Our work shows that friction provides an experimentally accessible tuning parameter for designing controlled active flows.

Observing short-range orientational order in small-molecule liquids

Local molecular ordering in liquids has attracted a lot of interest from researchers investigating crystallization, but is still poorly understood on the molecular scale. Classical nucleation theory (CNT), a macroscopic thermodynamic description of condensation, has shortcomings when dealing with clusters consisting of tens of molecules. Cluster formation and local order fluctuations in liquid media are difficult to study due to the limited spatial resolution of electron- and photon-imaging methods. We used NMR relaxometry to demonstrate the existence of dynamic clusters with short-range orientational order in nominally isotropic liquids consisting of elongated molecules. We observed clusters in liquids where the local ordering is driven by polar, steric, and hydrogen-bond interactions between the molecules. In the case of a liquid crystal, measuring the local orientational order fluctuations allowed us to observe the size of these clusters diverging when approaching the phase transition from the isotropic to the nematic phase. These fluctuations are described in terms of rotational elasticity as a consequence of the correlated reorientations of the neighbouring molecules. Our quantitative observations of the dynamic clusters in liquids, numbering about ten or fewer molecules, indicate that this is a general phenomenon in various types of liquids.

Binary salt structure classification with convolutional neural networks: Application to crystal nucleation and melting point calculations

Convolutional neural networks are constructed and validated for the crystal structure classification of simple binary salts such as the alkali halides. The inputs of the neural network classifiers are the local bond orientational order parameters of Steinhardt, Nelson, and Ronchetti [Phys. Rev. B 28, 784 (1983)], which are derived solely from the relative positions of atoms surrounding a central reference atom. This choice of input gives classifiers that are invariant to density, increasing their transferability. The neural networks are trained and validated on millions of data points generated from a large set of molecular dynamics (MD) simulations of model alkali halides in nine bulk phases (liquid, rock salt, wurtzite, CsCl, 5-5, sphalerite, NiAs, AntiNiAs, and β-BeO) across a range of temperatures. One-dimensional time convolution is employed to filter out short-lived structural fluctuations. The trained neural networks perform extremely well, with accuracy up to 99.99% on a balanced validation dataset constructed from millions of labeled bulk phase structures. A typical analysis using the neural networks, including neighbor list generation, order parameter calculation, and class inference, is computationally inexpensive compared to MD simulations. As a demonstration of their accuracy and utility, the neural network classifiers are employed to follow the nucleation and crystal growth of two model alkali halide systems, crystallizing into distinct structures from the melt. We further demonstrate the classifiers by implementing them in automated MD melting point calculations. Melting points for model alkali halides using the most commonly employed rigid-ion interaction potentials are reported and discussed.

Observation of an Orientational Glass in a Superlattice of Elliptically-Faceted CdSe Nanocrystals.

Extensive prior work has shown that colloidal inorganic nanocrystals coated with organic ligand shells can behave as artificial atoms and, as such, form superlattices with different crystal structures and packing densities. Although ordered superlattices present a high degree of long-range positional order, the relative crystallographic orientation of the inorganic nanocrystals with respect to each other tends to be random. Recent works have shown that superlattices can achieve orientational alignment through combinations of nanocrystal faceting and ligand modification, as well as selective metal particle attachment to particular facets. These studies have focused on the assembly of high-symmetry nanocrystals, such as cubes and cuboctahedra. Here, we study the assembly of elliptically faceted CdSe/CdS core/shell nanocrystals with one distinctive crystallographic orientation along the major elliptical axis. We show that the nanocrystals form an unexpectedly well-ordered translational superlattice, with a degree of order comparable to that achieved with higher-symmetry nanocrystals. Additionally, we show that, due to the particles' faceted shape, the superlattice is characterized by an orientational glass phase in which only certain orientations are possible due to entropically frustrated crystallization. In this phase, the nanocrystals do not exhibit a local orientational ordering but rather have distinct orientations that emerge at different locations within the same domain. The distinct orientations are a result of a facet-to-facet lock-in mechanism that occurs during the self-assembly process. These facet-to-facet alignments force the nanocrystals to tilt on different lattice planes forming different projections that we termed apparent polydispersity. Our experimental realization of an orientational glass phase for multifaceted semiconducting nanocrystals can be used to investigate how this phase is formed and how it can be utilized for potential optical, electrical, and thermal transport applications.

Structural transition in cellulose triacetate films

Electron microscopy data are used to comparative analysis of the topological structure of the surface of two samples of cellulose triacetate (CTA) films. The samples were obtained from CTA solutions without use (sample N 1) and with the use of a small sodium fluoride additive that lowers the viscosity of the solution (sample N2). It is shown that in sample N 1, the nodes of the physical network of macromolecules are periodically alternating regions of local orientation order --- microdomains of average size d~18 nm. In sample N 2, due to repackaging of microdomains on the scale R>d, a uniformly disordered fractal cluster of the mesophase CTA is formed. The fractalization of the surface and the growth of structural anisotropy are consistent with the decrease in the viscosity of the solution and explain the change in the deformation properties of sample N 2 compared to N 1. Keywords: polymer films, electron microscopy, microdomains, mesophase, structural transition, fractal clusters.

Структурный переход в пленках триацетата целлюлозы

Electron microscopy data are used to comparative analysis of the topological structure of the surface of two samples of cellulose triacetate (СTA) films. The samples were obtained from CTA solutions without use (sample №1) and with the use of a small sodium fluoride additive that lowers the viscosity of the solution (sample №2). It is shown that in sample №1, the nodes of the physical network of macromolecules are periodically alternating regions of local orientation order - microdomains of average size d~18 nm. In sample №2, due to repackaging of microdomains on the scale R >d, a uniformly disordered fractal cluster of the mesophase CTA is formed. The fractalization of the surface and the growth of structural anisotropy are consistent with the decrease in the viscosity of the solution and explain the change in the deformation properties of sample №2 compared to №1.

Hydrogen bonding in liquid water at 1 GPa : Molecular dynamics simulation study of TIP4P/2005 water model

Liquid water structure and dynamics at 1 GPa and in the temperature range 300–230 K is investigated here using molecular dynamics simulations of TIP4P/2005 water model. A recently reported hydrogen bond criterion is used to collect the hydrogen bonded water molecules. In the temperature range studied average local coordination was ≈7.3 and fraction of 3, 4 and 5 hydrogen bonded water molecules were 10, 60 and 20%, respectively. For 4 hydrogen bonded water, 2-Donor–2-Acceptor geometry is always preserved. For 5 hydrogen bonded water, fraction of acceptor bonds are more than the donors because donor bonds are more strained compared to the acceptor ones. Comparing the local orientational ordering in oxygens and hydrogens with ices V, VI and VII, we note striking similarities between ice V and high pressure liquid water. Dynamics show that intensities of bending and streching modes increase with decrease in temperature.

Frequency dependence of dielectric permittivity and conductivity of functionalized carbon nanotube-nematic liquid crystal nanocomposite

The addition of carbon nanotubes (CNTs) to nematic liquid crystal (NLC) medium is known to enhance the orientational order along with the enhancement in electro-optical and dielectric properties of the liquid crystal (LC). The studies on the dielectric behavior of LC-nanocomposites at wide range frequencies are essential for optimizing the LC based device performances. The nanocomposites of octadecylamine functionalized single-walled carbon nanotubes (ODA-SWCNTs) with NLC are studied with the aid of dielectric spectroscopy. The important parameters of LCs relevant to display related applications such as dielectric permittivity, relaxation frequency, threshold voltage, and conductivity are investigated over a wide range of frequency and temperatures in planar as well as homeotropic configurations. The doping of ODA-SWCNTs into the NLC increases the local orientational order in the nematic matrix due to the strong interaction between LC and CNT molecules. The optimum doping decreases threshold voltage due to enhancement of dielectric anisotropy and decrease in splay elastic constant. The experimental data obtained from impedance spectroscopy measurements are fitted with a suitable equivalent electric circuit model, and the estimated electrical components are studied as a function of temperature. Investigation on interfacial and bulk properties of pure and ODA-SWCNT nanocomposites of 7CB NLC are also discussed.

Thermodynamics and self-organization of strongly coupled Coulomb clusters: An experimental study

In this experimental work, the thermodynamics and self-organization of classical two-dimensional Coulomb clusters are studied as a function of the cluster size. The experiments are carried out in a DC glow discharge argon plasma in the dusty plasma experimental device for clusters with different number of particles. Hexagonal symmetry around each individual particle is quantified using the local orientational order parameter (|ψ6|) for all the configurations. The screened Coulomb coupling parameter, which plays a key role in determining the thermodynamic nature of a Coulomb cluster, is estimated using Langevin dynamics and found to be sensitive to the number of particles present in the cluster. In addition, the process of self-organization and the dynamics of individual particles of the cluster as it changes from a metastable state to the ground state are examined through the estimation of dynamic entropy. Our findings suggest an intimate link between the configurational ordering and the thermodynamics of a strongly coupled Coulomb cluster system—an insight that might be of practical value in analyzing and controlling the microdynamics of a wider class of finite systems.

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.

Accelerated annealing of colloidal crystal monolayers by means of cyclically applied electric fields

External fields are commonly applied to accelerate colloidal crystallization; however, accelerated self-assembly kinetics can negatively impact the quality of crystal structures. We show that cyclically applied electric fields can produce high quality colloidal crystals by annealing local disorder. We find that the optimal off-duration for maximum annealing is approximately one-half of the characteristic melting half lifetime of the crystalline phase. Local six-fold bond orientational order grows more rapidly than global scattering peaks, indicating that local restructuring leads global annealing. Molecular dynamics simulations of cyclically activated systems show that the ratio of optimal off-duration for maximum annealing and crystal melting time is insensitive to particle interaction details. This research provides a quantitative relationship describing how the cyclic application of fields produces high quality colloidal crystals by cycling at the fundamental time scale for local defect rearrangements; such understanding of dynamics and kinetics can be applied for reconfigurable colloidal assembly.