Hexatic Phase Research Articles

Entropy production of active Brownian particles going from liquid to hexatic and solid phases

Due to its inherent intertwinement with irreversibility, entropy production is a prime observable to monitor in systems of active particles. In this numerical study, entropy production in the liquid, hexatic and solid phases of a two-dimensional system of active Brownian particles is examined at both average and fluctuation level. The trends of averages as functions of density show no singularity and marked changes in their derivatives at the hexatic-solid transition. Distributions show instead peculiar tail structures interpreted by looking at microscopic configurations. Particles in regions of low local order generate tail values according to different dynamical mechanisms: they move towards empty regions or bounce back and forth into close neighbours. The tail structures are reproduced by a simple single-particle model including an intermittent harmonic potential.

Intercellular friction and motility drive orientational order in cell monolayers

Spatiotemporal patterns in multicellular systems are important to understanding tissue dynamics, for instance, during embryonic development and disease. Here, we use a multiphase field model to study numerically the behavior of a near-confluent monolayer of deformable cells with intercellular friction. Varying friction and cell motility drives a solid-liquid transition, and near the transition boundary, we find the emergence of local nematic order of cell deformation driven by shear-aligning cellular flows. Intercellular friction contributes to the monolayer's viscosity, which significantly increases the spatial correlation in the flow and, concomitantly, the extent of nematic order. We also show that local hexatic and nematic order are tightly coupled and propose a mechanical-geometric model for the colocalization of [Formula: see text] nematic defects and 5-7 disclination pairs, which are the structural defects in the hexatic phase. Such topological defects coincide with regions of high cell-cell overlap, suggesting that they may mediate cellular extrusion from the monolayer, as found experimentally. Our results delineate a mechanical basis for the recent observation of nematic and hexatic order in multicellular collectives in experiments and simulations and pinpoint a generic pathway to couple topological and physical effects in these systems.

Melting and freezing of a skyrmion lattice

We report comprehensive Monte-Carlo studies of the melting of skyrmion lattices (SkL) in systems of small, medium, and large sizes with the number of skyrmions ranging from 103to over 105. Large systems exhibit hysteresis similar to that observed in real experiments on the melting of SkLs. For sufficiently small systems which achieve thermal equilibrium, a fully reversible sharp solid-liquid transition on temperature with no intermediate hexatic phase is observed. A similar behavior is found on changing the magnetic field that provides the control of pressure in the SkL. We find that on heating the melting transition occurs via a formation of grains with different orientations of hexagonal axes. On cooling, the fluctuating grains coalesce into larger clusters until a uniform orientation of hexagonal axes is slowly established. The observed scenario is caused by collective effects involving defects and is more complex than a simple picture of a transition driven by the unbinding and annihilation of dislocation and disclination pairs.

Investigation of infra-red spectra of three chiral liquid crystalline compounds with different fluorosubstitution of benzene ring

The IR spectra of three liquid crystalline compounds, differing only by the number of fluorine atoms in the molecular core, are investigated. The DFT+D3/BLYP-def2SVP calculations for isolated molecules are applied for the band assignments of the experimental IR spectra collected in the crystal phase. Additional DFT calculations, including the B3LYP exchange-correlation functional and def2TZVPP basis set, are also performed for the compound without the fluorine atoms in the molecular core. The scaling factors between the experimental and calculated peak positions, obtained at different levels of theory, are compared. For all compounds, the absorption bands assigned to the C=O stretching vibrations are analyzed as a function of temperature in the isotropic liquid, smectic phases, and crystal phase. The formation of hydrogen bonding involving the C=O groups during crystallization is inferred. The differences in the crystallization temperature of three compounds and the presence of the hexatic smectic phase for only one compound are discussed.

Effect of disorder on phases across two-dimensional thermal melting.

We study melting in a two-dimensional system of classical particles with Gaussian-core interactions in disordered environments. The pure system validates the conventional two-step melting with a hexatic phase intervening between the solid and the liquid. This picture is modified in the presence of pinning impurities. A random distribution of pinning centers forces a hexaticlike low-temperature phase that transits into a liquid at a single melting temperature T_{m}^{RP}. In contrast, pinning centers located at randomly chosen sites of a perfect crystal anchor a solid at low temperatures which undergoes a direct transition to the liquid at T_{m}^{CP}. Thus, the two-step melting is lost in either case of disorder. We discuss the characteristics of melting depending on the nature of the impurities.

Cell Division and Motility Enable Hexatic Order in Biological Tissues.

Biological tissues transform between solid- and liquidlike states in many fundamental physiological events. Recent experimental observations further suggest that in two-dimensional epithelial tissues these solid-liquid transformations can happen via intermediate states akin to the intermediate hexatic phases observed in equilibrium two-dimensional melting. The hexatic phase is characterized by quasi-long-range (power-law) orientational order but no translational order, thus endowing some structure to an otherwise structureless fluid. While it has been shown that hexatic order in tissue models can be induced by motility and thermal fluctuations, the role of cell division and apoptosis (birth and death) has remained poorly understood, despite its fundamental biological role. Here we study the effect of cell division and apoptosis on global hexatic order within the framework of the self-propelled Voronoi model of tissue. Although cell division naively destroys order and active motility facilitates deformations, we show that their combined action drives a liquid-hexatic-liquid transformation as the motility increases. The hexatic phase is accessed by the delicate balance of dislocation defect generation from cell division and the active binding of disclination-antidisclination pairs from motility. We formulate a mean-field model to elucidate this competition between cell division and motility and the consequent development of hexatic order.

The influence of Gaussian pinning on the melting scenario of a two-dimensional soft-disk system: First-order versus continuous transition

Two-dimensional systems are realized experimentally as thin layers on a substrate. The substrate can have some imperfections (defects of the crystalline structure, chemical impurities, etc.) with strong interactions with particles within and near the defects. Such randomly distributed centers of strong interactions are called ”pinning centers”. The presence of random pinning can substantially change the behavior of the system. It not only shifts the melting point of the system, but can also change the melting scenario itself. In the present paper the influence of Gaussian pinning on the melting scenario of a two-dimensional system of soft disks is studied by means of molecular dynamics simulation. We randomly introduce into the system of soft disks a set of “pinning centers” which attract the particles via the Gauss potential. We observe that increasing the depth of a Gaussian well leads to a change in the melting scenario of the system: from melting occurring via a first-order liquid-hexatic transition followed by a continuous hexatic-crystal transition to two continuous transitions through an intermediate hexatic phase. We show that there are still two transition stages for strong disorder, but the melting scenario is qualitatively different from that for weak disorder. The results demonstrate that the simple kind of quenched disorder can significantly affect the melting scenario of two-dimensional systems and offer the possibility of their application for the interpretation of complex experiments.

Colloid phase separation dynamics driven by chiral turbulent flows

Hydrodynamic interactions significantly influence phase-ordering kinetics in complex fluids. While passive fluid phase separation is well studied, the impact of active components remains relatively unexplored. We examine pure- and quasi-two-dimensional mixtures of attractive colloids and self-rotating particles in a solvent. Varying rotor rotational speed and area fraction yield diverse dynamic patterns such as percolated networks and round droplets composed of passive colloids alone. At intermediate rotation speeds, inertial chiral flows, accompanied by the inverse energy cascade, lead to self-similar power-law coarsening with a growth exponent of 1/2. The flows spontaneously organize within fluid domains, exhibiting turbulent and chiral characteristics. Surprisingly, these turbulent flows can sustain hexatic order hydrodynamically stabilized by the Magnus force under certain conditions. Conversely, at higher speeds, nonlinear hydrodynamic interactions impede phase separation. Our findings illuminate the intriguing dynamic interplay between phase separation and chiral turbulence, effectively bridging the realms of phase ordering and turbulent physics. Published by the American Physical Society 2024

Electronic topology with bound defect charges promotes intermediate hexatic phase in two-dimensional melting

Electronic topology with bound defect charges promotes intermediate hexatic phase in two-dimensional melting

Effect of distribution shape on the melting transition, local ordering, and dynamics in a model size-polydisperse two-dimensional fluid

Abstract We study the effect of particle size polydispersity (δ) on the melting transition (T *), local ordering, solid–liquid coexistence phase and dynamics of two-dimensional Lennard–Jones fluids up to moderate polydispersity by means of computer simulations. The particle sizes are drawn at random from the Gaussian (G) and uniform (U) distribution functions. For these systems, we further consider two different kinds of particles, viz., particles having the same mass irrespective of size, and in the other case the mass of the particle scales with its size. It is observed that with increasing polydispersity, the value of T * initially increases due to improved packing efficiency (ϕ) followed by a decrease and terminates at δ ≈ 8% (U-system) and 14% (G-system) with no significant difference for both mass types. The interesting observation is that the particular value at which ϕ drops suddenly coincides with the peak of the heat capacity (CP ) curve, indicating a transition. The quantification of local particle ordering through the hexatic order parameter (Q 6), Voronoi construction and pair correlation function reveals that the ordering decreases with increasing δ and T. Furthermore, the solid–liquid coexistence region for the G-system is shown to be comparatively wider in the T–δ plane phase diagram than that for the U system. Finally, the study of dynamics reveals that polydisperse systems relax faster compared to monodisperse systems; however, no significant qualitative differences, depending on the distribution type and mass polydispersity, are observed.

Manifestation of the Hexatic Phase in Confined Two-Dimensional Systems with Circular Symmetry

Manifestation of the Hexatic Phase in Confined Two-Dimensional Systems with Circular Symmetry

Multiscale defect cluster excitations in the melting transitions of two-dimensional Yukawa systems

In this work, we numerically demonstrate and classify the intermittently emerged multiscale defect clusters (DCs) composed of few to tens of disclinations, in the two-stage solid-hexatic-liquid melting transition of a two-dimensional Yukawa system. We uncover the topological pathways for their formation and how the crystalline-ordered domains (CODs) with different lattice orientations nearby DCs can be formed, which affect the structural order variations in the transitions. It is found that the six basic processes: the pair generation (I), dissociation (II), scattering (III), propagation (IV), recombination (V), and pair annihilation (VI) of dislocations, each through a single bond-breaking-replacement process, govern DC evolutions. Small DCs composed of antiparallel dislocations through process I by localized particle-shear motion dominate in the solid phase. The further successive combination of processes II to IV, through successive bond-breaking-replacement rotations by stringlike cooperative hopping of several particles, are responsible for the formation of open and ring-shaped stringlike DCs composed of connected dislocations, free dislocations, free disclinations, and CODs enclosed by stringlike DCs, dominated in the hexatic phase. The spreading of neighboring small DCs or the emergence of new small DCs nearby can generate larger DCs with tens of dislocations. The combinations of reversed basic processes can break or diminish a DC. Even though the two-stage transitions can also be signified by the onsets of the rapid rises of the free disclinations and free dislocations successively, the increases of the number and averaged size of multiscale DCs enclosing CODs play the key roles for the successive losses of translational and orientational orders in the two-stage phase transitions. Published by the American Physical Society 2024

Manifestation of the hexatic phase in confined two-dimensional systems with circular symmetry

Quasi-two-dimensional systems play an important role in the manufacture of various devices for the needs of nanoelectronics. Obviously, the functional efficiency of such systems depends on their structure, which can change during phase transitions under the influence of external conditions (for example, temperature). Until now, the main attention has been focused on the search for signals of phase transitions in continuous two-dimensional systems. One of the central issues is the analysis of the conditions for the nucleation of the hexatic phase in such systems, which is accompanied by the appearance of defects in the Wigner crystalline phase at a certain temperature. However, both practical and fundamental questions arise about the critical number of electrons at which the symmetry of the crystal lattice in the system under consideration will begin to break and, consequently, the nucleation of defects will start. The dependences of the orientational order parameter and the correlation function, which characterize topological phase transitions, as functions of the number of particles at zero temperature have been studied. The calculation results allows us to establish the precursors of the phase transition from the hexagonal phase to the hexatic one for N = 92, 136, 187, considered as an example.

A physics-based tessellation algorithm for particle assemblies on arbitrary surfaces

Interacting particle assemblies embedded on a surface are often used to model biophysical systems and to study new colloidal materials. The configurations resulting from the particles interacting with each other and with their substrate affect the system's physical properties, which depend on local symmetries and defects. It is therefore important to identify the nature and location of defects in the particle assembly. This task is often achieved using either the Voronoi tessellation algorithm or order parameters. Although very useful, they present limitations, especially when the particle assemblies are embedded on irregular or highly deformed 3D surfaces. In this work, we present a novel algorithm to generate the tessellation of particle assemblies on 3D surfaces of arbitrary geometry. The algorithm is based on the particles' physical interactions and does not require a priori information on the surface geometry. The resulting cells in the tessellation represent each particle's interactions with its first ring of neighboring particles. The algorithm is tested using 2D and 3D surfaces, with or without periodic boundary conditions, with holes or fully covered by particles, of regular geometry or highly deformed shape, and in the presence of positive, zero, and negative Gaussian curvature. In all cases, the presented algorithm is capable of generating a tessellation representing the particle interactions and highlighting the location and nature of the assembly defects. Finally, the proposed algorithm is compared with both Voronoi and hexatic order parameters in several representative cases to highlight similarities with existing methods as well as the advantages of the newly proposed algorithm.

Observation of the hexatic phase in a two-dimensional complex plasma using machine learning.

Complex plasmas consist of ionized gas and charged solid microparticles, representing the plasma state of soft matter. We apply machine learning methods to investigate a melting transition in a two-dimensional complex plasma. A convolutional neural network is constructed and trained with the numerical simulation. The hexatic phase is successfully identified and the evolution of topological defects is studied during melting transition in both simulations and experiments.

Phase separation kinetics and cluster dynamics in two-dimensional active dumbbell systems.

Molecular dynamics simulations were employed to investigate the phase separation process of a two-dimensional active Brownian dumbbell model. We evaluated the time dependence of the typical size of the dense component using the scaling properties of the structure factor, along with the averaged number of clusters and their radii of gyration. The growth observed is faster than in active disk models, and this effect is further enhanced under stronger activity. Next, we focused on studying the hexatic order of the clusters. The length associated with the orientational order increases algebraically with time and faster than for spherical active Brownian particles. Under weak active forces, most clusters exhibit a uniform internal orientational order. However, under strong forces, large clusters consist of domains with different orientational orders. We demonstrated that the latter configurations are not stable, and given sufficient time to evolve, they eventually achieve homogeneous configurations as well. No gas bubbles are formed within the clusters, even when there are patches of different hexatic order. Finally, attention was directed towards the geometry and motion of the clusters themselves. By employing a tracking algorithm, we showed that clusters smaller than the typical size at the observation time exhibit regular shapes, while larger ones display fractal characteristics. In between collisions or break-ups, the clusters behave as solid bodies. Their centers of mass undergo circular motion, with radii increasing with the cluster size. The angular velocity of the center of mass equals that of the constituents with respect to their center of mass. These observations were rationalised with a simple mechanical model.

Structural determinants of collapse by a monomolecular mimic of pulmonary surfactant at the physiological temperature.

Pulmonary surfactant forms a thin film on the liquid that lines the alveolar air-sacks. When compressed by the decreasing alveolar surface area during exhalation, the films avoid collapse from the air/water interface and reduce surface tension to exceptionally low levels. To define better the structure of compressed films that determines their susceptibility to collapse, we measured how cholesterol affects the structure and collapse of dipalmitoyl phosphatidylcholine (DPPC) monolayers at physiological temperatures. Grazing incidence X-ray diffraction (GIXD) and grazing incidence X-ray off-specular scattering (GIXOS) established the lateral and transverse structures of films on a Langmuir trough at a surface pressure of 45 mN m-1, just below the equilibrium spreading pressure at which collapse begins. Experiments with captive bubbles at a surface pressure of 51 mN m-1 measured how the steroid affects isobaric collapse. Mol fractions of the steroid (Xchol) at 0.05 removed the tilt by the acyl chains of DPPC, shifted the unit cell from centered rectangular to hexagonal, and dramatically decreased the long-range order. Higher Xchol produced no further change in diffraction, suggesting that cholesterol partitions into a coexisting disordered phase. Cholesterol had minimal effect on rates of collapse until Xchol reached 0.20. Our results demonstrate that the decreased coherence length, indicating conversion of positional order to short-range, is insufficient to make a condensed monolayer susceptible to collapse. Our findings suggest a two-step process by which cholesterol induces disorder. The steroid would first convert the film with crystalline chains to a hexatic phase before generating a fully disordered structure that is susceptible to collapse. These results lead to far-reaching consequences for formulation of animal-derived therapeutic surfactants. Our results suggest that removal of cholesterol from these preparations should be unnecessary below Xchol = 0.20.

Reversible-to-irreversible transition of colloidal polycrystals under cyclic athermal quasistatic deformation.

Cyclic loading on granular packings and amorphous media exhibits a transition from reversible elastic behavior to irreversible plasticity. The present study compares the irreversibility transition and microscopic details of colloidal polycrystals under oscillatory tensile-compressive and shear strain. Under both modes, the systems exhibit a reversible to irreversible transition. However, the strain amplitude at which the transition is observed is larger in the shear strain than in the tensile-compressive mode. The threshold strain amplitude is confirmed by analyzing the dynamical properties, such as mobility and atomic strain (von Mises shear strain and the volumetric strain). The structural changes are quantified using a hexatic order parameter. Under both modes of deformation, dislocations and grain boundaries in polycrystals disappear, and monocrystals are formed. We also recognize the dislocation motion through grains. The key difference is that strain accumulates diagonally in oscillatory tensile-compressive deformation, whereas in shear deformation, strain accumulation is along the x or y axis.

Study of the positional and orientational contributions to the Helmholtz free energy of a finite hard-disk system. A molecular dynamics analysis of its hexatic transition

Based on an equilibrium thermodynamic scheme, this work studies the separation of the Helmholtz free energy of a hard-disk system into its positional and orientational contributions. For the positional part, an accurate two dimensional version of the Carnahan-Starling equation of state is proposed, while a simple ansatz of the one particle partition function for the orientational part is proposed. The latter expression, which contains information about the probability of the norm of the six-fold orientational order parameter, is obtained through molecular dynamics simulations. Perhaps due to finite size effects, the ordering of the fluid is not a sudden phenomenon: the fluid-hexatic phase transition is preceded by a linear increase in the orientational contribution to the pressure of the fluid. A similar result is obtained for the hexatic-solid phase transition. Thus, the hexatic first-order phase transition is located between two linear ordering processes, consistent with the KTHNY theory. The proposed separation also predicts the existence of first order fluid-hexatic phase transition by using two procedures: the first, based on a purely bimodal probability density function, produces a pressure with a van del Waals-like first-order phase transition, while the second, considering density fluctuations, results in a flattened pressure phase transition.

Identification of the melting line in the two-dimensional complex plasmas using an unsupervised machine learning method

Machine learning methods have been widely used in the investigations of the complex plasmas. In this paper, we demonstrate that the unsupervised convolutional neural network can be applied to obtain the melting line in the two-dimensional complex plasmas based on the Langevin dynamics simulation results. The training samples do not need to be labeled. The resulting melting line coincides with those obtained by the analysis of hexatic order parameter and supervised machine learning method.