Hexatic Phase Research Articles

Laser-induced melting of two-dimensional dusty plasma system in RF discharge

We present a detailed analysis of experimental study, which shows clear evidence of a two-stage melting process of a quasi-two-dimensional dusty plasma system in a high-frequency gas discharge. We accurately calculated global parameters of the orientational and translational order, as well as their susceptibilities to determine two critical points, related to “solid-to-hexatic” and “hexatic-to-liquid” phase transitions. The nature of the emerging defects and changes in their mutual concentration, in addition to the estimate of core energy of free dislocations also counts in favor of the formation of an intermediate hexatic phase. These results are fully consistent with the Berezinsky–Kosterlitz–Thouless theory.

Dynamical arrest of topological defects in 2D hyperuniform disk packings

We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.

Signatures of continuous hexatic-liquid transition in two-dimensional melting.

Recent studies have shown that the melting of two-dimensional crystals can be either continuous or discontinuous, relying on multiple parameters such as particle stiffness, density, and particle size dispersity. However, what determines the continuity or discontinuity of the two-dimensional melting remains elusive. Here we study the two-dimensional melting of binary mixtures of soft-core particles. The two particle species are different in either particle size or particle stiffness. Starting with the mono-component systems which exhibit discontinuous hexatic-liquid transition, we gradually increase the particle size or stiffness dispersity and find that the hexatic-liquid coexistent region shrinks and eventually vanishes above a critical dispersity. Therefore, the growth of disorder caused by the particle size or stiffness dispersity leads to the discontinuous-continuous transition of the two-dimensional melting. We further find that as long as the melting is continuous the defect concentrations on the boundary between hexatic and liquid phases remain almost constant, accompanied by an almost constant correlation length. These characteristic defect concentrations and correlation length are universal and independent of particle interactions, temperature, and type of particle dispersity, which act as signatures of the continuous two-dimensional melting.

Investigation of crystallization kinetics and its relationship with molecular dynamics for chiral fluorinated glassforming smectogen 3F5HPhH6.

The phase transitions, crystallization kinetics and molecular dynamics of (S)-4'-(1-methylheptylcarbonyl)biphenyl-4-yl 4-[5-(2,2,3,3,4,4,4-heptafluorobutoxy)pent-1-oxy] benzoate (3F5HPhH6) are investigated by differential scanning calorimetry, polarizing optical microscopy and broadband dielectric spectroscopy. The vitrification of the antiferroelectric hexatic phase is observed for cooling rates ≥5 K min-1 and the fragility index determined from dielectric data is mf ≈ 90. Two regimes of non-isothermal cold crystallization are distinguished using the Kissinger and Augis-Bennett methods in the heating rate ranges of 1-5 K min-1 (larger activation energy) and 8-20 K min-1 (lower activation energy). The correlation between the time of non-isothermal cold crystallization (using isothermal approximation) and relaxation time of the α-process is determined. The obtained coupling coefficient ξ ≈ 0.7 and temperature dependence of the crystallization rate Z from the Ozawa model imply a mainly diffusion-controlled cold crystallization below 275 K. The Avrami exponents n and Ozawa exponents nO determined for isothermal melt crystallization and non-isothermal cold crystallization, respectively, weigh in favour of two- rather than three-dimensional crystal growth. The transition between crystal phases is observed on heating, with a lower activation energy for 1-3 K min-1 than for 5-20 K min-1 rates.

Surface roughening, premelting and melting of monolayer and bilayer crystals.

Dimensionality often strongly affects material properties and phase transition behaviors, but its effects on crystal surfaces, such as roughening and premelting, have been poorly studied. Our simulation revealed that these surface behaviors are distinct in monolayer and multilayer Lennard-Jones (LJ) crystals. Solid surfaces fluctuate as capillary waves during the roughening process, but complete roughening is preempted by premelting. As the melting temperature is approached, the thickness of the premelted liquid layer approaches a constant (i.e., blocked premelting) for monolayer crystals, but diverges as a power law (i.e., complete premelting) for bilayer and trilayer crystals. The surface liquids of monolayer crystals contain crystalline patches and exhibits rough liquid-vapour and liquid-crystal interfaces, in contrast to the normal surface liquids of bilayer and trilayer crystals. Monolayer crystals melt heterogeneously from the surface without forming a hexatic phase and produce many vacancies.

Two-step melting of the Weeks-Chandler-Anderson system in two dimensions.

We present a detailed numerical simulation study of a two-dimensional system of particles interacting via the Weeks-Chandler-Anderson potential, the repulsive part of the Lennard-Jones potential. With the reduction of density, the system shows a two-step melting: a continuous melting of solid to hexatic phase, followed by a first-order melting of hexatic to liquid. The solid-hexatic melting is consistent with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) scenario and shows dislocation unbinding. The first-order melting of the hexatic to the liquid phase, on the other hand, displays defect-strings formed at the hexatic-liquid interfaces. We present a detailed phase diagram in the density-temperature plane.

Three-step melting of hard superdisks in two dimensions.

We explore the link between the melting scenarios of two-dimensional systems of hard disks and squares through replica-exchange Monte Carlo simulations of hard superdisks. The well-known melting scenarios are observed in the disk and square limits, while we observe an unusual three-step scenario for dual shapes. We find that two mesophases mediate the melting: a hexatic phase and another fluid phase with a D_{2} local symmetry, we call it rhombatic, where both bond and particle orientational orders are quasi-long-range. Our results show that not only can the melting process of liquid-crystal forming molecules be complicated, where elongated shapes stabilize several mesophases, but also that of anisotropic quasispherical molecules.

Chiral Active Hexatics: Giant Number Fluctuations, Waves, and Destruction of Order.

Active materials, composed of internally driven particles, have properties that are qualitatively distinct from matter at thermal equilibrium. However, the most spectacular departures from equilibrium phase behavior are thought to be confined to systems with polar or nematic asymmetry. In this Letter, we show that such departures are also displayed by more symmetric phases such as hexatics if, in addition, the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density have giant number fluctuations. If the rotation rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large length scale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them nonmutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

Phase behavior of Lennard-Jones particles in two dimensions

The phase diagram of the prototypical two-dimensional Lennard-Jones (LJ) system, while extensively investigated, is still debated. In particular, there are controversial results in the literature with regard to the existence of the hexatic phase and the melting scenario. Here we study the phase behavior of two-dimensional range-limited LJ particles via large-scale numerical simulations. We demonstrate that at a high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. The hexatic phase occurs in a density range that vanishes as the temperature decreases so that at low-temperature melting occurs via a first-order liquid-solid transition. The temperature where the hexatic phase disappears is well above the liquid-gas critical temperature. The evolution of the density of topological defects confirms this scenario.

Binary mixtures of bent-core molecules forming distinct types of B4 phase nano- and microfilament morphologies

ABSTRACT The remarkable ability of certain molecules with a bent molecular shape to form hierarchically self-assembled helical building blocks with negative Gaussian or cylindrical curvature featuring in-layer hexatic ordering– so-called B4 phases – has quickly transformed these molecules into desirable building blocks for a variety of potential applications in optics, energy harvesting, and metamaterials. We here demonstrate that these building blocks, helical nanofilaments, helical microfilaments, and heliconical-layered nanocylinders, can to some degree be predictably blended. Supported by scanning as well as transmission electron microscopy and variable angle x-ray scattering data, the three bent-core compounds, each forming exactly one of these B4 morphologies, in binary mixtures at a 1:1 molar ratio, form either the third missing, or one of the two but with opposite handedness, or a random mixture of the two selected morphologies with larger overall dimensions. Furthermore, for two of the mixtures the a priori predicted handedness of the chiral filaments was experimentally confirmed. The third mixture with a priori predicted antagonistic handedness of the initial morphologies forms a combination of the two, one apparently achiral and the other one with opposite handedness.

Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

Active matter at high density: Velocity distribution and kinetic temperature.

We consider the solid or hexatic non-equilibrium phases of an interacting two-dimensional system of active Brownian particles at high density and investigate numerically and theoretically the properties of the velocity distribution function and the associated kinetic temperature. We obtain approximate analytical predictions for the shape of the velocity distribution and find a transition from a Mexican-hat-like to a Gaussian-like distribution as the persistence time of the active force changes from the small to the large persistence regime. Through a detailed numerical and theoretical analysis of the single-particle velocity variance, we report an exact analytical expression for the kinetic temperature of dense spherical self-propelled particles that holds also in the non-equilibrium regimes with large persistence times and discuss its range of validity.

Effect of particle size distribution on polydisperse hard disks.

Using Monte Carlo simulations, we systematically investigate the effect of particle size distribution on the phase behavior of polydisperse hard disks. Compared with the commonly used Gaussian-like polydisperse hard disks [P. Sampedro Ruiz, Q.-l. Lei, and R. Ni, Commun. Phys. 2, 70 (2019)], we find that the phase behavior of polydisperse hard-disk systems with lognormal and triangle distributions is significantly different. In polydisperse hard-disk systems of lognormal distributions, although the phase diagram appears similar to that of Gaussian-like polydisperse hard disks, the re-entrant melting of the hexatic or solid phase cannot be observed in sedimentation experiments. For polydisperse hard-disk systems of triangle distributions, the phase behavior is qualitatively different from the Gaussian-like and lognormal distributions, and we cannot reach any system of true polydispersity larger than 0.06, which is due to the special shape of the triangle distribution. Our results suggest that the exact particle size distribution is of primary importance in determining the phase behavior of polydisperse hard disks, and we do not have a universal phase diagram for different polydisperse hard-disk systems.

The influence of an applied magnetic field on the clusters formed by Stockmayer supracolloidal magnetic polymers

Using Molecular Dynamics computer simulations, we study how an applied magnetic field influences the shape, integrity and internal structure of clusters formed by Stockmayer supracolloidal magnetic polymers (SMPs). We consider SMPs of four different topologies: chain-, Y-, X- and ring-like ones. We find that the highest macroscopic deformation and the strongest monomer rearrangements from a liquid to a local hexatic order is observed for clusters formed by chain-like SMPs. The highest magnetic susceptibility, however, is exhibited by the clusters composed of Y- and X-like SMPs. Clusters formed by ring-like SMPs are basically not affected by the field strengths considered here. It is worth mentioning that those fields are sufficient to cause the dissociation of the clusters formed by other topologies of SMPs.

Skyrmion Lattice Phases in Thin Film Multilayer

AbstractPhases of matter are ubiquitous with everyday examples including solids and liquids. In reduced dimensions, particular phases, such as the 2D hexatic phase and corresponding phase transitions occur. A particularly exciting example of 2D ordered systems are skyrmion lattices, where in contrast to previously studied 2D colloid systems, the skyrmion size and density can be tuned by temperature and magnetic fields. This allows for the system to be driven from a liquid phase to the onset of a hexatic phase as deduced from the analysis of the hexagonal order. Using coarse‐grained molecular dynamics simulations of soft disks, the skyrmion interaction potentials are determined, and it is found that the simulations are able to reproduce the phase behavior. This shows that not only the static behavior of skyrmions is qualitatively well described in terms of a simple 2D model system but skyrmion lattices are versatile and tunable 2D model systems that allow for studying phases and phase transitions in reduced dimensions.

Hybrid materials from tri-aryl amine organogelators and poly[vinyl chloride] networks

Hybrid thermoreversible gels have been prepared from polyvinyl chloride (PVC) and tri-aryl tri-amines organogelators (TATA-C11) in bromobenzene. A thermodynamic investigation by DSC has shown that the TATA-C11 formation and melting temperatures are not altered by the presence of PVC chains, nor are the formation and melting enthalpies. Scanning electron microscopy observations have revealed as each network are clearly distinguished, so that the hybrid gel is simply a combination at the micron level of both original gels. X-ray diffraction experiments have shown that the TATA-C11 structure in bromobenzene differs from its solid state, and is rather reminiscent of a hexatic phase, possibly due to the occurrence of a molecular compound. The structure of the TATA-C11 moiety does not change in the hybrid gel. Finally, the rheological properties have been studied. It is observed that the modulus of the hybrid gel greatly exceeds the Voigt's upper limit (larger than a simple additivity of the moduli). This effect is examined in the light of a possible de-solvation of the amorphous part of the PVC fibrils (de-plasticization).

Dense hard disk ordering: influence of bidispersity and quenched disorder

Using Monte Carlo simulations, the impact on structural ordering in two-dimensional systems via the interplay of size bidispersity and quenched disorder in the form of an externally applied spatially random potential, is studied for a system of hard disks. By scanning across a wide range of dense packing fractions, size ratios and roughness of the applied potential, the phase diagram is constructed, which demonstrates that both quenched and size disorders shift the onset of translational order to higher packings, while maintaining the presence of the intermediate hexatic phase. At larger disorder strengths, the signatures of structural order are absent within the range of investigated packing fractions. Further, the dynamics with increasing potential strength is analysed for the mono-component system to obtain a spatio-temporal description of the melting process. Finally, the influence of the externally rough field on the Mermin–Wagner fluctuations, characteristic to two-dimensional systems, is investigated.

Melting of a skyrmion lattice to a skyrmion liquid via a hexatic phase.

The phase transition most commonly observed is probably melting, a transition from ordered crystalline solids to disordered isotropic liquids. In three dimensions, melting is a single, first-order phase transition. In two-dimensional systems, however, theory predicts a general scenario of two continuous phase transitions separated by an intermediate, oriented liquid state, the so-called hexatic phase with short-range translational and quasi-long-range orientational orders. Such hexatic phases occur in colloidal systems, Wigner solids and liquid crystals, all composed of real-matter particles. In contrast, skyrmions are countable soliton configurations with non-trivial topology and these quasi-particles can form two-dimensional lattices. Here we show, by direct imaging with cryo-Lorentz transmission electron microscopy, that magnetic field variations can tune the phase of the skyrmion ensembles in Cu2OSeO3 from a two-dimensional solid through the long-speculated skyrmion hexatic phase to a liquid. The local spin order persists throughout the process. Remarkably, our quantitative analysis demonstrates that the aforementioned topological-defect-induced crystal melting scenario well describes the observed phase transitions.

Attraction Tames Two-Dimensional Melting: From Continuous to Discontinuous Transitions.

Two-dimensional systems may admit a hexatic phase and hexatic-liquid transitions of different natures. The determination of their phase diagrams proved challenging, and indeed, those of hard disks, hard regular polygons, and inverse power-law potentials have only recently been clarified. In this context, the role of attractive forces is currently speculative, despite their prevalence at both the molecular and colloidal scale. Here, we demonstrate, via numerical simulations, that attraction promotes a discontinuous melting scenario with no hexatic phase. At high-temperature, Lennard-Jones particles and attractive polygons follow the shape-dominated melting scenario observed in hard disks and hard polygons, respectively. Conversely, all systems melt via a first-order transition with no hexatic phase at low temperature, where attractive forces dominate. The intermediate temperature melting scenario is shape dependent. Our results suggest that, in colloidal experiments, the tunability of the strength of the attractive forces allows for the observation of different melting scenarios in the same system.

Vertical Lamellae Formed by Two-Step Annealing of a Rod-Coil Liquid Crystalline Block Copolymer Thin Film.

Silicon-containing block copolymer thin films with high interaction parameter and etch contrast are ideal candidates to generate robust nanotemplates for advanced nanofabrication, but they typically form in-plane oriented microdomains as a result of the dissimilar surface energies of the blocks. Here, we describe a two-step annealing method to produce vertically aligned lamellar structures in thin film of a silicon-containing rod–coil thermotropic liquid crystalline block copolymer. The rod–coil block copolymer with the volume fraction of the Si-containing block of 0.22 presents an asymmetrical lamellar structure in which the rod block forms a hexatic columnar nematic liquid crystalline phase. A solvent vapor annealing step first produces well-ordered in-plane cylinders of the Si-containing block, then a subsequent thermal annealing promotes the phase transition from in-plane cylinders to vertical lamellae. The pathways of the order–order transition were examined by microscopy and in situ using grazing incidence small-angle X-ray scattering and wide-angle X-ray scattering.