Hexatic phase in the two-dimensional Gaussian-core model

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.

Understanding the glassy dynamics from melting temperatures in binary glass-forming liquids

It is natural to expect that small particles in binary mixtures move faster than large ones. However, in binary glass-forming liquids with soft-core particle interactions, we observe the counterintuitive dynamic reversal between large and small particles along with the increase of pressure by performing molecular dynamics simulations. The structural relaxation (dynamic heterogeneity) of small particles is faster (weaker) than large ones at low pressures, but becomes slower (stronger) above a crossover pressure. In contrast, this dynamic reversal never happens in glass-forming liquids with hard-core interactions. We find that the difference of the effective melting temperatures felt by large and small particles can be used to understand the dynamic reversal. In binary mixtures, we derive effective melting temperatures of large and small particles simply from the conversion of units and find that particles with a higher effective melting temperature usually undergo a slower and more heterogeneous relaxation. The presence (absence) of the dynamic reversal in soft-core (hard-core) systems is simply due to the non-monotonic (monotonic) behavior of the melting temperature as a function of pressure. Interestingly, by manipulating the relative softness between large and small particles, we obtain a special case of soft-core systems, in which large particles always have higher effective melting temperatures than small ones. As a result, the dynamic reversal is totally eliminated. Our work provides another piece of evidence of the underlying connections between the properties of non-equilibrium glass-formers and equilibrium crystal-formers.

Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.

Two-Dimensional Melting of Two- and Three-Component Mixtures

We elucidate the interplay between diverse two-dimensional melting pathways and establish solid-hexatic and hexatic-liquid transition criteria via the numerical simulations of the melting transition of two- and three-component mixtures of hard polygons and disks. We show that a mixture's melting pathway may differ from its components and demonstrate eutectic mixtures that crystallize at a higher density than their pure components. Comparing the melting scenario of many two- and three-component mixtures, we establish universal melting criteria: the solid and hexatic phases become unstable as the density of topological defects, respectively, overcomes ρ_{d,s}≃0.046 and ρ_{d,h}≃0.123.

Anomalous behavior of a two-dimensional Hertzian disk system

The anomalous behavior of a two-dimensional system of Hertzian disks with exponent α=7/2 has been studied using the method of molecular dynamics. The phase diagram of this system is the melting line of a triangular crystal with several maxima and minima. Waterlike density and diffusion anomalies have been found in the reentrant melting regions. Noteworthy, a density anomaly has been observed not only in the liquid and hexatic but also in the solid phase. The calculations of the phonon spectra of longitudinal and transverse modes have yielded negative dependence of the frequency of transverse modes on density along all directions in the regions with a density anomaly. This indicates an association of the density anomaly with transverse oscillations of the crystal lattice. The regions of density and diffusion anomalies have been drawn on the phase diagram. It has been found that the stability regions of anomalous diffusion extend to temperatures well above the maximum melting point T=0.0058 of the triangular crystal.

Elongation and percolation of defect motifs in anisotropic packing problems

We examine the regime between crystalline and amorphous packings of anisotropic objects on surfaces of different genus by continuously varying their size distribution or shape from monodispersed spheres to bidispersed mixtures or monodispersed ellipsoidal particles; we also consider an anisotropic variant of the Thomson problem with a mixture of charges. With increasing anisotropy, we first observe the disruption of translational order with an intermediate orientationally ordered hexatic phase as proposed by Nelson, Rubinstein and Spaepen, and then a transition to amorphous state. By analyzing the structure of the disclination motifs induced, we show that the hexatic-amorphous transition is caused by the growth and connection of disclination grain boundaries, suggesting this transition lies in the percolation universality class in the scenarios considered.

Sensitivity of pair statistics on pair potentials in many-body systems

We study the sensitivity and practicality of Henderson's theorem in classical statistical mechanics, which states that the pair potential v(r) that gives rise to a given pair correlation function g₂(r) [or equivalently, the structure factor S(k)] in a classical many-body system at number density ρ and temperature T is unique up to an additive constant. While widely invoked in inverse-problem studies, the utility of the theorem has not been quantitatively scrutinized to any large degree. We show that Henderson's theorem has practical shortcomings for disordered and ordered phases for certain densities and temperatures. Using proposed sensitivity metrics, we identify illustrative cases in which distinctly different potential functions give very similar pair correlation functions and/or structure factors up to their corresponding correlation lengths. Our results reveal that due to a limited range and precision of pair information in either direct or reciprocal space, there is effective ambiguity of solutions to inverse problems that utilize pair information only, and more caution must be exercised when one claims the uniqueness of any resulting effective pair potential found in practice. We have also identified systems that possess virtually identical pair statistics but have distinctly different higher-order correlations. Such differences should be reflected in their individually distinct dynamics (e.g., glassy behaviors). Finally, we prove a more general version of Henderson's theorem that extends the uniqueness statement to include potentials that involve two- and higher-body interactions.

Phase behavior of a two-dimensional core-softened system: new physical insights

In this work, we report results of extensive computer simulations regarding the phase behavior of a core-softened system. By using structural and thermodynamic descriptors, as well as self-diffusion coefficients, we provide a comprehensive view of the rich phase behavior displayed by the particular instance of the model studied in here. Our calculations agree with previously published results focused on a smaller region in the temperature-density parameter space (Dudalov et al 2014 Soft Matter 10 4966). In this work, we explore a broader region in this parameter space, and uncover interesting fluid phases with low-symmetry local order, that were not reported by previous works. Solid phases were also found, and have been previously characterized in detail by (Kryuchkov et al 2018 Soft Matter 14 2152). Our results support previously reported findings, and provide new physical insights regarding the emergence of order as disordered phases transform into solids by providing radial distribution function maps and specific heat data. Our results are summarized in terms of a phase diagram.

Accurate determination of the translational correlation function of two-dimensional solids

The identification of the different phases of a two-dimensional (2D) system, which might be solid, hexatic, or liquid, requires the accurate determination of the correlation function of the translational and bond-orientational order parameters. According to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory, in the solid phase the translational correlation function decays algebraically, as a consequence of the Mermin-Wagner long-wavelength fluctuations. However, recent results have shown an exponential-like decay. By revisiting different definitions of the translational correlation function commonly used in the literature, here we clarify that the observed exponential-like decay in the solid phase results from an inaccurate determination of the symmetry axis of the solid; the expected power-law behavior is recovered when the symmetry axis is properly identified. We show that, contrary to the common assumption, the symmetry axis of a 2D solid is not fixed by the direction of its global bond-orientational parameter, and we introduce an approach allowing one to determine the symmetry axis from a real space analysis of the sample.

Orientational correlations in fluids with quenched disorder

Snapshots of colloidal particles moving on disordered two-dimensional substrates can be used to extract equal-time many-body correlations in their positions. To understand the systematics of these correlations, we perform Monte Carlo simulations of a two-dimensional model fluid placed in a quenched disordered background. We use configurations generated from these simulations to compute translational and orientational two-point correlations at equal time, concentrating on correlations in local orientational order as a function of density and disorder strength. We calculate both the disorder averaged version of conventional two-point correlation functions for orientational order, as well as the disorder averaged version of a novel correlation function of time-averaged disorder-induced inhomogeneities in local orientation analogous to the Edwards-Anderson correlation function in spin systems. We demonstrate that these correlations can exhibit interesting nonmonotonic behavior in proximity to the underlying fluid-solid transition and suggest that this prediction should be experimentally accessible.

Phase diagram for two-dimensional layer of soft particles

The phase diagram of a monolayer of soft particles described by the Daoud-Cotton model for star polymers is presented. Ground state calculations and grand canonical Monte Carlo simulations are used to determine the phase behavior as a function of the number of arms on the star and the areal coverage of the soft particles. The phase diagram exhibits rich behavior including reentrant melting and freezing and solid-solid transitions with triangular, stripe, honeycomb and kagome phases. These structures in 2D are analogous to the structures observed in 3D. The evolution of the structure factor with density is qualitatively similar to that measured in experiments for polymer grafted nanocrystals [Chen et al., Macromolecules, 2017, 50, 9636].

Two-dimensional crystals of star polymers: a tale of tails

The formation of non-hexagonal crystalline structures by the organisation of colloidal nanoparticles often involves the use of complex particles with anisotropic shape or interactions or the imposition of non-uniform external fields. Here we explore how unusual symmetries can be created using experimentally realistic particles that interact through isotropic and purely repulsive potentials. In particular, we use simulations to explore the phase behavior of two-dimensional systems of star polymers. We uncover how the tail of the pair potential has a large role in dictating the phase behavior. Star polymers interacting in the far field with a Gaussian potential only form hexagonal phases, while an exponential tail gives rise to stable primitive oblique and honeycomb lattices. We identify the ratio in strength between long and short range interactions and the nature of the transition between these regimes as crucial parameters to predict when non-hexagonal crystals of star polymers can be stable. This leads to experimental design rules for creating star polymers which should exhibit unusual lattice formation.

Static and dynamic properties of two-dimensional Coulomb clusters

We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional confinements across the crossover from solid- to liquid-like behaviors. While static correlations that investigate the translational and bond orientational order in the confinements show the footprints of hexatic-like phase at low temperatures, dynamics of the particles slow down considerably in this phase, reminiscent of a supercooled liquid. Using density correlations, we probe long-lived heterogeneities arising from the interplay of the irregularity in the confinement and long-range Coulomb interactions. The relaxation at multiple time scales show stretched-exponential decay of spatial correlations in irregular traps. Temperature dependence of characteristic time scales, depicting the structural relaxation of the system, show striking similarities with those observed for the glassy systems, indicating that some of the key signatures of supercooled liquids emerge in confinements with lower spatial symmetries.

Translationally invariant colloidal crystal templates

We show that dynamic, feed-back controlled optical traps, whose positions depend on the instantaneous local configuration of particles in a pre-determined way, can stabilise colloidal particles in finite lattices of any given symmetry. Unlike in a static template, the crystal so formed is invariant under uniform translations and retains all possible zero energy modes. We demonstrate this in silico by stabilising the unstable two-dimensional square lattice in a model soft solid with isotropic interactions.

Two-dimensional melting of colloids with long-range attractive interactions

The solid-liquid melting transition in a two-dimensional (2-D) attractive colloidal system is visualized using superparamagnetic colloids that interact through a long-range isotropic attractive interaction potential, which is induced using a high-frequency rotating magnetic field. Various experiments, supported by Monte Carlo simulations, are carried out over a range of interaction potentials and densities to determine structure factors, Lindermann parameters, and translational and orientational order parameters. The system shows a first-order solid-liquid melting transition. Simulations and experiments suggest that dislocations and disclinations simultaneously unbind during melting. This is in direct contrast with reports of 2-D melting of paramagnetic particles that interact with a repulsive interaction potential.

Structure and dynamics in network-forming materials

The study of the structure and dynamics of network-forming materials is reviewed. Experimental techniques used to extract key structural information are briefly considered. Strategies for building simulation models, based on both targeting key (experimentally-accessible) materials and on systematically controlling key model parameters, are discussed. As an example of the first class of materials, a key target system, SiO₂, is used to highlight how the changing structure with applied pressure can be effectively modelled (in three dimensions) and used to link to both experimental results and simple structural models. As an example of the second class the topology of networks of tetrahedra in the MX₂ stoichiometry are controlled using a single model parameter linked to the M-X-M bond angles. The evolution of ordering on multiple length-scales is observed as are the links between the static structure and key dynamical properties. The isomorphous relationship between the structures of amorphous Si and SiO₂ is discussed as are the similarities and differences in the phase diagrams, the latter linked to potential polyamorphic and 'anomalous' (e.g. density maxima) behaviour. Links to both two-dimensional structures for C, Si and Ge and near-two-dimensional bilayers of SiO₂ are discussed. Emerging low-dimensional structures in low temperature molten carbonates are also uncovered.

One-dimensional Gaussian-core fluid: ordering and crossover from normal diffusion to single-file dynamics

The peculiarity of a bounded pair potential in combination with strong confinement brings some quite interesting new phenomenology in the structure and dynamics of one-dimensional colloidal systems. Such behaviour is atypical in comparison with colloidal systems interacting with potentials that diverge at the origin. In this contribution, by means of molecular dynamics simulations, a confined one-dimensional model of particles interacting via a Gaussian-core pair potential is studied. We explore the effects of confinement, density and temperature on the structural and dynamical correlation functions. Our findings indicate that the static and dynamic liquid-state anomalies already reported in open systems are also present in this 1D model system. Using the radial distribution function and the static structure factor to characterise the spatial ordering, it is observed that the system remains fluid at all densities. However, when the reduced temperature is above 0.03, it displays typical features of a liquid regime, i.e., there exist short-range spatial correlations among particles. In contrast, at lower temperatures and densities, where the particle-particle interaction dominates, the system behaves structurally and dynamically similar to a hard-core repulsive system. In such a region, interestingly, there is a crossover from a liquid to a solid-like regime. At any given temperature, the system undergoes a sort of reentrant structural behaviour as the density increases. At either high densities or temperatures, particle correlations vanish, thus, the system exhibits structural and dynamical properties similar to those of an ideal gas. To examine a possible correlation between the structural anomalies and the diffusive behaviour, the mean-square displacement and the self-intermediate scattering function are also computed. From these observables, we establish the thermodynamic phase-space points where the dynamical behaviour is non-monotonic. In conjunction with the observed anomalous diffusion, we have found a dynamical crossover from single-file diffusion, which is characteristic of one-dimensional systems with a well-defined hard-core, to the ordinary Fickian diffusion present in open systems.

Density Affects the Nature of the Hexatic-Liquid Transition in Two-Dimensional Melting of Soft-Core Systems

We find that both continuous and discontinuous hexatic-liquid transitions can happen in the melting of two-dimensional solids of soft-core disks. For three typical model systems, Hertzian, harmonic, and Gaussian-core models, we observe the same scenarios. These systems exhibit reentrant crystallization (melting) with a maximum melting temperature T_{m} happening at a crossover density ρ_{m}. The hexatic-liquid transition at a density smaller than ρ_{m} is discontinuous. Liquid and hexatic phases coexist in a density interval, which becomes narrower with increasing temperature and tends to vanish approximately at T_{m}. Above ρ_{m}, the transition is continuous, in agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory. For these soft-core systems, the nature of the hexatic-liquid transition depends on density (pressure), with the melting at ρ_{m} being a plausible transition point from discontinuous to continuous hexatic-liquid transition.

Grain-boundary-induced melting in quenched polycrystalline monolayers

Melting in two dimensions can successfully be explained with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario which describes the formation of the high-symmetry phase with the thermal activation of topological defects within an (ideally) infinite monodomain. With all state variables being well defined, it should hold also as freezing scenario where oppositely charged topological defects annihilate. The Kibble-Zurek mechanism, on the other hand, shows that spontaneous symmetry breaking alongside a continuous phase transition cannot support an infinite monodomain but leads to polycrystallinity. For any nonzero cooling rate, critical fluctuations will be frozen out in the vicinity of the transition temperature. This leads to domains with different director of the broken symmetry, separated by a defect structure, e.g., grain boundaries in crystalline systems. After instantaneously quenching a colloidal monolayer from a polycrystalline to the isotropic fluid state, we show that such grain boundaries increase the probability for the formation of dislocations. In addition, we determine the temporal decay of defect core energies during the first few Brownian times after the quench. Despite the fact that the KTHNY scenario describes a continuous phase transition and phase equilibrium does not exist, melting in polycrystalline samples starts at grain boundaries similar to first-order phase transitions.

From Crystals to Disordered Crystals: A Hidden Order-Disorder Transition

To distinguish between order and disorder is of fundamental importance to understanding solids. It becomes more significant with recent observations that solids with high structural order can behave like disordered solids, while properties of disordered solids can approach crystals under certain circumstance. It is then imperative to understand when and how disorder takes effect to deviate the properties of a solid from crystals and what the correct factors are to control the behaviours of solids. Here we answer these questions by reporting the finding of a hidden order-disorder transition from crystals to disordered crystals for static packings of frictionless spheres. While the geometric indicators are mostly blind to the transition, disordered crystals already exhibit properties apart from crystals. The transition approaches the close packing of hard spheres, giving rise to the singularity of the close packing point. We evidence that both the transition and properties of disordered crystals are jointly determined by the structural order and density. Near the transition, the elastic moduli and coordination number of disordered crystals show particular pressure dependence distinct from known behaviours of both crystals and jammed solids. The discovery of the transition therefore reveals some unknown aspects of solids.

Random pinning changes the melting scenario of a two-dimensional core-softened potential system

In experiments two-dimensional systems are realized mainly on solid substrates, which introduce quenched disorder due to some inherent defects. The defects of substrates influence the melting scenario of the systems and have to be taken into account in the interpretation of experimental results. We present the results of molecular dynamics simulations of a two-dimensional system with a core-softened potential in which a small fraction of the particles is pinned, inducing quenched disorder. Ppotentials of this type are widely used for the qualitative description of systems with waterlike anomalies. In our previous publications it was shown that the system demonstrates an anomalous melting scenario: at low densities the system melts through two continuous transitions in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory with an intermediate hexatic phase, while at high densities the conventional first-order melting transition takes place. We find that the well-known disorder-induced widening of the hexatic phase occurs at low densities, while in the high-density part of the phase diagram random pinning transforms the first-order melting into two transitions: a continuous KTHNY-like solid-hexatic transition and a first-order hexatic-isotropic liquid transition.

Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases

Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space R^{d}. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter.

Probing the existence of phase transitions in one-dimensional fluids of penetrable particles

Phase transitions in one-dimensional classical fluids are usually ruled out by using van Hove's theorem. A way to circumvent the conclusions of the theorem is to consider an interparticle potential that is everywhere bounded. Such is the case of, e.g., the generalized exponential model of index 4 (GEM-4 potential), which in three dimensions gives a reasonable description of the effective repulsion between flexible dendrimers in a solution. An extensive Monte Carlo simulation of the one-dimensional GEM-4 model [S. Prestipino, Phys. Rev. E 90, 042306 (2014)] has recently provided evidence of an infinite sequence of low-temperature cluster phases, however, also suggesting that upon pushing the simulation forward what seemed a true transition may eventually prove to be only a sharp crossover. We hereby investigate this problem theoretically by use of three different and increasingly sophisticated approaches (i.e., a mean-field theory, the transfer matrix of a lattice model of clusters, and the exact treatment of a system of point clusters in the continuum) to conclude that the alleged transitions of the one-dimensional GEM-4 system are likely just crossovers.

Soft repulsive interactions, particle rearrangements and size selection in the self-assembly of nanoparticles at liquid interfaces

In the adsorption of nanoparticles at liquid interfaces, soft and short ranged repulsive effective interactions between the nanoparticles at the interface may eventually induce crowding, slow dynamics and jamming at high surface coverage. These phenomena can interfere during the adsorption process, significantly slowing down its kinetics. Here, by means of numerical simulations, we find that modifying the effective interactions, which can be achieved for example by grafting differently functionalized polymer shells on the bare nanoparticles, may qualitatively change such interplay. In particular our results suggest that, in the presence of ultrasoft particle interactions such as the ones described by a Gaussian Core Model potential, a small size polydispersity can be sufficient to decouple the adsorption kinetics from the slow dynamics that develops at the interface, due to a qualitative change from an irreversible adsorption controlled by particle rearrangements at the interface to one dominated by size selection mechanisms. These findings may be useful to achieve higher surface coverages and faster adsorption kinetics.

Cluster phases of penetrable rods on a line

Phase transitions are uncommon among homogeneous one-dimensional fluids of classical particles owing to a general nonexistence result due to van Hove. A way to circumvent van Hove's theorem is to consider an interparticle potential that is finite everywhere. Of this type is the generalized exponential model of index 4 (GEM4 potential), a model interaction which in three dimensions provides an accurate description of the effective pair repulsion between dissolved soft macromolecules (e.g., flexible dendrimers). Using specialized free-energy methods, I reconstruct the equilibrium phase diagram of the one-dimensional GEM4 system, showing that, apart from the usual fluid phase at low densities, it consists of an endless sequence of cluster fluid phases of increasing pressure, having a sharp crystal appearance for low temperatures. The coexistence line between successive phases in the sequence invariably terminates at a critical point. Focussing on the first of such transitions, I show that the growth of the two-cluster phase from the metastable ordinary fluid is extremely slow, even for large supersaturations. Finally, I clarify the apparent paradox of the observation of an activation barrier to nucleation in a system where, due to the dimensionality of the hosting space, the critical radius is expected to vanish.

Specific heat in two-dimensional melting

We report the specific heat cN around the melting transition(s) of micrometer-sized superparamagnetic particles confined in two dimensions, calculated from fluctuations of positions and internal energy, and corresponding Monte Carlo simulations. Since colloidal systems provide single particle resolution, they offer the unique possibility to compare the experimental temperatures of the peak position of cN(T) and symmetry breaking, respectively. While order parameter correlation functions confirm the Kosterlitz-Thouless-Halperin-Nelson-Young melting scenario where translational and orientational order symmetries are broken at different temperatures with an intermediate so called hexatic phase, we observe a single peak of the specific heat within the hexatic phase, with excellent agreement between experiment and simulation. Thus, the peak is not associated with broken symmetries but can be explained with the total defect density, which correlates with the maximum increase of isolated dislocations. The absence of a latent heat strongly supports the continuous character of both transitions.

Two-stage melting induced by dislocations and grain boundaries in monolayers of hard spheres

Melting in two-dimensional systems has remained controversial as theory, simulations, and experiments show contrasting results. One issue that obscures this discussion is whether or not theoretical predictions on strictly 2D systems describe those on quasi-2D experimental systems, where out-of-plane fluctuations may alter the melting mechanism. Using event-driven molecular dynamics simulations, we find that the peculiar two-stage melting scenario of a continuous solid-hexatic and a first-order hexatic-liquid transition as observed for a truly 2D system of hard disks [Bernard and Krauth, Phys. Rev. Lett., 2011, 107, 155704] persists for a quasi-2D system of hard spheres with out-of-plane particle motions as high as half the particle diameter. By calculating the renormalized Young's modulus, we show that the solid-hexatic transition is of the Kosterlitz-Thouless type and occurs via dissociation of bound dislocation pairs. In addition, we find a first-order hexatic-liquid transition that seems to be driven by spontaneous proliferation of grain boundaries.

How dimensionality changes the anomalous behavior and melting scenario of a core-softened potential system?

We present a computer simulation study of the phase diagram and anomalous behavior of two-dimensional (2D) and three-dimensional (3D) classical particles repelling each other through an isotropic core-softened potential. As in the analogous three-dimensional case, in 2D a reentrant-melting transition occurs upon compression under not too high pressure, along with a spectrum of thermodynamic and dynamic anomalies in the fluid phase. However, in two dimensions the order of the region of anomalous diffusion and the region of structural anomaly is inverted in comparison with the 3D case, where there exists a water-like sequence of anomalies, and has a silica-like sequence. In the low density part of the 2D phase diagram, melting is a continuous two-stage transition, with an intermediate hexatic phase. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario for this melting transition. On the other hand, at high density part of the phase diagram one first-order transition takes place.

Melting of a finite-sized two-dimensional colloidal crystal

We have studied the melting process of a finite-sized two-dimensional colloidal crystal by video microscopy. The local area fraction ϕ and the local hexatic orientational order parameter ψ(6) have been evaluated for respective Voronoi cells in the crystal. The histogram of ϕ exhibits a peak and the peak ϕ continuously decreases with the time elapsed. The histogram of |ψ(6)| shows an abrupt broadening for ϕ < 0.65. This critical value of ϕ is the transition point between the hexatic and dense liquid phases in finite crystal. We have also evaluated ϕ and |ψ(6)| as a function of the distance from the center of the crystal r. ϕ(r) is almost constant within the crystal and monotonously decreases with the time elapsed. |ψ(6)(r)| gradually decreases with r but there is the core with |ψ(6) = 1 at earlier time stage. The temporal change of the average ϕ within the crystal is qualitatively explained by the slow diffusion of the particles situated at the crystal edge. The steric repulsion between the particles within the crystal enhances the expansion rate of the crystal edge. Overall melting behavior is same in the crystals with different sizes. We have also studied the melting of a finite-sized crystal composed of soft-core particles by Brownian dynamics simulation and verified the finite-size effect on the melting process. The simulated behavior is qualitatively in good agreement with the experimental results.

Anomalous melting scenario of the two-dimensional core-softened system

We present a computer simulation study of the phase behavior of two-dimensional (2D) classical particles repelling each other through an isotropic core-softened potential. As in the analogous three-dimensional (3D) case, a reentrant-melting transition occurs upon compression for not too high pressures, along with a spectrum of waterlike anomalies in the fluid phase. However, in two dimensions in the low density part of the phase diagram melting is a continuous two-stage transition, with an intermediate hexatic phase. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young scenario for this melting transition. On the other hand, at the high density part of the phase diagram one first-order transition takes place.

Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder

Using both video microscopy of superparamagnetic colloidal particles confined in two dimensions and corresponding computer simulations of repulsive parallel dipoles, we study the formation of fluctuating orientational clusters and topological defects in the context of the KTHNY-like melting scenario under quenched disorder. We analyze cluster densities, average cluster sizes, and the population of noncluster particles, as well as the development of defects, as a function of the system temperature and disorder strength. In addition, the probability distribution of clustering and orientational order is presented. We find that the well-known disorder-induced widening of the hexatic phase can be traced back to the distinct development characteristics of clusters and defects along the melting transitions from the solid phase to the hexatic phase to the isotropic fluid.

Two-dimensional melting under quenched disorder

We study the influence of quenched disorder on the two-dimensional melting behavior of superparamagnetic colloidal particles, using both video microscopy and computer simulations of repulsive parallel dipoles. Quenched disorder is introduced by pinning a fraction of the particles to an underlying substrate. We confirm the occurrence of the Kosterlitz-Thouless-Halperin-Nelson-Young scenario and observe an intermediate hexatic phase. While the fluid-hexatic transition remains largely unaffected by disorder, the hexatic-solid transition shifts to lower temperatures with increasing disorder. This results in a significantly broadened stability range of the hexatic phase. In addition, we observe spatiotemporal critical(like) fluctuations, which are consistent with the continuous character of the phase transitions. Characteristics of first-order transitions are not observed.

Volume crossover in deeply supercooled water adiabatically freezing under isobaric conditions

The irreversible return of a supercooled liquid to stable thermodynamic equilibrium often begins as a fast process which adiabatically drives the system to solid-liquid coexistence. Only at a later stage will solidification proceed with the expected exchange of thermal energy with the external bath. In this paper we discuss some aspects of the adiabatic freezing of metastable water at constant pressure. In particular, we investigated the thermal behavior of the isobaric gap between the molar volume of supercooled water and that of the warmer ice-water mixture which eventually forms at equilibrium. The available experimental data at ambient pressure, extrapolated into the metastable region within the scheme provided by the reference IAPWS-95 formulation, show that water ordinarily expands upon (partially) freezing under isenthalpic conditions. However, the same scheme also suggests that, for increasing undercoolings, the volume gap is gradually reduced and eventually vanishes at a temperature close to the currently estimated homogeneous ice nucleation temperature. This behavior is contrasted with that of substances which do not display a volumetric anomaly. The effect of increasing pressures on the alleged volume crossover from an expanded to a contracted ice-water mixture is also discussed.

Glassy Interfacial Dynamics of Ni Nanoparticles: Part I Colored Noise, Dynamic Heterogeneity and Collective Atomic Motion

Most condensed materials exhibit a significant fraction of atoms, molecules or particles that are strongly interacting with each other, while being configured geometrically at any instant of time in an 'amorphous' state having a relatively uniform density. Recently, both simulations and experiments have revealed that the dynamics of diverse condensed amorphous materials is generally characterized by significant heterogeneity in the local mobility and by progressively increasing collective motion upon cooling that takes the form of string-like collective particle rearrangements. The direct experimental observation of this type of collective motion, which has been directly linked to the growing relaxation times of glass-forming materials, and its quantification under different thermodynamic conditions, has so far been restricted to colloidal and driven granular fluids. The present work addresses the fundamental problem of how to determine the scale of this type of collective motion in materials composed of molecules or atoms. The basic premise of our work is that large scale dynamic particle clustering in amorphous materials must give rise to large fluctuations in particle mobility so that transport properties, especially those related to particle mobility, should naturally exhibit noise related to the cooperative motion scale. In our initial exploratory study seeking a relationship of this kind, we find 1/fα or 'colored noise', in both potential energy and particle displacements fluctuations of the atoms within the glassy interfacial layer of Ni nanoparticles (NPs). A direct relation between the particle displacement (mobility) noise exponent α and the average polymerization index of the string-like collective motion L is observed for a range of NP sizes, temperatures and for surface doping of the NPs with other metal atoms (Ag, Au, Pt) to change of fragility of the glassy interfacial layer at the surface of the Ni NPs. We also introduce a successful analytic model to understand this relationship between α and L.