We investigate theoretically the freezing behaviour of a two-dimensional (2D) system of hard discs on a one-dimensional (1D) external potential (typically called laser-induced freezing). As shown by earlier theoretical and numerical studies, one observes freezing of the modulated liquid upon increase of the substrate potential amplitude, and re-entrant melting back into the modulated liquid when the substrate potential amplitude is increased even further. The purpose of our present work is to calculate the freezing and re-entrant melting phase diagram based on information from the bulk system. To this end, we employ an integrated pressure-balance equation derived from density functional theory [Phys. Rev. E \textbf{101}, 012609 (2020)]. Furthermore, we define a measure to quantify the influence of registration effects that qualitatively explain re-entrant melting. Despite severe approximations, the calculated phase diagram shows good agreement with the known phase diagram obtained by Monte Carlo simulations.
A self-organized system composed of classical particles confined in a two-dimensional parabolic trap and interacting through a potential with a short-range attractive part and long-range repulsive part is studied as function of temperature. The influence of the competition between the short-range attractive part of the inter-particle potential and its long-range repulsive part on the melting temperature is studied. Different behaviors of the melting temperature are found depending on the screening length ($κ$) and the strength ($B$) of the attractive part of the inter-particle potential. A re-…
We studied the phase behavior of charged and sterically stabilized colloids using confocal microscopy in a less polar solvent (dielectric constant 5.4). Upon increasing the colloid volume fraction we found a transition from a fluid to a body centered cubic crystal at 0.0415+/-0.0005, followed by re-entrant melting at 0.1165+/-0.0015. A second crystal of different symmetry, random hexagonal close-packed, was formed at a volume fraction around 0.5, similar to that of hard spheres. We attribute the intriguing phase behavior to particle interactions that depend strongly on volume fraction, mainly …
Because of long-wavelength fluctuations, the nature of solids and phase transitions in 2D are different from those in 3D systems, and have been heavily debated in past decades, in which the focus was on the existence of hexatic phase. Here, by using large scale computer simulations, we investigate the melting transition in 2D systems of polydisperse hard disks. We find that, with increasing the particle size polydispersity, the melting transition can be qualitatively changed from the recently proposed two-stage process to the Kosterlitz-Thouless-Halperin-Nelson-Young scenario with significantl…
Confinement can have a dramatic effect on the behavior of all sorts of particulate systems and it therefore is an important phenomenon in many different areas of physics and technology. Here, we investigate the role played by the softness of the confining potential. Using grand canonical Monte Carlo simulations, we determine the phase diagram of three-dimensional hard spheres that in one dimension are constrained to a plane by a harmonic potential. The phase behavior depends strongly on the density and on the stiffness of the harmonic confinement. Whilst we find the familiar sequence of confin…
The effect of polydispersity on the freezing transition of hard spheres is examined within a moment description. At low polydispersities a single fluid-to-crystal transition is recovered. With increasing polydispersity we find a density above which the crystal melts back into an amorphous phase. The range of densities over which the crystalline phase is stable shrinks with increasing polydispersity until, at a certain level of polydispersity, the crystal disappears completely from the equilibrium phase diagram. The two transitions converge to a single point which we identify as the polydispers…
We test the validity of some widely used phenomenological criteria for the localization of the fluid-solid transition thresholds against the phase diagrams of particles interacting through the exp-6, inverse-power-law, and Gaussian potentials. We find that one-phase rules give, on the whole, reliable estimates of freezing/melting points. The agreement is ordinarily better for a face-centered-cubic solid than for a body-centered-cubic crystal, even more so in the presence of a pressure-driven re-entrant transition of the solid into a denser fluid phase, as found in the Gaussian-core model.
We use polydispersity in size as a control parameter to explore certain aspects of melting and freezing transitions in a system of Lennard-Jones spheres. Both analytical theory and computer simulations are employed to establish a potentially interesting relationship between observed terminal polydispersity in Lennard-Jones polydisperse spheres and prediction of the same in the integral equation based theoretical analysis of liquid-solid transition. As we increase polydispersity, solid becomes inherently unstable because of the strain built up due to the size disparity. This aspect is studied h…
We describe experiments on monodisperse spherical particles in an annular cell geometry, vibrated from below and sheared from above. This system shows a freezing/melting transition such that under sufficient vibration a crystallized state is observed, which can be melted by sufficient shear. We characterize the hysteretic transition between these two states, and observe features reminiscent of both a jamming transition and critical phenomena.
We generalize previous approach of Khrapak and Morfill [J. Chem. Phys. {\bf 134}, 094108 (2011)] to construct simple and sufficiently accurate freezing and melting equations for the conventional Lennard-Jones (LJ) system to $n$-6 LJ systems, using the accurate results for the triple points of these systems published by Sousa {\it et al.} [J. Chem. Phys. {\bf 136}, 174502 (2012)].
Analyzing three approximate methods to locate liquid-solid coexistence in simple systems, an observation is made that all of them predict the same functional dependence of the temperature on density at freezing and melting of the conventional Lennard-Jones system. The emerging equations can be written as $T={\mathcal A}ρ^4+{\mathcal B}ρ^2$ in normalized units. We suggest to determine the values of the coefficients ${\mathcal A}$ at freezing and melting from the high-temperature limit, governed by the inverse twelfth power repulsive potential. The coefficients ${\mathcal B}$ can be determined f…
A simple model of dimerizing hard spheres with highly nontrivial fluid-solid phase behaviour is proposed. The model is studied using the recently proposed resummed thermodynamic perturbation theory for central force (RTPT-CF) associating potentials. The phase diagram has the fluid branch of the fluid-solid coexistence curve located at a temperatures lower than those of the solid branch. This unusual behaviour is related to the strong dependence of the system excluded volume on the temperature, which for the model at hand decreases with increasing temperature. This effect can be also seen for a…
The invariance of several structural and dynamical properties of the Lennard-Jones (LJ) system along the freezing and melting lines is interpreted in terms of the isomorph theory. First the freezing/melting lines for LJ system are shown to be approximated by isomorphs. Then we show that the invariants observed along the freezing and melting isomorphs are also observed on other isomorphs in the liquid and crystalline phase. Structure is probed by the radial distribution function and the structure factor and dynamics is probed by the mean-square displacement, the intermediate scattering function…
Freezing and melting of Ar condensed in a granular packing of template-grown arrays of linear mesopores (SBA-15, mean pore diameter 8 nanometer) has been studied by specific heat measurements C as a function of fractional filling of the pores. While interfacial melting leads to a single melting peak in C, homogeneous and heterogeneous freezing along with a delayering transition for partial fillings of the pores result in a complex freezing mechanism explainable only by a consideration of regular adsorption sites (in the cylindrical mesopores) and irregular adsorption sites (in niches of the ro…
We have measured the phase behavior of a binary mixture of like-charged colloidal spheres with a size ratio of 0.9 and a charge ratio of 0.96 as a function of particle number density n and composition p. Under exhaustively deionized conditions the aqueous suspension forms solid solutions of body centered cubic structure for all compositions. The freezing and melting lines as a function of composition show opposite behavior and open a wide, spindle shaped coexistence region. Lacking more sophisticated treatments, we model the interaction in our mixtures as an effective one-component pair energy…
Freezing and melting of large three-dimensional complex plasmas under microgravity conditions is investigated. The neutral gas pressure is used as a control parameter to trigger the phase changes: Complex plasma freezes (melts) by decreasing (increasing) the pressure. Evolution of complex plasma structural properties upon pressure variation is studied. Theoretical estimates allow us to identify main factors responsible for the observed behavior.
We investigate the behavior of hydrated sulfonated polysulfones over a range of ion contents through differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FTIR), and molecular dynamics (MD) simulations. Experimental evidence shows that at comparable ion contents, the spacing between the ionic groups along the polymer backbone can significantly impact the amount of melting water present in the polymer. When we only consider water molecules that can hydrogen bond to four neighboring water molecules as the melting water, the MD simulation results are found to agree wit…
In titration experiments with NaOH we have determined the full phase diagram of charged colloidal spheres in dependence on the particle density n, the particle effective charge Zeff and the concentration of screening electrolyte c using microscopy, light and Ultra Small Angle X-Ray Scattering (USAXS). For sufficiently large n the system crystallizes upon increasing Zeff at constant c and melts upon increasing c at only slightly altered Zeff. In contrast to earlier work equilibrium phase boundaries are consistent with a universal melting line prediction from computer simulation, if the elastici…
We present a molecular dynamics simulation study of the phase diagram and melting scenarios of two-dimensional Hertzian spheres with exponent 7/2. We have found multiple re-entrant melting of a single crystal with a triangular lattice in a wide range of densities from 0.5 to 10.0. Depending on the position on the phase diagram, the triangular crystal has been shown to melt through both two-stage melting with a first-order hexatic - isotropic liquid transition and a continuous solid - hexatic transition as well as in accordance with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKT…
The nonequilibrium dynamical behaviour that arises when two ordered two-dimensional monolayers of particles are sheared over each other is studied in Brownian dynamics simulations. A curious sequence of nonequilibrium states is observed as the driving rate is increased, the most striking of which is a sliding state with irregular alternation between disordered and ordered states. We comment on possible mechanisms underlying these cycles, and experiments that could observe them.
Antifreeze proteins (AFPs) evolved in cold-adapted organisms and serve to protect them against freezing in cold conditions by arresting ice crystal growth. Recently, we have shown quantitatively that adsorption of AFPs not only prevents ice from growing but also from melting. This melting inhibition by AFPs, which results in superheated ice (Celik et al, PNAS 2010), is not a well-known phenomenon. Here we present our recent findings in which the Ca2+ - dependent hyperactive AFP from Marinomonas primoryensis (MpAFP) clearly displays this property. Additionally, we found that an ice crystal that…
We present a simple density functional theory for the solid phases of systems of particles interacting via soft-core potentials. In particular, we apply the theory to particles interacting via repulsive point Yukawa and Gaussian pair potentials. We find qualitative agreement with the established phase diagrams for these systems. The theory is able to account for the bcc-fcc solid transitions of both systems and the re-entrant melting that the Gaussian system exhibits.
Hierarchical self-assembly consisting of local associations of simple building-blocks for the formation of complex structures widely exists in nature, while the essential role of local assembly remains unknown. In this work, by using computer simulations, we study a simple model system consisting of associating colloidal hemispheres crystallizing into face-centered-cubic crystals comprised of spherical dimers of hemispheres, focusing on the effect of dimer formation on the hierarchical crystallization. We found that besides assisting the crystal nucleation because of increasing the symmetry of…
We study the phenomenon of laser induced freezing, within a numerical renormalization scheme which allows explicit comparison with a recent defect mediated melting theory. Precise values for the `bare' dislocation fugacities and elastic moduli of the 2-d hard disk system are obtained from a constrained Monte Carlo simulation sampling only configurations {\em without} dislocations. These are used as inputs to appropriate renormalization flow equations to obtain the equilibrium phase diagram which shows excellent agreement with earlier simulation results. We show that the flow equations need to …
2D competitive systems shows a large variety of solid and aggregate patterns, re-entrant fluid phase, a continuous melting as predicted by the KTHNY theory and, in some cases, waterlike anomalies. In this paper, we employ Langevin Dynamics simulations of a ramp-like core-softened fluid that have two characteristic length scales and all the features mentioned above. Analyzing the fluid phase of this system, Bordin and Barbosa [Phys. Rev. E 97, 022604 (2018)] reported the existence of two waterlike anomalous region. Now, we revisit this problem focusing in the low temperature regime and a larger…
We present a numerical study of the phase behavior of repulsively interacting active polar particles that align their active velocities nematically. The amplitude of the active velocity, and the noise in its orientational alignment control the active nature of the system. At high values of orientational noise, the structural fluid undergoes a continuous nematic-isotropic transition in active orientation. This transition is well separated from an active phase separation, characterized by the formation of high density hexatic clusters, observed at lower noise strengths. With increasing activity,…
The effects of an externally applied one-dimensional periodic potential on the freezing/melting behaviour of two-dimensional systems of colloidal particles with a short-range attractive interaction are studied using Monte Carlo simulations. In such systems, incommensuration results when the periodicity of the external potential does not match the length-scale at which the minimum of the attractive potential occurs. To study the effects of this incommensuration, we consider two different models for the system. Our simulations for both these models show the phenomenon of reentrant freezing as th…
We investigate the phase behaviour of a two-dimensional colloidal model system of ultra-soft particles on a substrate which varies periodically along one spatial direction. Our calculations are based on mean-field density functional theory for a system of particles interacting via an ultra-soft potential, that is, the generalized exponential model with index four (\mbox{GEM-4}). For suitable substrate periodicities (with commensurability parameter $p=2$), we find a succession of phase transitions from a modulated liquid to a locked smectic and then to a locked floating solid phase. The appeara…
Combining model experiments and theory, we investigate the dense phases of polar active matter beyond the conventional flocking picture. We show that above a critical density flocks assembled from self-propelled colloids arrest their collective motion, lose their orientational order and form solids that actively rearrange their local structure while continuously melting and freezing at their boundaries. We establish that active solidification is a first-order dynamical transition: active solids nucleate, grow, and slowly coarsen until complete phase separation with the polar liquids they coexi…
The nature of freezing and melting transitions for a system of model colloids interacting by a DLVO potential in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling analyses of various thermodynamic quantities like the order parameter, its cumulants etc. are used to map the phase diagram of the system for various values of the reduced screening length $κa_{s}$ and the amplitude of the external potential. We find clear indication of a reentrant liquid phase over a significant region of the parameter space. Our simulations ther…
Depending on the volume fraction and interparticle interactions, colloidal suspensions can form different phases, ranging from fluids, crystals, and glasses to gels. For soft microgels that are made from thermoresponsive polymers, the volume fraction can be tuned by temperature, making them excellent systems to experimentally study phase transitions in dense colloidal suspensions. However, investigations of phase transitions at high particle concentration and across the volume phase transition temperature in particular, are challenging due to the deformability and possibility for interpenetrat…
Using Lifshitz theory we assess the role of van der Waals forces at interfaces of ice and water. The results are combined with measured structural forces from computer simulations to develop a quantitative model of the surface free energy of premelting films. This input is employed within the framework of wetting theory and allows us to predict qualitatively the behavior of quasi-liquid layer thickness as a function of ambient conditions. Our results emphasizes the significance of vapor pressure. The ice vapor interface is shown to exhibit only incomplete premelting, but the situation can shif…
Freezing in charged porous media can induce significant pressure and cause damage to tissues and functional materials. We formulate a thermodynamically consistent theory to model freezing phenomena inside charged heterogeneous porous space. Two regimes are distinguished: free ions in open pore space lead to negligible effects of freezing point depression and pressure. On the other hand, if nano-fluidic salt trapping happens, subsequent ice formation is suppressed due to the high concentration of ions in the electrolyte. In this case, our theory predicts that freezing starts at a significantly …
We examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials which do not diverge at the origin, are free of attractive parts and decay fast enough to zero as the interparticle separation r goes to infinity. By employing a mean field-density functional theory which is shown to become exact at high temperatures and/or densities, we establish a criterion which determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature.
We investigate by direct numerical solution of appropriate renormalization flow equations, the validity of a recent dislocation unbinding theory for laser induced freezing/melting in two dimensions. The bare elastic moduli and dislocation fugacities which are inputs to the flow equations are obtained for three different 2-d systems (hard disk, inverse $12^{th}$ power and the Derjaguin-Landau-Verwey-Overbeek potentials) from a restricted Monte Carlo simulation sampling only configurations {\em without} dislocations. We conclude that (a) the flow equations need to be correct at least up to third…
Close to the triple point, the surface of ice is covered by a thin liquid layer (so-called quasi-liquid layer) which crucially impacts growth and melting rates. Experimental probes cannot observe the growth processes below this layer, and classical models of growth by vapor deposition do not account for the formation of premelting films. Here, we develop a mesoscopic model of liquid-film mediated ice growth, and identify the various resulting growth regimes. At low saturation, freezing proceeds by terrace spreading, but the motion of the buried solid is conveyed through the liquid to the outer…
We present experimental evidence for a first-order freezing/melting phase transition in a nonequilibrium system -- an oscillated two-dimensional isobaric granular fluid. The steady-state transition occurs between a gas and a crystal and is characterized by a discontinuous change in both density and temperature. It is suppressed if the number of particles is incommensurate with the cell size, shows rate-dependent hysteresis, and obeys the Lindemann criterion for melting. Further, the measured equation of state both above and below the phase transition compares well with theory.
Melting of two dimensional (2D) clusters of classical particles is studied using Brownian dynamics and Langevin molecular dynamics simulations. The particles are confined by a circular hard wall or a parabolic external potential and interact through a dipole or a screened Coulomb potential. We found that with decreasing strength of the inter--particle interaction clusters with short-range inter-particle interaction which are confined by a hard wall exhibit a re-entrant behavior in its orientational order.
In this work we present a numerical study, based on molecular dynamics simulations, to estimate the freezing point of hard spheres and hypersphere systems in dimension D = 4, 5, 6 and 7. We have studied the changes of the Radial Distribution Function (RDF) as a function of density in the coexistence region. We started our simulations from crystalline states with densities above the melting point, and moved down to densities in the liquid state below the freezing point. For all the examined dimensions (including D = 3) it was observed that the height of the first minimum of the RDF changes in a…
Melting/freezing are canonical examples of discontinuous phase transitions, for which no pretransitional effects in the liquid phase are expected.For the solid phase, weak premelting effects are evidenced. This report shows long-range, critical-like, pretransitional effect in liquid thymol detected in Electrooptic Kerr effect (EKE) studies. Notable is the negative sign of EKE pretransitional anomaly. Studies are supplemented by high-resolution by dielectric constant temperature-related scan, which revealed a weak premelting effect in the solid phase. Both EKE and dielectric constant show a 'cr…
The equation of state of a hard sphere fluid at high density should exhibit a simple pole at the random close packing limit. Here we show that trying to obtain a compact semi-empirical equation of state simultaneously compatible with that asymptotic behaviour and with the known virial coefficients raises an analytical difficulty which can be solved if a glassy transition occurs in the disordered metastable phase at a density intermediate between the freezing point and the random close packing limit, numerically close to the melting point. The estimated value for the transition point, which is …
To develop an understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier-Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that, as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially the temporal oscillations …
Phase behavior of large three-dimensional complex plasma systems under microgravity conditions onboard the International Space Station is investigated. The neutral gas pressure is used as a control parameter to trigger phase changes. Detailed analysis of structural properties and evaluation of three different melting/freezing indicators reveal that complex plasmas can exhibit melting by increasing the gas pressure. Theoretical estimates of complex plasma parameters allow us to identify main factors responsible for the observed behavior. The location of phase states of the investigated systems …
The properties of a macroscopic assembly of weakly-repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to cluster supersolid as a function of pressure. We develop a thermodynamically rigorous treatment of the different phases of the system by adopting a variational formulation of the condensate wave function --- represented as a sum of Gaussians --- that is amenable to exact manipulations. Not only is this description quantitatively accurate, but it is also capable to…
We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold. This simple functional describes the elastic interaction of weakly deformable bodies and, therefore, it is a reliable physical model of soft macromolecules, like star polymers and globular micelles. Using thermodynamic integration and extensive Monte Carlo simulations, we computed accurate free energies of the fluid phase and a large number of crystal structure…
The phase diagram of star polymer solutions in a good solvent is obtained over a wide range of densities and arm numbers by Monte Carlo simulations. The effective interaction between the stars is modeled by an ultrasoft pair potential which is logarithmic in the core-core distance. Among the stable phases are a fluid as well as body-centered cubic, face-centered cubic, body-centered orthogonal, and diamond crystals. In a limited range of arm numbers, reentrant melting and reentrant freezing transitions occur for increasing density.
The surface freezing and surface melting transitions exhibited by a model two-dimensional soft matter system is studied. The behaviour when confined within a wedge is also considered. The system consists of particles interacting via a soft purely repulsive pair potential. Density functional theory (DFT) is used to calculate density profiles and thermodynamic quantities. The external potential due to the confining walls is modelled via a hard-wall with an additional repulsive Yukawa potential. The surface phase behaviour depends on the range and strength of this repulsion: When the repulsion st…
Using Monte Carlo simulations, we systematically investigate the effect of particle size distribution on the phase behaviour of polydisperse hard disks. Compared with the commonly used Gaussian-like polydisperse hard disks [Commun. Phys. 2, 70 (2019)], we find that the phase behaviour of polydisperse hard-disk systems with lognormal and triangle distributions are 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 hexatic or solid phase can n…
We study the phase behavior of hard spheres confined between two parallel hard plates using extensive computer simulations. We determine the full equilibrium phase diagram for arbitrary densities and plate separations from one to five hard-sphere diameters using free energy calculations. We find a first-order fluid-solid transition, which corresponds to either capillary freezing or melting depending on the plate separation. The coexisting solid phase consists of crystalline layers with either triangular or square symmetry. Increasing the plate separation, we find a sequence of crystal structur…
