Gas-liquid Coexistence Region Research Articles

Maxwell's equal area law for Vaidya-Bonner-de Sitter black hole under Lorentz invariance violation

In this study, we investigate the tunneling of fermions with arbitrary spin near the event horizon of a nonstationary Vaidya-Bonner-de Sitter (VBdS) black hole under Lorentz invariance violation (LIV). The modified Hawking temperature of VBdS black holes is calculated by using tortoise coordinate transformation, Feynman prescription, and Wentzel–Kramers–Brillouin approximation. By considering the cosmological constant as a thermodynamic pressure in the extended phase space, we construct a Maxwell's equal area law under LIV and study the phase transitions of VBdS black hole in , , and planes. The LIV increases the length of the liquid-gas coexistence region. The thermodynamic quantities such as the entropy, heat capacity, Helmholtz free energy, internal energy, enthalpy, and Gibbs free energy of the VBdS black hole are discussed. These quantities tend to increase under LIV. The stability of the black hole is also discussed in the presence of LIV.

Ordering kinetics in the active Ising model.

We undertake a numerical study of the ordering kinetics in the two-dimensional (2D) active Ising model (AIM), a discrete flocking model with a conserved density field coupled to a nonconserved magnetization field. We find that for a quench into the liquid-gas coexistence region and in the ordered liquid region, the characteristic length scale of both the density and magnetization domains follows the Lifshitz-Cahn-Allen growth law, R(t)∼t^{1/2}, consistent with the growth law of passive systems with scalar order parameter and nonconserved dynamics. The system morphology is analyzed with the two-point correlation function and its Fourier transform, the structure factor, which conforms to the well-known Porod's law, a manifestation of the coarsening of compact domains with smooth boundaries. We also find the domain growth exponent unaffected by different noise strengths and self-propulsion velocities of the active particles. However, transverse diffusion is found to play the most significant role in the growth kinetics of the AIM. We extract the same growth exponent by solving the hydrodynamic equationsof the AIM.

Bifurcation of solutions of Ornstein–Zernike equation in the gas–liquid coexistence region of simple fluids

One objective of this paper is to investigate bifurcation of solutions of Ornstein–Zernike equation in liquid state theory for the gas–liquid coexistence region of simple fluids. The analysis uses a discrete form of the Ornstein–Zernike equation in real space, together with a closure relation which provides nearly self consistent thermodynamic properties of fluids governed by interaction potentials like the Lennard-Jones potential. Accurate asymptotic forms of correlation functions are incorporated in the real space algorithm so as to mitigate the influence of cutoff length used in the discrete approximations. The global error reduction of this algorithm is similar to that of Simpson’s rule. It is found that there is no spinodal on the vapor side on a sub-critical isotherm. However, there is a density at which compressibility vanishes, but this lies on a nonphysical branch. There are fold bifurcation points on the vapor and liquid sides together with a ‘no-real-solution-region’ in between. This is followed by a region of negative compressibility extending up to the spinodal on the liquid side. Importantly, it is found that in regions where compressibility is non-positive, there are infinite number of solutions to OZE which violate an integral constraint that is needed for applications to thermodynamics. The emerging picture is somewhat similar to that in the case of the hypernetted-chain-closure. It is also found that complex solutions connect the physical solutions that exist outside the ‘no-real-solution-region’ as well as in region of negative compressibility. The second objective of the paper, in the light of bifurcation scenario, is to evolve an interpretation of the coupling-parameter expansion of correlation functions pertaining to the region of negative compressibility. It is shown that the expansion provides an accurate description of results of the restricted ensembles, implied in mean field theories and simulation methods. Bifurcation of singlet density to an in-homogeneous distribution at a spinodal is also established using a simple equation, which uses the direct correlation function. Thus the paper re-establishes the fact that restriction to a homogeneous singlet density is the root cause of all inconsistencies found in the gas–liquid coexistence region.

Motility-induced phase separation of soft active Brownian particles

Motility-induced phase separation (MIPS) is the hallmark of non-equilibrium phase transition in active matter. Here, by means of Brownian dynamics simulations, we determine the phase behavior and the critical point for phase separation induced by motility of a two-dimensional system of soft active Brownian particles, whose interaction is modeled by the generalized purely repulsive Weeks–Chandler–Andersen potential. We refer to this model as soft active Brownian particles. We determine and analyze the influence of particle softness on the MIPS and show that the liquid–gas coexistence region is wider, the softer the interparticle interactions becomes. Moreover, the critical value of the self-propulsion velocity at which diluted and dense phases start to coexist also increases; as a consequence, the softer the particle interaction is, the bigger self-propulsion velocities are needed in order to observe a MIPS.

Isospin effect on quark matter instabilities

We have studied the mechanical and chemical instabilities as well as the liquid-gas-like phase transition in isospin asymmetric quark matter based on the NJL and the pNJL model. Areas of the mechanical instability region and the liquid-gas coexistence region are seen to be enlarged with a larger quark matter symmetry energy or in the presence of strange quarks. Our study shows that the light cluster yield ratio observed in relativistic heavy-ion collisions may not be affected much by the uncertainties of the isospin effect, and favors a smooth hadron-quark phase transition in compact stars as well as their mergers.

Isospin-dependent phase diagram of nuclear matter

In this article we obtain the phase diagram of nuclear matter extending it from the traditional two-dimensional density-temperature plane to three-dimensional space of density, temperature, and isospin asymmetry. We identify the liquid-gas coexistence region by means of Maxwell constructions over pressure-volume isotherms. Such pressure-density equations of state were constructed from data obtained from interpolating results from molecular dynamics simulations of infinite nuclear systems in the liquid phase those of Fermi gases at low (sub-saturation) densities. The molecular dynamics results were used to obtain the energy per nucleon and pressure for systems with densities and temperatures in the ranges ρ=0.01 to 0.2 fm−3, T between 1 and 15 MeV, and with isospin content of x = Z/A = 0.3, 0.35, 0.4, 0.45 and 0.5. The results indicate that symmetric and asymmetric matter are self-bound and show a coexistence region that extends, approximately, to densities of up to ρ0/2, temperatures of up to 16 MeV, and down to proton fractions of 13%.

A corresponding-state framework for the structural transition of supercritical fluids across the Widom delta.

This work proposes a classification algorithm based on the radical Voronoi tessellation to define the Widom delta, supercritical gas-liquid coexistence region, of polyatomic molecules. Specifically, we use a weighted mean-field classification method to classify a molecule into either gaslike or liquidlike. Classical percolation theory methods are adopted to understand the generality of the structural transition and to locate the Widom delta. A structural analysis on various supercritical fluids shows that the proposed method detects the influence of the attractive interaction on the structural transition of supercritical fluids. Moreover, we demonstrate that the supercritical gas-liquid coexistence region of water overlaps with the ridges of the response function maxima. From the pressure-temperature relation, a three-parameter corresponding state theorem is derived, which states that the fraction of gaslike molecules of a substance is equal to that of another if their reduced pressure, reduced temperature, and the critical compressibility factor are the same.

Dynamics of a network fluid within the liquid-gas coexistence region.

Low-density networks of molecules or colloids are formed at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim's theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid-gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface tension (coarsening), when the valence is limited, the slow relaxation proceeds through the formation of an intermediate non-equilibrium gel via a geometrical percolation transition in the Random Percolation universality class. We show that the slow dynamics is universal, being also observed outside the coexistence region at low temperatures in the single phase region.

Symmetry energy in the liquid–gas mixture

Results from classical molecular dynamics simulations of infinite nuclear systems with varying density, temperature and isospin content are used to calculate the symmetry energy at low densities. The results show an excellent agreement with the experimental data and corroborate the claim that the formation of clusters has a strong influence on the symmetry energy in the liquid–gas coexistence region.

Stabilizing the hexagonal close packed structure of hard spheres with polymers: Phase diagram, structure, and dynamics.

We study the phase behaviour of a binary mixture of colloidal hard spheres and freely jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and co-workers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures.

Low-density phases ofHe3monolayers adsorbed on graphite

Quantum Monte Carlo simulations at zero temperature of a $^3$He monolayer adsorbed on graphite, either clean or preplated with $^4$He, unexpectedly point to a gas-liquid phase transition at a very low areal density of the order of 0.01\AA$^{-2}$. This result stems from an essentially unbiased calculation of the ground state energy for an infinite, defect-free substrate which interacts with He atoms via a realistic potential, whereas the interaction between two He atoms includes two- and three-body terms. The sensitivity of the gas-liquid coexistence region on the model Hamiltonian employed is discussed.

Gas-liquid phase coexistence and crossover behavior of binary ionic fluids with screened Coulomb interactions.

We study the effects of an interaction range on the gas-liquid phase diagram and the crossover behavior of a simple model of ionic fluids: an equimolar binary mixture of equisized hard spheres interacting through screened Coulomb potentials which are repulsive between particles of the same species and attractive between particles of different species. Using the collective variables theory, we find explicit expressions for the relevant coefficients of the effective φ{4} Ginzburg-Landau Hamiltonian in a one-loop approximation. Within the framework of this approximation, we calculate the critical parameters and gas-liquid phase diagrams for varying inverse screening length z. Both the critical temperature scaled by the Yukawa potential contact value and the critical density rapidly decrease with an increase of the interaction range (a decrease of z) and then for z<0.05 they slowly approach the values found for a restricted primitive model (RPM). We find that gas-liquid coexistence region reduces with an increase of z and completely vanishes at z≃2.78. Our results clearly show that an increase in the interaction range leads to a decrease of the crossover temperature. For z≃0.01, the crossover temperature is the same as for the RPM.

Phase behavior and critical activated dynamics of limited-valence DNA nanostars

Colloidal particles with directional interactions are key in the realization of new colloidal materials with possibly unconventional phase behaviors. Here we exploit DNA self-assembly to produce bulk quantities of "DNA stars" with three or four sticky terminals, mimicking molecules with controlled limited valence. Solutions of such molecules exhibit a consolution curve with an upper critical point, whose temperature and concentration decrease with the valence. Upon approaching the critical point from high temperature, the intensity of the scattered light diverges with a power law, whereas the intensity time autocorrelation functions show a surprising two-step relaxation, somehow reminiscent of glassy materials. The slow relaxation time exhibits an Arrhenius behavior with no signs of criticality, demonstrating a unique scenario where the critical slowing down of the concentration fluctuations is subordinate to the large lifetime of the DNA bonds, with relevant analogies to critical dynamics in polymer solutions. The combination of equilibrium and dynamic behavior of DNA nanostars demonstrates the potential of DNA molecules in diversifying the pathways toward collective properties and self-assembled materials, beyond the range of phenomena accessible with ordinary molecular fluids.

Gibbs Density Surface of Fluid Argon: Revised Critical Parameters

A phase diagram of simple fluids, based upon percolation transition loci determined from literature experimental density-pressure isotherms of argon, shows three fluid phases. The liquid phase spans all temperatures from a metastable amorphous ground state to supercritical temperatures. There is a supercritical mesophase of a colloidal nature between two percolation transition loci, PA and PB, that bound the existences of liquid and gas phases, respectively. There is no ‘critical point’ on the Gibbs density surface. When two percolation transitions have the same pressure, i.e., on intersection of the loci in the \(p\)–\(T\) plane, an equilibrium ‘line of critical states’ is thermodynamically defined. This description of criticality yields slightly different values of critical parameters than those hitherto obtained by interpolation of experimental \(p\)–\(\rho \)–\(T\) data from the coexistence region. Revised values of the critical temperature (\(T_\mathrm{c})\) and critical pressure (\(p_\mathrm{c})\) of argon can be obtained from the original high precision thermodynamic measurements for fluid argon, using only data from one-phase supercritical isotherms. Values of coexisting densities at \(T_\mathrm{c}\) and the density loci of the percolation transitions that bound the existence of supercritical gas and liquid phases for \(T>T_\mathrm{c}\) are also reported. Percolation loci, for \(T<T_\mathrm{c}\), extend into the gas–liquid coexistence region to become the spinodal lines that limit the existence of metastable gas and liquid phases.

Chiral thermodynamics of nuclear matter

The free energy and the equation of state of isospin-asymmetric nuclear matter are calculated at finite temperature up to three loop order in the framework of in-medium chiral perturbation theory, systematically incorporating one- and two-pion exchange dynamics to this order. Effects from the two-pion exchange with explicit {\Delta}-isobar excitation are included, as well as three-body forces. We construct the phase diagram of nuclear matter for different proton fractions x_p and investigate the dependence of nuclear matter properties on the isospin-asymmetry. A detailed study of the liquid-gas phase transition is performed. For isospin-symmetric nuclear matter we find a critical temperature of 15.1 MeV; as the isospin-asymmetry is increased, the liquid-gas coexistence region decreases until it disappears at x_p \approx 0.05, while nuclear matter becomes unbound at x_p \approx 0.12. The quadratic expansion of the free energy in the asymmetry parameter {\delta} is a good approximation at low temperature even for large {\delta}. An estimate of chiral four-body correlations in nuclear and neutron matter is also performed and the corrections from such four-body interactions are found to be small.

Thermodynamics and diffusion in size-symmetric and asymmetric dense electrolytes

MD simulation results for model size-symmetric and asymmetric electrolytes at high densities and temperatures (well outside the liquid-gas coexistence region) are generated and analyzed focusing on thermodynamic and diffusion properties. An extension of the mean spherical approximation for electrolytes originally derived for charged hard sphere fluids is adapted to these systems by exploiting the separation of short range and Coulomb interaction contributions intrinsic to these theoretical models and is found to perform well for predicting equation of state quantities. The diffusion coefficients of these electrolytes can also be reasonably well predicted using entropy scaling ideas suitably adapted to charged systems and mixtures. Thus, this approach may provide an avenue for studying dense electrolytes or complex molecular systems containing charged species at high pressures and temperatures.

Nuclear symmetry energy effects on liquid-gas phase transition in hot asymmetric nuclear matter

The liquid-gas phase transition in hot asymmetric nuclear matter is investigated within relativistic mean-field model using the density dependence of nuclear symmetry energy constrained from the measured neutron skin thickness of finite nuclei. We find symmetry energy has a significant influence on several features of liquid-gas phase transition. The boundary and area of the liquid-gas coexistence region, the maximal isospin asymmetry and the critical values of pressure and isospin asymmetry all of which systematically increase with increasing softness in the density dependence of symmetry energy. The critical temperature below which the liquid-gas mixed phase exists is found higher for a softer symmetry energy.

Self-organization of magnetic nanoparticles: A Monte Carlo study

To understand the self-organization of magnetic nanocrystals in an applied field, we perform Monte Carlo simulations of Stockmayer fluids confined between two parallel walls. The system is examined in the gas-liquid coexistence region of its phase diagram and the field is applied perpendicular to the walls. Gibbs ensemble simulations are carried out to determine the phase coexistence curves of the confined Stockmayer fluid. In canonical simulations, different types of organizations appear dependent on particle density: columns, walls, and elongated and spherical holes. The morphology and size of structures are in good agreement with results obtained by free energy minimization and experiments. The influence of a distribution of particle sizes on the particle organization is investigated.

Theoretical and numerical study of the phase diagram of patchy colloids: Ordered and disordered patch arrangements

We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.

A global investigation of phase equilibria using the perturbed-chain statistical-associating-fluid-theory approach

The recently developed perturbed-chain statistical-associating-fluid theory (PC-SAFT) is investigated for a wide range of model parameters including the parameter m representing the chain length and the thermodynamic temperature T and pressure p. This approach is based upon the first-order thermodynamic perturbation theory for chain molecules developed by Wertheim [M. S. Wertheim, J. Stat. Phys. 35, 19 (1984); ibid. 42, 459 (1986)] and Chapman et al. [G. Jackson, W. G. Chapman, and K. E. Gubbins, Mol. Phys. 65, 1 (1988); W. G. Chapman, G. Jackson, and K. E. Gubbins, ibid. 65, 1057 (1988)] and includes dispersion interactions via the second-order perturbation theory of Barker and Henderson [J. A. Barker and D. Henderson, J. Chem. Phys. 47, 4714 (1967)]. We systematically study a hierarchy of models which are based on the PC-SAFT approach using analytical model calculations and Monte Carlo simulations. For one-component systems we find that the analytical model in contrast with the simulation results exhibits two phase-separation regions in addition to the common gas-liquid coexistence region: One phase separation occurs at high density and low temperature. The second demixing takes place at low density and high temperature where usually the ideal-gas phase is expected in the phase diagram. These phenomena, which are referred to as "liquid-liquid" and "gas-gas" equilibria, give rise to multiple critical points in one-component systems, as well as to critical end points and equilibria of three fluid phases, which can usually be found in multicomponent mixtures only. Furthermore, it is shown that the liquid-liquid demixing in this model is not a consequence of a "softened" repulsive interaction as assumed in the theoretical derivation of the model. Experimental data for the melt density of polybutadiene with molecular mass Mw=45,000 gmol are correlated here using the PC-SAFT equation. It is shown that the discrepancies in modeling the polymer density at ambient temperature and high pressure can be traced back to the liquid-liquid phase separation predicted by the equation of state at low temperatures. This investigation provides a basis for understanding possible inaccuracies or even unexpected phase behavior which can occur in engineering applications of the PC-SAFT model aiming at predicting properties of macromolecular substances.