Vapor-liquid Phase Coexistence Research Articles

Predicting phase coexistence and adsorption isotherms of classical and quantum fluids using the microcanonical-ensemble perturbation theory (MEPT)

The Microcanonical-Ensemble Perturbation Theory (MEPT) of Sastre et al. (2018) [7] has been extended to study the vapor-liquid phase coexistence of binary and ternary mixtures of fluids. The attractive interactions between chains of molecules are represented as monomer segments interacting via a square-well pair potential. Calculations for the thermodynamic properties and phase behavior of square-well monomer chains are considered and compared with experimental data. Molecular parameters have been obtained to model the phase behavior of real fluids such as n-alkanes (from C1 to C12), nitrogen, perfluoromethane, carbon dioxide, i-butane, i-pentane, neon, and hydrogen. Furthermore, the capability of the MEPT approach in predicting critical and azeotropic lines of binary and ternary mixtures is explored. The results demonstrate that the MEPT approach provides a robust description of the phase behavior of mixtures containing chains of fluids. Additionally, we have integrated the MEPT approach with the two-dimensional Statistical Associating Fluid Theory for fluids interacting via variable range potentials (SAFT-VR-2D) to investigate the effect of quantum contributions on both phase behavior and adsorption. Remarkable improvements are observed when both higher order perturbation terms of the Helmholtz free energy and quantum contributions are included in the predictions of the phase behavior of quantum fluids such as neon and hydrogen. In all cases, the theoretical results exhibit favorable comparisons with experimental data in a wide range of compositions, pressures, and temperatures.

The role of the second virial coefficient in the vapor-liquid phase coexistence of anisotropic square-well particles

We examine the role of the second virial coefficient in the vapor-liquid (VL) phase coexistence of anisotropic hard bodies with square-well attractions of variable range. According to the extended law of corresponding states, the parameters of hard body interactions and attractions can be built into the reduced density and the reduced second virial coefficients, respectively, which gives rise to the collapse of all VL binodals in the reduced second virial coefficient vs. reduced density plane. The second virial perturbation theory shows that the shape dependence appears as an extra parameter in the phase behavior of anisotropic particles, which does not make possible the perfect collapse of the VL binodals for varying shapes. Interestingly, the binodal curves go closely together and even cross each other in the liquid side allowing to define a quasi-master curve. The existence of an almost perfect master curve is confirmed by replica-exchange Monte Carlo simulations for oblate square-well ellipsoids with several shape anisotropies.

Entropy scaling close to criticality: From simple to metallic systems.

Entropy has recently drawn considerable interest both as a marker to detect the onset of phase transitions and as a reaction coordinate, or collective variable, to span phase transition pathways. We focus here on the behavior of entropy along the vapor-liquid phase coexistence and identify how the difference in entropy between the two coexisting phases vary in ideal and metallic systems along the coexistence curve. Using flat-histogram simulations, we determine the thermodynamic conditions of coexistence, critical parameters, including the critical entropy, and entropies along the binodal. We then apply our analysis to a series of systems that increasingly depart from ideality and adopt a metal-like character, through the gradual onset of the Friedel oscillation in an effective pair potential, and for a series of transition metals modeled with a many-body embedded-atoms force field. Projections of the phase boundary on the entropy-pressure and entropy-temperature planes exhibit two qualitatively different behaviors. While all systems modeled with an effective pair potential lead to an ideal-like behavior, the onset of many-body effects results in a departure from ideality and a markedly greater exponent for the variation of the entropy of vaporization with temperature away from the critical temperature.

Equilibrium properties of penetrable soft spheres

Using the Weeks-Chandler-Andersen separation scheme, we explored equilibrium properties of fully penetrable soft spheres with an attractive tail. When the radial distribution function of the reference system is computed by means of the integral equation theory using the hyper-netted-chain closure, this separation scheme predicts pressure-density isotherms, vapour-liquid phase coexistence, and surface tension in good agreement with the results from Monte Carlo simulations even though the attractive portion of the interparticle potential has a significant effect on the radial distribution function. Despite its simplicity, the model potential we studied, with a certain parameter value, exhibits a non-monotonic temperature dependence of the liquid phase density over a wide range of pressure.

Gibbs ensemble Monte Carlo with solvent repacking: phase coexistence of size–asymmetrical binary Lennard-Jones mixtures

We describe a Monte Carlo method for simulation of vapour–liquid phase coexistence in size-asymmetrical Lennard–Jones (LJ) binary mixtures. The method incorporates the Solvent Repacking Monte Carlo (SRMC) approach, which offers efficient trial moves for the exchange of a large particle for several small particles, into the Gibbs Ensemble Monte Carlo (GEMC) method. SRMC yields a significant efficiency improvement in simulation of dilute large species mixtures at low temperature compared to the original GEMC method with identity exchange moves. Vapor–liquid phase diagrams are reported for LJ mixtures with a diameter ratio of 1:2 with well depth ratios and 2, producing spindle-type, azeotrope and closed loop types of phase diagram, respectively.

Corresponding states vapour–liquid phase equilibria of confined square–well fluid

Corresponding states vapour–liquid phase equilibria of confined square-well fluid are studied by means of grand-canonical transition-matrix Monte Carlo simulation and histogram reweighting method. In this study, square-well fluid is considered under hard and attractive slit pore confinements ranging from 1.5 to 40 molecular diameters. Corresponding states vapour–liquid phase coexistence envelopes display insignificant effect of wall−fluid interaction for slit pore confinements ranging from 1.5 to 3 molecular diameters. On the other hand, significant effect of wall−fluid interaction on the corresponding state coexistence envelope is observed for slit pore confinements ranging from 4 to 40 molecular diameters. Moreover, at a given slit width, shrinking in corresponding state coexistence envelope is observed with increase in the wall−fluid interaction. However, in the larger slit pore width of 30 to 40 molecular diameters, shrinking in the corresponding state vapour–liquid coexistence envelopes become indifferent with the stronger wall−fluid interactions studied in this work. Structural behaviour of coexisting phases in slit pores are also investigated through local density profiles, to understand the overall behaviour of corresponding states coexistence envelopes. Fluctuating positive and negative deviations in the corresponding state spreading pressure with respect to corresponding bulk value is observed for studied wall−fluid interactions and slit pore confinements.

Fragmentation dynamics of liquid–metal droplets under ultra-short laser pulses

We present the measurements and theoretical analysis of the deformation and fragmentation of spherical liquid–metal drops by picosecond and subpicosecond laser pulses. In the experiments, 60 μm droplets of Sn–In alloy were irradiated by Ti:Sa laser pulses with a peak energy fluence of ∼100 J cm−2. The observed evolution of the droplet shape dramatically differs from that previously reported for nanosecond pulses. Invoking 2D hydrodynamic simulations, we explain how, due to the specifics of matter dynamics in the liquid–vapor phase coexistence region, a liquid droplet is transformed into a characteristic acorn-like expanding shell with two inner cavities. High sensitivity of the measured shell parameters to the details of the equation of state and metastable dynamics suggests that such experiments offer new possibilities in exploration of thermophysical properties of metals in the region of liquid–vapor phase transition.

Effect of surface-screening parameter of the Yukawa potential model on vapour–liquid phase coexistence and critical-point properties of confined Yukawa fluid

We report the effect of surface-screening parameter of Yukawa potential model on vapour–liquid phase coexistence and critical-point properties of slit–pore-confined Yukawa fluid, using grand canonical transition-matrix Monte Carlo along with the histogram reweighting method. The effect of surface-screening parameter on the vapour–phase coexistence density is insignificant for the studied system. On the other hand, significant effect of surface-screening parameter is observed on liquid phase coexistence density. With increasing surface-screening parameter, liquid phase coexistence density decreases. Critical-point properties have shown monotonic decreasing trends with increase in surface-screening parameter. Moreover, the effect of change of surface-screening parameter is least on critical temperature changes as compared to critical density and critical pressure changes for the studied Yukawa system in this work.

The Similarity Relations Set on the Basis of Symmetrization of the Liquid-Vapor Phase Diagram.

An approach to symmetrize the liquid-vapor phase coexistence curve is proposed. It is based on the introduction of the lattice-like density x = ρ1/(ρ1 + ρ2), where ρ1 and ρ2 are the densities along the liquid-gas binodal. The global symmetrical phase diagram is created using experimental and simulation data for the real substances and models (noble gases, polyatomic molecules, organic substances and two metals, van der Waals system, Lennard-Jones system). The pressure and the temperature along the binodal are shown to satisfy some new similarity relations.

Molecular Dynamics Study of Aqueous NaCl Solutions: Flash Crystallization Caused by Solution Phase Change

Solutions under sub- or supercritical conditions receive much attention because of their significance in geology and industrial applications. One of the most important properties is their very low salt solubility, which leads to rapid crystallization. The morphology of sodium chloride crystals formed in supercritical fluids has been shown to be affected by the presence of the high-concentration liquid phase and low-concentration vapor phase [Armellini and Tester, J. Supercritical Fluid 4, 254–264 (1991)]. However, because of the short time scales involved, experimental observation of the underlying mechanism is difficult. In the present study, microsecond-scale molecular dynamics, which provide insight with picosecond resolution, were conducted for the NaCl salt–solution interfacial system at sub- and super-critical conditions. We propose the utilization of the correlation between the number density of ions and water to parameterize the solution phase. This correlation and the two-dimensional number densities provide insight into flash crystallization at the atomic scale. Vapor–liquid phase coexistence was found at high pressure and the diffusive high-concentration liquid phase could transport sodium and chloride ions to form a compact solid phase. In contrast, an isolated crystal forms at low pressure owing to the rapid volume expansion of the vapor phase.

MCCCS Towhee: a tool for Monte Carlo molecular simulation

The history of the Monte Carlo for complex chemical systems Towhee open source Monte Carlo molecular simulation tool is discussed. A proof is given that the Widom insertion method for computing the chemical potential is formally correct even when combined with the most general version of arbitrary trial distribution configurational-bias Monte Carlo. A simulation strategy for computing single component vapour–liquid phase coexistence curves is presented as a guide for inexperienced practitioners of Monte Carlo simulations. A review of papers that cite the Towhee code is presented. The paper concludes with a discussion about releasing and sustaining a simulation package that uses an open source software license.

Empty liquid state and self-assembly of high valence non-spherical colloidal systems

A vapour–liquid phase coexistence with vanishing critical volume fraction (empty liquid) is predicted in some model systems of attractive hard ellipsoids. The trends in critical density and temperature do not depend on the ellipsoid shape and the range of the square-well attraction. Our theoretical and simulation studies show transparently that the empty liquid limit is due to the competition between the anisotropic attractive and repulsive interactions. Additionally, the nematic phase is destabilized by the square-well attraction for both prolate and oblate shapes. The demand to maximize the number of bonds while keeping a relatively low excluded volume leads to special structures such as the cubatic and star-shaped cluster phases at low temperatures. The liquid branch of the vapour–liquid binodal is always isotropic for oblates, while it can be isotropic or cluster-like for prolates. Our results predict the occurrence of an empty liquid state in high valence anisotropic colloidal systems.

Towards understanding the empty liquid of colloidal platelets: vapour–liquid phase coexistence of square-well oblate ellipsoids

We study the phase behaviour of hard oblate ellipsoids with superimposed short-ranged oblate-shaped square-well attractions using the replica exchange Monte Carlo method and a simple van der Waals type perturbation theory. By fixing the square-well range (λ = 0.25σ‖), we examine the effect of varying the oblates aspect ratio, k = σ⊥/σ‖, on the density profiles, vapour–liquid and isotropic–nematic phase transitions. We observe that the formation of a liquid phase with vanishing density, an empty liquid, is possible with increasing aspect ratio. Surprisingly, the increasing shape anisotropy does not shift the stability region of the nematic phase to low densities, while the oblate-shaped square-well attraction favours disordered states. For k > 1.5, the critical temperature and packing fraction monotonically decrease with k, while the isotropic–nematic phase boundary moves towards higher packing fractions with decreasing temperature for all k. Simulations show that oblates preferably orientate their faces parallel to the vapour–liquid interface when located at the liquid side of the interface region and perpendicular when located at the vapour side.

Vapor-liquid phase coexistence and transport properties of two-dimensional oligomers

Grand-canonical transition-matrix Monte Carlo and histogram reweighting techniques are used herein to study the vapor-liquid coexistence properties of two-dimensional (2D) flexible oligomers with varying chain lengths (m = 1-8). The phase diagrams of the various 2D oligomers follow the correspondence state (CS) principle, akin to the behavior observed for bulk oligomers. The 2D critical density is not influenced by the oligomer chain length, which contrasts with the observation for the bulk oligomers. Line tension, calculated using Binder's formalism, in the reduced plot is found to be independent of chain length in contrast to the 3D behavior. The dynamical properties of 2D fluids are evaluated using molecular dynamics simulations, and the velocity and pressure autocorrelation functions are investigated using Green-Kubo (GK) relations to yield the diffusion and viscosity. The viscosity determined from 2D non-equilibrium molecular dynamics simulation is compared with the viscosity estimated from the GK relations. The GK relations prove to be reliable and efficient for the calculation of 2D transport properties. Normal diffusive regions are identified in dense oligomeric fluid systems. The influence of molecular size on the diffusivity and viscosity is found to be diminished at specific CS points for the 2D oligomers considered herein. In contrast, the viscosity and diffusion of the 3D bulk fluid, at a reduced temperature and density, are strongly dependent on the molecular size at the same CS points. Furthermore, the viscosity increases and the diffusion decreases multifold in the 2D system relative to those in the 3D system, at the CS points.

Vapor-liquid equilibrium properties for confined binary mixtures involving CO2, CH4, and N2 from Gibbs ensemble Monte Carlo simulations

The effects of solid-fluid interactions on the vapor-liquid phase diagram, coexistence density, relative volatility and vaporization enthalpy have been investigated for confined binary systems of CO2-CH4, CO2-N2 and CH4-N2. The Gibbs ensemble Monte Carlo (GEMC) simulation results indicate that the confinement and the solid-fluid interaction have significant influences on the vapor-liquid equilibrium properties. The confinement and the strength of the solid-fluid interaction make the p-xi phase diagram move to higher pressure regions. They also make the two-phase region become narrower for each binary mixture. The strength of the solid-fluid interactions can cause increases in the coexistence liquid and vapor densities, and cause the decrease of the relative volatility and the vaporization enthalpy for the systems studied. As the pore width is decreased, the two-phase region of the binary mixture becomes narrower.

Phase Coexistence and a Critical Point in Ultracold Neutral Plasmas

We show the existence of the liquid-vapor phase coexistence and a critical point for strongly coupled ions in ultracold neutral (UCN) plasmas. Expressions for the free energy of UCN plasmas and an equation of state for the ions are obtained in the mean field approximation. A van der Waals-like isotherm shows the existence of a critical point in UCN plasmas. Depending on the ion temperature, the ions are shown to exist in a mixed vapor-liquid phase for a range of the ion Coulomb coupling parameter Γ(i) (defined by the ratio between the ion interaction and the ion kinetic energies), and in a strongly coupled liquid state for values of Γ(i) above this range. The estimates of critical constants show that it may be possible to observe these phenomena in the present day UCN plasmas.

Re-entrant phase behavior for systems with competition between phase separation and self-assembly

In patchy particle systems where there is a competition between the self-assembly of finite clusters and liquid-vapor phase separation, re-entrant phase behavior can be observed, with the system passing from a monomeric vapor phase to a region of liquid-vapor phase coexistence and then to a vapor phase of clusters as the temperature is decreased at constant density. Here, we present a classical statistical mechanical approach to the determination of the complete phase diagram of such a system. We model the system as a van der Waals fluid, but one where the monomers can assemble into monodisperse clusters that have no attractive interactions with any of the other species. The resulting phase diagrams show a clear region of re-entrance. However, for the most physically reasonable parameter values of the model, this behavior is restricted to a certain range of density, with phase separation still persisting at high densities.

Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study

We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite L×L×L boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density ρ in the simple fluid or the relative concentration x(A) of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the miscibility gap) to a slablike configuration of two parallel flat interfaces. Extending the analysis of Schrader et al., [Phys. Rev. E 79, 061104 (2009)], we extract the surface free energy γ(R) of both spherical and cylindrical droplets and bubbles in the vapor-liquid case and present evidence that for R→∞ the leading order (Tolman) correction for droplets has sign opposite to the case of bubbles, consistent with the Tolman length being independent on the sign of curvature. For the symmetric binary mixture, the expected nonexistence of the Tolman length is confirmed. In all cases and for a range of radii R relevant for nucleation theory, γ(R) deviates strongly from γ(∞) which can be accounted for by a term of order γ(∞)/γ(R)-1∝R(-2). Our results for the simple Lennard-Jones fluid are also compared to results from density functional theory, and we find qualitative agreement in the behavior of γ(R) as well as in the sign and magnitude of the Tolman length.

Molecular dynamics simulation with weak coupling to heat and material baths

A method for performing molecular dynamics simulation in the grand canonical ensemble is developed. The molecular dynamics, with coupling to an external bath, simulation method of [Berendsen et al., J. Chem. Phys. 81, 3684 (1984)] is extended for this purpose. Here the physical system of interest consists of real indistinguishable particles plus one fractional particle, whose potential energy of interaction with the rest of particles is scaled by a coupling parameter, ranging dynamically between zero and one. This coupling changes the number of particles in the system gradually and dynamically, depending on the target values of the excess chemical potential, temperature, and volume. A nonlinear scaling scheme has been adopted to scale the potential energy of interaction of the fractional particle with the rest of the system. The method has been employed to predict the density of compressed Lennard-Jones fluid, compatible with the target values of temperature and the excess chemical potential, over a wide range of temperatures and densities. The method has further been applied to do molecular dynamics simulation in the grand canonical ensemble for water and to predict its vapor-liquid phase coexistence point. The results obtained using this method are in complete agreement with previously reported results in the literature.

Explicit and implicit modeling of nanobubbles in hydrophobic confinement

Water at normal conditions is a fluid thermodynamically close to the liquid-vapor phase coexistence and features a large surface tension. This combination can lead to interesting capillary phenomena on microscopic scales. Explicit water molecular dynamics (MD) computer simulations of hydrophobic solutes, for instance, give evidence of capillary evaporation on nanometer scales, i.e., the formation of nanometer-sized vapor bubbles (nanobubbles) between confining hydrophobic surfaces. This phenomenon has been exemplified for solutes with varying complexity, e.g., paraffin plates, coarse-grained homopolymers, biological and solid-state channels, and atomistically resolved proteins. It has been argued that nanobubbles strongly impact interactions in nanofluidic devices, translocation processes, and even in protein stability, function, and folding. As large-scale MD simulations are computationally expensive, the efficient multiscale modeling of nanobubbles and the prediction of their stability poses a formidable task to the'nanophysical' community. Recently, we have presented a conceptually novel and versatile implicit solvent model, namely, the variational implicit solvent model (VISM), which is based on a geometric energy functional. As reviewed here, first solvation studies of simple hydrophobic solutes using VISM coupled with the numerical level-set scheme show promising results, and, in particular, capture nanobubble formation and its subtle competition to local energetic potentials in hydrophobic confinement.