Liquid Coexistence Research Articles

Prediction of Vapor–Liquid Coexistence Properties and Critical Points of Polychlorinated Biphenyls from Monte Carlo Simulations with the TraPPE–EH Force Field

Gibbs ensemble Monte Carlo simulations using the explicit-hydrogen version of the transferable potentials for phase equilibria (TraPPE–EH) force field were carried out to predict the vapor–liquid coexistence and critical properties of biphenyl, monochlorinated biphenyls, and of 16 polychlorinated biphenyls. The predictions are in very good agreement with the limited experimental data. Transferring the TraPPE–EH Lennard-Jones parameters from benzene to construct biphenyl yields predicted critical properties and normal boiling temperature with an average deviation of less than 1 %. The saturated vapor pressures for biphenyl, 2-chorobiphenyl, and 4-chlorobiphenyl fall within 10 % of the experimental data. Overall, the critical temperatures increase nearly linearly with the number of chlorine substituents and are correlated with the dipole moment for the monochlorinated isomers. In contrast, 4,4′-dichlorobiphenyl, the most elongated compound, exhibits the highest critical temperature among the disubstituted biphenyls.

III. Study of critical and maximum temperatures of coexistence of liquid and gas phase in hydrocarbons binary mixtures of aromatic hydrocarbons with alkanes and cycloalkanes

Form of the phase diagrams in the coordinates “temperature-density”, critical and maximum temperature of liquid and vapor phases coexistence for binary mixtures (n-C5, n-C6, n-C8, n-C11)+benzene, n-C5+toluene and н-C5+2-methylbiphenyl were determined by isochoric method. Their interrelation with the difference of the critical temperatures of components forming the mixture was determined. The prediction method was developed and tested using own experimental and literature data on critical and maximum temperatures of binary mixtures of aromatic hydrocarbons with alkanes and cycloalkanes.

Mie Potentials for Phase Equilibria: Application to Alkenes

Transferable united-atom force fields based on Mie potentials are presented for alkenes. Monte Carlo simulations in the grand canonical ensemble, combined with histogram reweighting, are used to determine vapor–liquid coexistence curves, vapor pressures, heats of vaporization, boiling points, and critical properties for 1-alkenes from ethene to 1-octene. To assess the transferability of the optimized parameters, additional calculations are performed for the cis and trans isomers of 2-butene and 2-pentene and the dienes 1,3-butadiene and 1,5-hexadiene. Saturated liquid densities for the 1-alkenes, 2-pentenes, and 1,5-hexadiene are predicted to within 1 % of experimental data, while deviations of (2 to 5) % from experiment were observed for cis-2-butene and 1,3-butadiene, respectively. Vapor pressures for the alkenes are predicted to within (2 to 15) % of experiment, with errors increasing with chain length and at lower temperatures. Critical temperatures are predicted to within 1 % of experiment for all molecules except for 1,3-butadiene, where the critical temperature is under-predicted by 3.5 %. Transferability is further evaluated through calculations of binary mixture vapor–liquid equilibria. Predictions of the Mie potentials for ethane + propene and 1-butane + 1-hexene are indistinguishable from experimental data.

Prediction of Vapor–Liquid Coexistence Data for p-Cymene Using Equation of State Methods and Monte Carlo Simulations

A naturally occurring aromatic organic compound, p-cymene, finds applications as reaction intermediate, solvent in production of pharmaceuticals, fragrances, and fine chemicals. The experimental vapor liquid equilibria (VLE) data of p-cymene is available at pressures up to 537.4 kPa. In this study, the thermodynamic properties of p-cymene are determined using structure property correlations combined with equations of state (EoS) and molecular simulation techniques. Two molecular simulation techniques, Gibbs ensemble Monte Carlo (GEMC) and grand canonical-transition matrix Monte Carlo (GC-TMMC) have been employed for prediction of VLE. The estimates of properties, including vapor pressures, heats of vaporization, coexistence densities, and critical properties have been compared with available experimental data. The thermodynamic properties predicted by molecular simulations and also that obtained from Peng–Robinson (PR) and volume translated Peng–Robinson (VTPR) EoS are generally, in broad agreement with the experimental data. Further, GEMC results for coexistence densities and saturation vapor pressures are compared with that from GC-TMMC technique.

Layering transitions and solvation forces in an asymmetrically confined fluid

We consider a simple fluid confined between two parallel walls (substrates), separated by a distance L. The walls exert competing surface fields so that one wall is attractive and may be completely wet by liquid (it is solvophilic) while the other is solvophobic. Such asymmetric confinement is sometimes termed a "Janus Interface." The second wall is: (i) purely repulsive and therefore completely dry (contact angle θ = 180°) or (ii) weakly attractive and partially dry (θ is typically in the range 160-170°). At low temperatures, but above the bulk triple point, we find using classical density functional theory (DFT) that the fluid is highly structured in the liquid part of the density profile. In case (i), a sequence of layering transitions occurs: as L is increased at fixed chemical potential μ close to bulk gas-liquid coexistence μco, new layers of liquid-like density develop discontinuously. In contrast to confinement between identical walls, the solvation force is repulsive for all wall separations and jumps discontinuously at each layering transition and the excess grand potential exhibits many metastable minima as a function of the adsorption. For a fixed temperature T = 0.56TC, where TC is the bulk critical temperature, we determine the transition lines in the L, μ plane. In case (ii), we do not find layering transitions and the solvation force oscillates about zero. We discuss how our mean-field DFT results might be altered by including effects of fluctuations and comment on how the phenomenology we have revealed might be relevant for experimental and simulation studies of water confined between hydrophilic and hydrophobic substrates, emphasizing it is important to distinguish between cases (i) and (ii).

Thermodynamics of Phase Coexistence and Metal–Nonmetal Transition in Mercury: Assessment of Effective Potentials via Expanded Wang–Landau Simulations

We present molecular simulation results on the thermodynamics of phase transitions (specifically, the vapor-liquid and metal-nonmetal transitions) in mercury, as predicted by effective potential models. We use a recently developed method, known as Expanded Wang-Landau simulations, to determine the grand-canonical partition function of systems of mercury atoms. Using the statistical mechanics formalism, we are then able to determine all thermodynamic properties of the system, including the Gibbs free energy and entropy. Prior experimental and theoretical work has emphasized the strong interplay between the vapor-liquid coexistence and the metal-nonmetal transition. We therefore start by assessing the accuracy of the effective potentials considered in this work through a comparison to the available experimental data. We then analyze the thermodynamics of the nonmetal liquid-metal liquid transition, characterized by sharp variations in the rate of change of Gibbs free energy and enthalpy as a function of density. We also identify a crossover density (10.5 g/cm(3)) consistent with the results of recent ab initio calculations and with the experiment.

Liquid–Liquid Phase Equilibria and Critical Phenomena of the Binary Mixture Nitrobenzene + n-Nonane

The liquid–liquid coexistence curve for nitrobenzene + n-nonane has been measured in a wide temperature range. The values of the critical exponent β obtained from the liquid–liquid equilibrium data...

Heat capacities and asymmetric criticality of the (liquid + liquid) coexistence curves for {dimethyl carbonate + n-undecane, or n-tridecane}

The (liquid+liquid) coexistences and the critical behavior of isobaric heat capacity per unit volume for critical binary solutions {dimethyl carbonate+n-undecane, or n-tridecane} have been studied. The critical exponents β and α were deduced and found to be consistent with the 3D-Ising values. The critical amplitudes were determined and used to test the asymmetric criticality of coexistence curves. It was found that the heat capacity does play an important role in describing the asymmetric criticality of the coexistence curves.

Application of the Firefly and Luus–Jaakola algorithms in the calculation of a double reactive azeotrope

The calculation of reactive azeotropes is an important task in the preliminary design and simulation of reactive distillation columns. Classically, homogeneous nonreactive azeotropes are vapor–liquid coexistence conditions where phase compositions are equal. For homogeneous reactive azeotropes, simultaneous phase and chemical equilibria occur concomitantly with equality of compositions (in the Ung–Doherty transformed space). The modeling of reactive azeotrope calculation is represented by a nonlinear algebraic system with phase equilibrium, chemical equilibrium and azeotropy equations. This nonlinear system can exhibit more than one solution, corresponding to a double reactive azeotrope. In a previous paper (Platt et al 2013 J. Phys.: Conf. Ser. 410 012020), we investigated some numerical aspects of the calculation of reactive azeotropes in the isobutene + methanol + methyl-tert-butyl-ether (with two reactive azeotropes) system using two metaheuristics: the Luus–Jaakola adaptive random search and the Firefly algorithm. Here, we use a hybrid structure (stochastic + deterministic) in order to produce accurate results for both azeotropes. After identifying the neighborhood of the reactive azeotrope, the nonlinear algebraic system is solved using Newton's method. The results indicate that using metaheuristics and some techniques devoted to the calculation of multiple minima allows both azeotropic coordinates in this reactive system to be obtains. In this sense, we provide a comprehensive analysis of a useful framework devoted to solving nonlinear systems, particularly in phase equilibrium problems.

Partitioning of Si and platinum group elements between liquid and solid Fe–Si alloys

Crystallization of the Earth’s inner core fractionates major and minor elements between the solid and liquid metal, leaving physical and geochemical imprints on the Earth’s core. For example, the density jump observed at the Inner Core Boundary (ICB) is related to the preferential partitioning of lighter elements in the liquid outer core. The fractionation of Os, Re and Pt between liquid and solid during inner core crystallization has been invoked as a process that explains the observed Os isotopic signature of mantle plume-derived lavas (Brandon et al., 1998; Brandon and Walker, 2005) in terms of core–mantle interaction. In this article we measured partitioning of Si, Os, Re and Pt between liquid and solid metal. Isobaric (2 GPa) experiments were conducted in a piston-cylinder press at temperatures between 1250°C and 1600°C in which an imposed thermal gradient through the sample provided solid–liquid coexistence in the Fe–Si system. We determined the narrow melting loop in the Fe–Si system using Si partitioning values and showed that order–disorder transition in the Fe–Si solid phases can have a large effect on Si partitioning. We also found constant partition coefficients (DOs, DPt, DRe) between liquid and solid metal, for Si concentrations ranging from 2 to 12 wt%. The compact structure of Fe–Si liquid alloys is compatible with incorporation of Si and platinum group elements (PGEs) elements precluding solid–liquid fractionation. Such phase diagram properties are relevant for other light elements such as S and C at high pressure and is not consistent with inter-elemental fractionation of PGEs during metal crystallization at Earth’s inner core conditions. We therefore propose that the peculiar Os isotopic signature observed in plume-derived lavas is more likely explained by mantle source heterogeneity (Meibom et al., 2002; Baker and Krogh Jensen, 2004; Luguet et al., 2008).

Critical and maximum temperatures of coexistence of liquid and gas phase in hydrocarbons binary mixtures. II. Maximum temperatures of coexistence of liquid and gas phase in alkane binary mixtures

This work systematizes the data published to date on the maxcondentherm for 27 binary mixtures of alkanes (first component – C1–C4 and second component – C2–C10 and the mixtures which contain 2-methylpentane, 2-methylhexane, 2-methylheptane and 2-methyloctane). The abilities of combination methods and limits of their use were defined in application to prediction of the maxcondentherm for binary mixtures of alkanes.

Force field comparison and thermodynamic property calculation of supercritical CO2 and CH4 using molecular dynamics simulations

Thermodynamic properties of carbon dioxide and methane have been calculated under supercritical conditions up to 900K and 100MPa using isothermal-isobaric molecular dynamics simulations and the multistate Bennett acceptance ratio (MBAR) technique. Seven different carbon dioxide force fields (two single-site models, three rigid three-site models, and two fully flexible three-site models) were considered for preliminary density calculation. Those showing better accuracy when compared to experimental results were used to calculate the volume expansivity, isothermal compressibility, isobaric and isochoric heat capacities, Joule–Thomson coefficient, and speed of sound. The same properties were also calculated for methane using two different single-site models.The results show that force fields originally parameterized and optimized to reproduce vapor–liquid coexistence curves may be able to give accurate predictions of other thermodynamic properties in an extended temperature and pressure range. The results obtained with molecular simulations are generally more accurate than predictions with the Peng–Robinson equation of state, especially near critical conditions and at high pressures. Furthermore, the MBAR technique is successfully applied to improve the accuracy of results, decrease calculation uncertainties and reduce the number of simulations required to provide reliable property predictions over a range of temperatures and pressures. Recommendations are made as to which force fields are most accurate for the set of properties computed here.

Molecular dynamics study of melting curve, entropy of fusion and solid–liquid interfacial energy of cobalt under pressure

We performed molecular dynamics (MD) simulations with the two embedded atom method (EAM) potentials to calculate the melting curves of cobalt over a wide range of pressure. Zhou׳s EAM potential can produce satisfying results, in better agreement with the experiment compared with Pun׳s. Based on Zhou׳s potential, we simulated the melting of Co with two approaches, i.e., the one-phase (hysteresis) method and two-phase (solid–liquid coexistence) method. Both approaches can effectively reduce the superheating, and their results are in the close proximity at the applied pressures. With the one-phase method, during the investigation of the entropy of fusion of Co, we found that with the pressure increasing, the entropy of fusion decreases rapidly first and then oscillates with pressure; when the pressure is beyond 100GPa, the entropy of fusion shows less pressure effect. When taking account of the solid–liquid interfacial energy at different pressures, we found that it increases monotonically with pressure, and can be well described as a fifth-order polynomial relation. Moreover, the thermal equation of state (EOS) and the temperature dependence of atomic structures of Co have been obtained successfully.

Phase Coexistence in Ternary Lipid Mixtures Containing POPC and Phytosterols, Ergosterol or 7-Dehydrocholesterol

2H-NMR spectroscopy was used to investigate the occurrence of phase coexistence in multilamellar vesicles of DPPC and POPC (33mol%: 33mol%) with either stigmasterol, brassicasterol, ergosterol or 7-DHC (each 33mol%). In all cases, the sn-1 chains of DPPC and POPC were deuterated in turn, and 2H-NMR spectra were measured for both lipid components as a function of temperature between 5 oC and 48 oC. The chain order of DPPC was found to be greater than that of POPC in all the above mixtures. An equimolar DPPC/POPC membrane exhibits a clear solid-ordered (so)-liquid disordered (ld) transition between 5 oC and about 33 oC as observed for each lipid by a fairly steep reduction in the average spectral width. Adding sterol generally results in a more gradual change in average spectral width over this temperature range. Depending on the particular sterol, NMR spectra taken in this temperature range either appeared poorly resolved (“blurry”) or displayed coexisting liquid ordered (lo) and ld spectra. Liquid-liquid phase coexistence is observed in DPPC/POPC/ergosterol mixtures. The spectra for DPPC/POPC/ brassicasterol only exhibited liquid-liquid coexistence when a small concentration (0.02 mol%) of the fluorescent lipid dye TR-DHPE was added to the system. Only one liquid phase was observed for either DPPC/POPC/7DHC or DPPC/POPC/stigmasterol. In summary, our interest was to study how liquid phase coexistence in DPPC/POPC/sterol is modified by small changes in the sterol structure. These studies show that ergosterol is the most effective sterol in fostering phase coexistence. Note that in comparison to cholesterol, which does not cause micron scale phase coexistence in DPPC/POPC, ergosterol has an extra double in the fused ring, as well as a double bond at C22. Possible connections between the detailed sterol structures and these observations will be discussed.

Temperature dependence of the crystal-liquid interfacial free energy and the endpoint of the melting line

The crystal-liquid interfacial free energy γ has been calculated as a function of the crystal orientation in a molecular dynamics experiment in a system of Lennard-Jones (LJ) particles with a cutoff radius of the potential rc(*)=rc/σ=6.78 at a triple-point temperature Tt(*)=kBTt/ε=0.692 and temperatures above (in the region of the stable coexistence of liquid and solid phases) and below (metastable continuation of the coexistence curve of liquid and solid phases) the temperature Tt(*). At T(*)=Tt(*), for determining γ use was made of the method of cleaving potential. The temperature dependence of γ on the crystal-liquid coexistence curve has been determined by the Gibbs-Cahn thermodynamic integration method. In the region of stable phase coexistence (T(*)>Tt(*)) good agreement with the data of Davidchack and Laird [J. Chem. Phys. 118, 7651 (2003)] has been obtained with respect to the character of the temperature dependence of γ and the orientation anisotropy. In the region of metastable phase coexistence (T(*)<Tt(*)) at the approach to the endpoint of the melting line (TK(*)=0.529) (the existence of which was established first by Baidakov and Protsenko [Phys. Rev. Lett. 95, 015701 (2005)]) the interfacial free energy decreases, approaching at T(*)=TK(*) the orientation-averaged value γ0K(*)=γ0Kσ(2/ε)=0.365. The paper discusses the behavior of the excess interfacial energy, excess interfacial entropy and excess interfacial stress on the metastable extension of the melting line and close to T(*)=TK(*).

Wetting Transition in Water

Optical images were used to study the wetting behavior of water on graphite, sapphire, and quartz along the liquid vapor coexistence curve from room temperature to 300 °C. Wetting transitions were identified by the temperature at which the contact angle decreased to zero and also by the disappearance of dropwise condensation. These two methods yielded consistent values for the wetting temperatures, which were 185 °C, 234 °C, and 271 °C for water on quartz, sapphire, and graphite, respectively. We compare our results with the theoretical predictions based on a simplified model of the water-substrate potential and sharp interfaces.

Surface Thermodynamic Analysis of Fluid Confined in a Cone and Comparison with the Sphere–Plate and Plate–Plate Geometries

The behavior of pure fluid confined in a cone is investigated using thermodynamic stability analysis. Four situations are explained on the basis of the initial confined phase (liquid/vapor) and its pressure (above/below the saturation pressure). Thermodynamic stability analysis (a plot of the free energy of the system versus the size of the new potential phase) reveals whether the phase transition is possible and, if so, the number and type (unstable/metastable/stable) of equilibrium states in each of these situations. Moreover we investigated the effect of the equilibrium contact angle and the cone angle (equivalent to the confinement's surface separation distance) on the free energy (potential equilibrium states). The results are then compared to our previous study of pure fluid confined in the gap between a sphere and a flat plate and the gap between two flat plates.1 Confined fluid behavior of the four possible situations (for these three geometries) can be explained in a unified framework under two categories based on only the meniscus shape (concave/convex). For systems with bulk-phase pressure imposed by a reservoir, the stable coexistence of pure liquid and vapor is possible only when the meniscus is concave.

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.

The liquid–liquid coexistence curves of {x nitrobenzene + (1 − x) 2-methylpentane} and {x nitrobenzene + (1 − x) isooctane} in the critical region

The liquid–liquid coexistence curves for {x nitrobenzene+(1−x) 2-methylpentane} and {x nitrobenzene+(1−x) isooctane} were measured and the critical exponents and the critical amplitudes are deduced. The critical exponents were found to be consistent with the 3D-Ising value. The experiment results are analyzed to examine the dependences of the width and the asymmetry of the coexistence curves on the molar volume of the branched alkane. These dependences were also discussed through the Landau–Ginsburg–Wilson type model and the complete scaling theory.

Modelling and interpreting the isotopic composition of water vapour in convective updrafts

Abstract. The isotopic compositions of water vapour and its condensates have long been used as tracers of the global hydrological cycle, but may also be useful for understanding processes within individual convective clouds. We review here the representation of processes that alter water isotopic compositions during processing of air in convective updrafts and present a unified model for water vapour isotopic evolution within undiluted deep convective cores, with a special focus on the out-of-equilibrium conditions of mixed-phase zones where metastable liquid water and ice coexist. We use our model to show that a combination of water isotopologue measurements can constrain critical convective parameters, including degree of supersaturation, supercooled water content and glaciation temperature. Important isotopic processes in updrafts include kinetic effects that are a consequence of diffusive growth or decay of cloud particles within a supersaturated or subsaturated environment; isotopic re-equilibration between vapour and supercooled droplets, which buffers isotopic distillation; and differing mechanisms of glaciation (droplet freezing vs. the Wegener–Bergeron–Findeisen process). As all of these processes are related to updraft strength, particle size distribution and the retention of supercooled water, isotopic measurements can serve as a probe of in-cloud conditions of importance to convective processes. We study the sensitivity of the profile of water vapour isotopic composition to differing model assumptions and show how measurements of isotopic composition at cloud base and cloud top alone may be sufficient to retrieve key cloud parameters.