Liquid-vapor Coexistence Curve Research Articles

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.

Electric conductivities of 1:1 electrolytes in high-temperature ethanol along the liquid–vapor coexistence curve. II. Tetraalkylammonium bromides

The molar electrolyte conductivities of dilute solutions of the tetramethyl, tetraethyl, tetra-n-propyl, and tetra-n-butylammonium bromides were measured in ethanol along the liquid-vapor coexistence curve up to 160 °C. The limiting molar electrolyte conductivities and the molar association constants were obtained from the analysis of the concentration dependence of the conductivity. The ionic friction coefficients were estimated from the electrolyte conductivities. On the basis of the present data together with the literature ones at higher densities (lower temperatures) and comparisons with the continuum dielectric friction theory, the density (temperature) dependence of the translational friction coefficients of the tetraalkylammonium ions were discussed in the range of 0.810 ≥ ρ ≥ 0.634 g cm(-3) (-5 °C ≤ t ≤ 160 °C). The dielectric friction effect was important for the tetramethylammonium ion in the whole range studied. The tetraethylammonium ion showed a relatively small friction coefficient in ambient condition indicating the structure-loosening effect around the ion, while the dielectric friction effect became more important as the density reduces and the temperature raises. For the tetra-n-butylammonium ion, the friction coefficients were determined mainly by the bulky size effect. The tetra-n-propylammonium ion showed an intermediate tendency between the tetraethylammonium and tetra-n-butylammonium ions.

Equation of state of a long-range triangular-well fluid

We have devoloped a completely analytical equation of state for the long-range triangular-well (LR-TW) fluid of variable well width () as a function of temperature and density based on the augmented van der Waals theory. Hard spheres with a short-range Yukawa attraction are used as the reference fluid. We present the vapour–liquid coexistence curve and thermodynamic properties such as pressure and internal energy. Comparison with computer simulation data and the first- and second-order Barker–Henderson perturbation theory results are discussed.

Phase separation in asymmetric binary mixture of large hexagonal and small rhombus particles described within the generalised Frenkel–Louis model

The generalised Frenkel–Louis model, which is defined for asymmetric binary mixture of large hexagonal and small rhombus particles on a hexagonal lattice, is exactly solved by establishing a rigorous mapping equivalence with the one-component lattice-gas model and the corresponding spin-1/2 Ising model on a triangular lattice. This precise approach enables one to investigate in detail how the phase separation and critical behaviour in a close vicinity of demixing depends on pressure and inter-particle interactions. The binary mixture with the attractive inter-particle interaction exhibits diverse coexistence curves including asymmetric liquid–vapour coexistence curves, symmetric or asymmetric liquid–liquid coexistence curves, while asymmetric liquid–liquid coexistence curves always occur in the binary system with the repulsive inter-particle interaction.

Density of Vapor and Liquid Pentafluorobenzene Along the Saturation Line

The density of vapor and liquid pentafluorobenzene along the liquid–vapor coexistence curve has been studied by a gamma-ray attenuation technique over the temperature range from 293.5K to 530.9K. According to measurements, the coordinates of the critical point are TC = (531.04 ± 0.05) K and ρC = (518.8 ± 2) kg · m−3. The critical exponent β of the coexistence curve equals 0.345 ± 0.005. The results of our measurements were compared with data available in the literature. The height dependence of the density of a two-phase sample was investigated in relation to the temperature and time. These experiments made it possible to determine the isothermal compressibility of liquid and vapor phases near the critical point.

Asymmetry of the vapor–liquid coexistence curve: The asymptotic behavior of the "diameter"

We analyze, without resort to any model field-mixing scheme, the leading temperature-dependent term in the "diameter" of the coexistence curve asymptotically close to the vapor–liquid critical point. For this purpose, we use a simple non-parametric equation of state which we develop by meeting several general requirements. Namely, we require that the desired equation (1) lead to correct asymptotic behavior for a limited number of the fluid's parameters along selected thermodynamic paths, (2) reveal a Van der Waals loop below the critical point, and (3) be consistent with a rigorous definition of the isothermal compressibility in the critical region. For the temperature interval in question, the proposed equation approximates experimental data with an accuracy comparable to those given by Schofield's parametric equation and by other authors' equations. The desired term is obtained by applying the Maxwell rule to the equation and can be represented as D 2 β | τ| 2 β , where | τ| = | T − T c |/ T c and β is the critical exponent for the order parameter. The amplitude D 2 β is determined explicitly for the volume–temperature and entropy–temperature planes. The results obtained are contrasted with experiment to estimate the values of the amplitude coefficients of the nonanalytic terms in the "diameters" for the volume–temperature and density–temperature planes.

Optimisation of multiple time-step hybrid Monte Carlo Wang–Landau simulations in the isobaric–isothermal ensemble for the determination of phase equilibria

We discuss the optimisation as well as the convergence of a recently developed molecular simulation method using a Wang–Landau sampling scheme, combined with multiple time-step hybrid Monte Carlo (MC) simulations in the isothermal–isobaric ensemble, to determine vapour–liquid equilibria. This method has the advantage of being simple to use, as only a single simulation run at a given temperature directly gives the coexistence properties, and of being transferable to any kind of fluid, since the method is readily applicable to any molecular architecture. We apply this method to two branched alkanes, isopentane and isobutane, and discuss how we optimise the various simulation parameters. The vapour–liquid coexistence curve as well as the critical point obtained in this work are in excellent agreement with those found experimentally and in previous work using a combination of the Gibbs ensemble MC method with the configurational bias technique.

Molecular dynamics simulation of potassium along the liquid-vapor coexistence curve

The applicability of pair potential functions to liquid alkali metals is questionable. On the one hand, some recent reports in the literature suggest the validity of two-parameter pair-wise additive Lennard-Jones (LJ) potentials for liquid alkali metals. On the other hand, there are some reports suggesting the inaccuracy of pair potential functions for liquid metals. In this work, we have performed extensive molecular dynamics simulations of vapor-liquid phase equilibria in potassium to check the validity of the proposed LJ potentials and to improve their accuracy by changing the LJ exponents and taking into account the temperaturedependencies of the potential parameters. We have calculated the orthobaric liquid and vapor densities of potassium using LJ (12–6), LJ (8.5–4) and LJ (5–4), effective pair potential energy functions. The results show that using an LJ (8.5–4) potential energy function with temperature-independent parameters, e and σ, is inadequate to account for the vapor-liquid coexistence properties of potassium. Taking into account the temperature-dependencies of the LJ parameters, e(T) and σ(T), we obtained the densities of coexisting liquid and vapor potassium in a much better agreement with experimental data. Changing the magnitude of repulsive and attractive contributions to the potential energy function shows that a two-parameter LJ (5–4) potential can well reproduce the densities of liquid and vapor potassium. The results show that LJ (5–4) potential with temperature-dependent parameters produces the densities of liquid and vapor potassium more accurately, compared to the results obtained using LJ (12–6) and LJ (8.5–4) potential energy functions.

Dewetting-induced globule-coil transitions of model polymers and possible implications high-temperature and low-pressure unfolding of proteins

A thermodynamic analysis of high-temperature and low-pressure unfolding of proteins using a coarse-grained multiscale simulation combined with a liquid-state density-functional theory is presented. In this study, a hydrophobic polymer chain is employed as a probe molecule for investigating qualitative changes in a hydration free energy surface acting on proteins with changes in temperature and pressure. When water is heated so that its vapor pressure is equal to the atmospheric pressure, it boils. Long-ranged dewetting or drying caused by a hydrophobic planar wall and a large hydrophobic solute surface is significantly enhanced as it approaches the liquid-vapor coexistence curve of water. In this study, we demonstrate that high-temperature and low-pressure unfolding of the polymer chain is interpreted as dewetting-induced unfolding that occurs as it approaches the liquid-vapor coexistence. The unfolding of proteins due to high-temperature and low-pressure denaturation enhances the long-ranged dewetting or drying around them. The long-ranged dewetting phenomenon is considered to be originating from positive changes in both volume and entropy due to the high-temperature and low-pressure denaturation of the proteins.

Evolution of the liquid-vapor coexistence of the hard-core Yukawa fluid as a function of the interaction range

The present work is devoted to the study of the liquid-vapor coexistence curve of hard-core Yukawa fluids for range parameter lambda, going from 0.5 to 7 by means of an integral equation approach. Both binodal and spinodal lines are computed and compared to available simulation data, and the integral equation used appears to be accurate. We also compare two methods for determining the coordinates of the critical point. The first one, using the rectilinear diameter law, appears to be less accurate than the second one based on the heat capacity at constant volume. It is found that the critical temperature decreases as the range of the interactions increases and that the liquid-vapor coexistence disappears for lambda greater than 6.

Computer Simulations on Aggregation of Acetic Acid in the Gas Phase, Liquid Phase, and Supercritical Carbon Dioxide

Computer simulations including semiempirical molecular orbital and Monte Carlo methods were employed to investigate the aggregation of acetic acid in the gas phase, liquid phase, and supercritical carbon dioxide. The binary vapor-liquid coexistence curves of the CO(2)/acetic acid mixtures were calculated at 313.2, 333.2, and 353.2 K and are in excellent agreement with experimental measurements. Two sets of rigorous hydrogen-bonding criteria were established for the hydrogen bonding at the hydroxyl oxygen and carbonyl oxygen, respectively. With the criteria, detailed statistics of hydrogen bonding states and distribution of aggregate sizes and structures were fully investigated and compared in the three phases, which will shed light on the development of more rigorous and accurate real associated solution models in the future.

Liquid/vapor coexistence and surface tension of the Sutherland fluid with a variable range of interaction: Computer simulation and perturbation theory studies

The liquid-vapor phase diagram and surface tension for the Sutherland fluids with a variable range of interaction have been determined by canonical Monte Carlo simulations and compared with the augmented van der Waals analytic theory. The theory, based on a short-range Yukawa reference, performs well for medium-range models but its accuracy deteriorates with the shortening range due to deteriorating accuracy of the underlined analytic mean spherical approximation solution for the reference Yukawa potential. The simulation results are also analyzed from the point of the extended principle of corresponding states and it is shown that the surface tension and also, to a certain degree of accuracy, the vapor-liquid coexistence curve satisfy the principle.

Electric conductivities of 1:1 electrolytes in high-temperature ethanol along the liquid-vapor coexistence curve. I. NaBr, KBr, and CsBr

The molar electric conductivities Lambda of NaBr, KBr, and CsBr were measured in liquid ethanol at temperatures from 60 to 220 degrees C along the liquid-vapor coexistence curve. The limiting molar electrolyte conductivities Lambda(o) and the molar association constants K(A) were determined by the analysis of the concentration dependence of Lambda. The friction coefficients zeta for the Na(+), K(+), Cs(+), and Br(-) ions were estimated from Lambda(o) by an assumption that the cationic transference number of KBr is independent of temperature and density. The density dependences of zeta thus obtained together with literature values at higher densities (lower temperatures) were examined. zeta increases with decreasing density at densities above 2.0rho(c), where rho(c)=0.276 g cm(-3) is the critical density. At lower densities, the density dependences of zeta depend on ion. The relative contribution of the nonviscous effect in zeta was estimated by Deltazeta/zeta, where Deltazeta was the difference between zeta and the Stokes friction coefficient. At densities above 2.7rho(c), Deltazeta/zeta slightly decreases with decreasing density except for the Cs(+) ion. At densities below 2.7rho(c), Deltazeta/zeta increases with decreasing density and the density dependence is larger for larger ion. The results at densities above 2.2rho(c) were well explained by the Hubbard-Onsager (HO) dielectric friction theory [J. Hubbard, J. Chem. Phys. 68, 1649 (1978)] based on the sphere-in-continuum model. Below 2.2rho(c), however, experimental Deltazeta/zeta tends to be larger than the prediction of the HO theory. The lower limit density of the validity range of the HO theory is slightly higher in ethanol than in methanol.

Ergodic Convergence Times for Molecular Liquids

A problem common to all molecular dynamics and Monte Carlo simulations used to estimate fluid properties is how to decide when adequate sampling of the phase space of the system has been realized. One procedure for addressing the sampling question is to construct the energy metric for the system. The energy metric provides an indication of when the time-averaged energies of the individual molecules converge to a common value (self-averaging). The time required for the value of the energy metric to decrease to 1% of its initial value is a useful indication that adequate sampling has been realized. The energy metric based ergodic convergence times for the molecular liquids water, acetonitrile, methanol, and carbon dioxide plus mixtures of water and methanol and of water and acetonitrile are reported. The convergence time τ for water is about 100 ps at ambient conditions; for carbon dioxide it is about 300 ps while for methanol it is about 800 ps. The convergence times for water/acetonitrile mixtures are much longer due to the microheterogeneous structure of the mixtures. The ergodic convergence time is an increasing function of the mole fraction of methanol in the mixtures. The convergence times for water along the liquid side of the liquid–vapor coexistence curve are found to decrease strongly as the temperature increases.

Molecular force field investigation for Sulfur Hexafluoride: A computer simulation study

Force fields for Sulfur Hexafluoride (SF 6) from the literature, were investigated by means of their ability to reproduce experimental data in a wide range of thermodynamic conditions, including liquid, gas, vapor–liquid coexistence curve as well as supercritical states. Experimental data include numerous PVT state points, corresponding structural properties in terms of radial distribution functions, diffusion coefficient and shear viscosity. The existing force fields were extensively examined in the framework of molecular dynamics simulations and it is found that they do not accurately reproduce the macroscopic properties of the fluid, especially at high densities. To overcome this problem with the aim to obtain improved potential parameters that better reproduce experimental data, a multi-variable optimization of the force field parameters procedure has been systematically applied based on the “Simplex” method. Finally, it is found that for some common functional forms of these force fields, the new optimized parameters predict better the experimental properties of SF 6 under investigation compared to the original ones.

Development of the trappe force field for ammonia

The transferable potentials for phase equilibria (TraPPE) force field is extended through the development of a non-polarizable five-site ammonia model. In this model, the electrostatic interactions are represented by three positive partial charges placed at the hydrogen position and a compensating partial charge placed on an M site that is located on the C3 molecular axis and displaced from the nitrogen atom toward the hydrogen atoms. The repulsive and dispersive interactions are represented by placing a single Lennard–Jones site at the position of the nitrogen atom. Starting from the five-site model by Impey and Klein (Chem. Phys. Lett. 1984, 104, 579), this work optimizes the Lennard–Jones parameters and the magnitude of the partial charges for three values of the M site displacement. This parameterization is done by fitting to the vapor–liquid coexistence curve of neat ammonia. The accuracy of the three resulting models (differing in the displacement of the M site) is assessed through computation of the binary vapor–liquid equilibria with methane, the structure and the dielectric constant of liquid ammonia. The five-site model with an intermediate displacement of 0.08 Å for the M site yields a much better value for the dielectric constant, whereas differences in the other properties are quite small.

Low-coordination phases of both crystalline and fluid states of alkali metals under extreme conditions of high and low densities, respectively

After a brief summary of early work, involving the present authors, relating to low coordination phases of some alkalis in either dense crystalline states at high pressure (e.g. Li) or low density metallic fluids near criticality (Cs and Rb), contact is made with the very recent density functional study by Pickard and Needs (Phys. Rev. Lett. 102, 146401 (2009)). Whereas these authors predict three- and four-fold coordination numbers for extremely high pressure crystalline phases of Li, we stress here the remarkable behaviour of the heavy alkali metallic fluids Cs and Rb along the liquid–vapour coexistence curve towards the critical point. Coordination numbers ∼8−10 near melting then reduce, as the density is lowered, to 2 at or near the critical point.

Mie Potentials for Phase Equilibria Calculations: Application to Alkanes and Perfluoroalkanes

Transferable united-atom force fields, based on n - 6 Lennard-Jones potentials, are presented for normal alkanes and perfluorocarbons. It is shown that by varying the repulsive exponent the range of the potential can be altered, leading to improved predictions of vapor pressures while also reproducing saturated liquid densities to high accuracy. Histogram-reweighting Monte Carlo simulations in the grand canonical ensemble are used to determine the vapor liquid coexistence curves, vapor pressures, heats of vaporization, and critical points for normal alkanes methane through tetradecane, and perfluorocarbons perfluoromethane through perfluorooctane. For all molecules studied, saturated liquid densities are reproduced to within 1% of experiment. Vapor pressures for normal alkanes and perfluorocarbons were predicted to within 3% and 6% of experiment, respectively. Calculations performed for binary mixture vapor-liquid equilibria for propane + pentane show excellent agreement with experiment, while slight deviations are observed for the ethane + perfluoroethane mixture.

Comprehensive study of the thermodynamic properties of fullerene C60 along the liquid–vapour coexistence

We present a theoretical model for calculating the thermodynamic properties of liquid C60 by means of an improved equation of state (EOS), in which the particles interact via pairwise interaction composed of hard-core plus suitable linear combinations of three Yukawa functions. The proposed EOS provides simple analytical expressions for Helmholtz free energy and pressure, which are the basic ingredients to compute the liquid–vapour coexistence curve of C60 as well as all other thermodynamic properties for the bulk liquid and vapour phases. The comparisons with computer simulation results, based on Girifalco potential, suggest the importance of treating the attractive tail of the potential accurately. It is to be noted that the obtained results of the thermodynamic properties along the binodal curve of C60 exhibit interesting features; in particular, the vapour phase shows abnormal behaviour of its isothermal compressibility and configurational heat capacity. The estimated critical parameters Tc = 2008.8 K, ρc = 0.50 nm−3 and Pc = 54.8 bars are in good agreement with NVT-Monte Carlo simulation predictions. The critical parameters of C60 are compared with those of liquid metals, non-metals and some hydrocarbons.

Properties of water along the liquid-vapor coexistence curve via molecular dynamics simulations using the polarizable TIP4P-QDP-LJ water model

We present an extension of the TIP4P-QDP model, TIP4P-QDP-LJ, that is designed to couple changes in repulsive and dispersive nonbond interactions to changes in polarizability. Polarizability is intimately related to the dispersion component of classical force field models of interactions, and we explore the effect of incorporating this connection explicitly on properties along the liquid-vapor coexistence curve of pure water. Parametrized to reproduce condensed-phase liquid water properties at 298 K, the TIP4P-QDP-LJ model predicts density, enthalpy of vaporization, self-diffusion constant, and the dielectric constant at ambient conditions to about the same accuracy as TIP4P-QDP but shows remarkable improvement in reproducing the liquid-vapor coexistence curve. TIP4P-QDP-LJ predicts critical constants of T(c)=623 K, rho(c)=0.351 g/cm(3), and P(c)=250.9 atm, which are in good agreement with experimental values of T(c)=647.1 K, rho(c)=0.322 g/cm(3), and P(c)=218 atm, respectively. Applying a scaling factor correction (obtained by fitting the experimental vapor-liquid equilibrium data to the law of rectilinear diameters using a three-term Wegner expansion) the model predicts critical constants (T(c)=631 K and rho(c)=0.308 g/cm(3)). Dependence of enthalpy of vaporization, self-diffusion constant, surface tension, and dielectric constant on temperature are shown to reproduce experimental trends. We also explore the interfacial potential drop across the liquid-vapor interface for the temperatures studied. The interfacial potential demonstrates little temperature dependence at lower temperatures (300-450 K) and significantly enhanced (exponential) dependence at elevated temperatures. Terms arising from the decomposition of the interfacial potential into dipole and quadrupole contributions are shown to monotonically approach zero as the temperature approaches the critical temperature. Results of this study suggest that self-consistently treating the coupling of phase-dependent polarizability with dispersion interactions in classical water force fields may be an important effect for the extension of polarizable water force fields to reproduce properties along the liquid-vapor coexistence envelope as well as near critical conditions. More importantly, the present study demonstrates the rather remarkable transferability of a water model parametrized to a single state point to other thermodynamic states. Further studies are recommended.