The special features of phase equilibria in α-pinene-water binary mixtures in the sub- and supercritical states

Phase equilibria in α-pinene-water binary mixtures under sub-and supercritical conditions were studied by thermodynamic modeling. The compositions and boiling points of three-phase heteroazeotropic mixtures were calculated as functions of pressure. The T and p regions of the existence of liquid-liquid and vapor-liquid two-phase mixtures were determined. The T _cmix and p _cmix critical curve coordinates depending on mixture composition were found. The T _cmix curve exhibited an anomaly in the form of a minimum. The T _Az-p _Az heteroazeotropic line ended at the minimum point of the critical curve.     

Molecular simulation of the phase behavior of fluids and fluid mixtures using the synthetic method

A new molecular simulation procedure is reported for determining the phase behavior of fluids and fluid mixtures, which closely follows the experimental synthetic method. The simulation procedure can be implemented using Monte Calro or molecular dynamics in either the microcanonical or canonical statistical ensembles. Microcanonical molecular dynamics simulations are reported for the phase behavior of both the pure Lennard-Jones fluid and a Lennard-Jones mixture. The vapor pressures for the pure fluid are in good agreement with Monte Carlo Gibbs ensemble and Gibbs-Duhem calculations. The Lennard-Jones mixture is composed of equal size particles, with dissimilar energy parameters (?(2)∕?(1) = 1∕2, ?(12)∕?(1) = 1∕2). The binary Lennard-Jones mixture exhibits liquid-liquid equilibria at high pressures and the simulation procedure allows us to estimate the coordinates of the high-pressure branch of the critical curve.     

Perfect wetting along a three-phase line: theory and molecular dynamics simulations

Wetting behavior along a three-phase equilibrium has been obtained by density gradient theory (DGT) and molecular dynamics simulations for a type-II equal size Lennard-Jones mixture. In order to perform a consistent comparison between both methodologies, the molecular parameters of this type of mixture were defined from the global phase diagram of equal size Lennard-Jones mixtures. We have found excellent agreement between predictions from the DGT (coupled to a Lennard-Jones equation for the bulk phases) and simulations results for both the phase and interface behavior, in the whole temperature, pressure, and concentration ranges. For all conditions explored in this work, this type-II mixture shows a three-phase equilibrium composed by a bulk immiscible liquid phase (L1) and a bulk gas phase (G) separated by a second immiscible liquid phase (L2). A similar phase distribution is obtained from the interfacial concentration profile in the whole range of conditions used in this work. This type of structure is a clear evidence that L2 completely wets the GL1 interface. The wetting behavior is also confirmed by the values and evolution of the interfacial tensions. In summary, this kind of type-II mixture does not show wetting transitions and exhibits a permanent perfect wetting in all the thermodynamic conditions explored here.     

Critical point estimation of the Lennard-Jones pure fluid and binary mixtures

The apparent critical point of the pure fluid and binary mixtures interacting with the Lennard-Jones potential has been calculated using Monte Carlo histogram reweighting techniques combined with either a fourth order cumulant calculation (Binder parameter) or a mixed-field study. By extrapolating these finite system size results through a finite size scaling analysis we estimate the infinite system size critical point. Excellent agreement is found between all methodologies as well as previous works, both for the pure fluid and the binary mixture studied. The combination of the proposed cumulant method with the use of finite size scaling is found to present advantages with respect to the mixed-field analysis since no matching to the Ising universal distribution is required while maintaining the same statistical efficiency. In addition, the accurate estimation of the finite critical point becomes straightforward while the scaling of density and composition is also possible and allows for the estimation of the line of critical points for a Lennard-Jones mixture.     

Systematic investigation of global phase behavior of polymer mixtures in the pressure-temperature plane

We investigate the critical lines of polymer mixtures in the presence of their vapor phase at the mathematical double point, where two critical lines meet and exchange branches, and its environment. The model used combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory. The critical line structure is displayed for various combinations of the chain length and system parameters in the pressure (P)-temperature (T) plane, as is usually done with experimental results. This type of work sheds light on the essential transition mechanism involved in the phase diagram's change of character, such as multi-critical points and mathematical double points, which are of great practical importance in supercritical fluid extraction processes. The P, T diagrams are discussed in accordance with the Scott and van Konynenburg binary phase diagram classification. We found that our P, T plots were in agreement with type II, type III, or type IV phase diagram behaviors. We also found that some of our phase diagrams represent the liquid-liquid equilibria in polymer solutions and mixtures.     

Solvatochromic behavior of phenol blue in CO2+ethanol and CO2+n-pentane mixtures in the critical region and local composition enhancement

The UV-Vis spectra of probe phenol blue in CO(2)+ethanol and CO(2)+n-pentane binary mixtures were studied at 308.15 K and different pressures. The experiments were conducted in both supercritical region and subcritical region of the mixtures by changing the compositions of the mixed solvents. On the basis of the experimental results the local compositions of the solvents about phenol blue were estimated by neglecting the size difference of CO(2) and the cosolvents. Then the local composition data were corrected by a method proposed in this work, which is mainly based on Lennard-Jones sphere model. It was demonstrated that the local mole fraction of the cosolvents is higher than that in the bulk solution at all the experimental conditions. In the near critical region of the mixed solvents the local composition enhancement, defined as the ratio of cosolvent mole fraction about the solute to that in the bulk solution, increased significantly as pressure approached the phase boundary from high pressure. The local composition enhancement was not considerable as pressure was much higher than the critical pressure. In addition, in subcritical region the degree of composition enhancement was much smaller and was not sensitive to pressure in the entire pressure range as the concentration of the cosolvents in the mixed solvents was much higher than the concentration at the critical point of the mixtures.     

Fluid-phase behavior of binary mixtures in which one component can have two critical points

We investigate theoretically the binary fluid-phase behavior of mixtures in which one water-like component can have two critical points. We consider three equal-sized nonpolar solutes that differ in the strength of their dispersive interactions (a1 < a2 < a3, where a denotes the van der Waals attractive parameter). In each case, we compare the phase behavior predicted using two sets of parameters for water: one giving rise to a pure component low-temperature liquid-liquid transition terminating at a critical point (two-critical-point parameter set), and one in which no such second critical point exists (singularity-free parameter set). Regardless of the parameter values used, we find five mixture critical lines. Using the two-critical-point parameter set, we find that a critical line originates at water's second critical point for aqueous mixtures involving solutes 1, 2, or 3. For mixtures involving solutes 1 or 2, this line extends towards low pressures and high temperatures as the solute mole fraction increases, and is closely related to the critical line originating at water's ordinary vapor-liquid critical point: these two critical lines are loci of upper and lower consolute points corresponding to the same liquid-liquid transition. In mixtures involving solute 2, the critical locus emanating from water's second critical point is shifted to higher temperatures compared to mixtures involving solute 1, and extends up to T approximately 310 K at moderate pressures (ca. 200 bars). This suggests the possibility of an experimentally accessible manifestation of the existence of a second critical point in water. For binary mixtures involving solutes 1 or 2, changing the water parameters from the two critical points to the singularity-free case causes the disappearance of a lower consolute point at moderate pressures. For binary mixtures involving solute 3, the differences between two-critical-point and singularity-free behaviors occur only in the experimentally difficult-to-probe low-temperature and high-pressure region.     

Global fluid phase equilibria and critical phenomena of selected mixtures using the crossover soft-SAFT equation

We present here the extension of the crossover soft-statistical associating fluid theory (soft-SAFT) equation of state to mixtures, as well as some illustrative applications of the methodology to mixtures of particular scientific and technological interest. The procedure is based on White's work (White, J. A. Fluid Phase Equilib. 1992, 75, 53) from the renormalization group theory, as for the pure fluids, with the isomorphism assumption applied to the mixtures. The equation is applied to three groups of mixtures: selected mixtures of n-alkanes, the CO2/n-alkane homologous series, and the CO2/1-alkanol homologous series. The crossover equation is first applied to the pure components of the mixtures, CO2 and the 1-alkanol family, while an available correlation is used for the molecular parameters of the n-alkane series (Llovell et al. J. Chem. Phys 2004, 121, 10715). A set of transferable molecular parameters is provided for the 1-alkanols series; these are accurate for the whole range of thermodynamic conditions. The crossover soft-SAFT equation is able to accurately describe these compounds near to and far from the critical point. The theory is then used to represent the phase behavior and the critical phenomena of the selected mixtures. We use binary interaction parameters xi and eta for dissimilar mixtures. These parameters are fitted at some particular conditions (one subcritical temperature or binary critical data) and used to predict the behavior of the mixture at different conditions (other subcritical conditions and/or critical conditions). The equation is able to capture the continuous change in the critical behavior of the CO2/n-alkane and the CO2/1-alkanol homologous series as the chain length of the second compound increases. Excellent agreement with experimental data is obtained, even in the most nonideal cases. The new equation is proved to be a powerful tool to study the global phase behavior of complex systems, as well as other thermodynamic properties of very challenging mixtures.     

The phase behavior of two-dimensional symmetrical mixtures

Using Monte Carlo simulation methods in the grand canonical and semigrand canonical ensembles, we study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles. We discuss the interplay between the demixing transition in a liquid and the freezing in detail. Phase diagrams for several systems characterized by different parameters describing interactions in the system are presented. It is explicitly demonstrated that different scenarios involving demixing and freezing transitions, described in our earlier paper [A. Patrykiejew and S. Soko?owski, Phys. Rev. E, 81, 012501 (2010)], are possible. In one class of systems, the λ-line representing a continuous demixing transition in a liquid phase starts at the liquid side of either the vapor-liquid or liquid-solid coexistence. The second class involves the systems in which the λ-line begins at the liquid side of the vapor-liquid coexistence, in the lower critical end point, and then terminates at the liquid side of the liquid-solid coexistence, in the upper critical end point. It is also shown that in such systems the solid phase may undergo a demixing transition at the temperature above the upper critical end point.     

Capillary condensation of a binary mixture in slit-like pores

We investigate the capillary condensation of two model fluid mixtures in slit-like pores, which exhibit different demixing properties in the bulk phase. The interactions between adsorbate particles are modeled by using Lennard-Jones (12,6) potentials and the adsorbing potentials are of the Lennard-Jones (9,3) type. The calculations are performed for different pore widths and at different concentrations of the bulk gas, by means of density functional theory. We evaluate the capillary phase diagrams and discuss their dependence on the parameters of the model. Our calculations indicate that a binary mixture confined to a slit-like pore may exhibit rich phase behavior.     

Determination of fluid-phase behavior using transition-matrix Monte Carlo: binary Lennard-Jones mixtures

We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.     

Effect of partial charge parametrization on the fluid phase behavior of hydrogen sulfide

The effect of partial charge parametrization on the fluid phase behavior of hydrogen sulfide is investigated with grand canonical histogram reweighting Monte Carlo simulations. Four potential models, based on a Lennard-Jones + point charge functional form, are developed. It is shown that Lennard-Jones parameters can be tuned such that partial charges for the sulfur atom in the range -0.40 < q(s) < -0.252 will lead to an accurate reproduction of experimental vapor-liquid equilibria. Each of the parameter sets developed in this work are used to predict the pressure composition behavior H2S-n-pentane at 377.6 K. While the mixture calculation provides a means of reducing the number of candidate parameter sets, multiple parameter sets were found to yield an excellent reproduction of both the pure component and mixture phase behavior.     

Phase equilibria and critical phenomena in fluid (n-alkane + water) systems at high pressures and temperatures

In fluid (n-alkane + water) mixtures (gas + gas) equilibria of the second type are found. Phase equilibria in fluid (n-pentane + water) and (n-heptane + water) were measured in the temperature range 600 to 675 K and at pressures from 15 to 170 MPa. The critical curve of these systems starts at the critical point of pure water and runs through a temperature minimum with increasing pressure. Experimental results are compared with previous studies and it is found that the data fit very well within the systematics of other (n-alkane + water) systems.     

Molecular theory of phase equilibria in model and real associated mixtures III. Binary solutions of inert gases and n-alkanes in ammonia and methanol

Using new molecular models of ammonia and methanol and thermodynamic perturbation theory, the global phase diagrams of model mixtures of these compounds with a van der Waals fluid, representing a simple nonpolar fluid, have been calculated. The global phase diagram of these mixtures is much richer than that of corresponding aqueous mixtures. More types of critical line behavior are found, including the presence of van Laar points and a small region where the mixtures exhibit a closed liquid-liquid immiscibility loop (Type VI phase behavior). The individual mixture components are characterized by two molecular parameters, which can be adjusted to their critical temperature and critical volume; the mixture model itself contains no adjustable parameters. It is shown that the theory gives qualitatively correct predietions of mixtures with n-alkanes. This includes the prediction of Type III critical line behavior for small and large values of the ratio of the critical temperatures of the components, and Type II over a large range of conditions, including the presence or absence of absolute or limited azeotropy, and temperature and pressure extrema of critical lines and their dependence on the number of carbon atoms.     

First-order mean-spherical approximation for interfacial phenomena: a unified method from bulk-phase equilibria study

The recently proposed first-order mean-spherical approximation (FMSA) [Y. Tang, J. Chem. Phys. 121, 10605 (2004)] for inhomogeneous fluids is extended to the study of interfacial phenomena. Computation is performed for the Lennard-Jones fluid, in which all phase equilibria properties and direct correlation function for density-functional theory are developed consistently and systematically from FMSA. Three functional methods, including fundamental measure theory for the repulsive force, local-density approximation, and square-gradient approximation, are applied in this interfacial investigation. Comparisons with the latest computer simulation data indicate that FMSA is satisfactory in predicting surface tension, density profile, as well as relevant phase equilibria. Furthermore, this work strongly suggests that FMSA is very capable of unifying homogeneous and inhomogeneous fluids, as well as those behaviors outside and inside the critical region within one framework.     

Monte Carlo versus molecular dynamics simulations in heterogeneous systems: an application to the n-pentane liquid-vapor interface

The Monte Carlo (MC) and molecular dynamics (MD) methodologies are now well established for computing equilibrium properties in homogeneous fluids. This is not yet the case for the direct simulation of two-phase systems, which exhibit nonuniformity of the density distribution across the interface. We have performed direct MC and MD simulations of the liquid-gas interface of n-pentane using a standard force-field model. We obtained density and pressure components profiles along the direction normal to the interface that can be very different, depending on the truncation and long range correction strategies. We discuss the influence on predicted properties of different potential truncation schemes implemented in both MC and MD simulations. We show that the MD and MC profiles can be made in agreement by using a Lennard-Jones potential truncated via a polynomial function that makes the first and second derivatives of the potential continuous at the cutoff distance. In this case however, the predicted thermodynamic properties (phase envelope, surface tension) deviate from experiments, because of the changes made in the potential. A further readjustment of the potential parameters is needed if one wants to use this method. We conclude that a straightforward use of bulk phase force fields in MD simulations may lead to some physical inconsistencies when computing interfacial properties.     

Investigation of the global phase behavior of polymer mixtures in the shield region

This paper is a contribution of our systematic investigation of the global phase behaviors of the chain molecules mixtures, i.e., polymer mixture solutions. The phase behavior of fluid mixtures is understood by the critical lines in fluid-gas diagrams. The critical lines of binary fluid system may, under circumstances, exhibit closed loops in the critical lines. A distinction is made between free critical loops, as described by type VI in the Scott and van Konynenburg classification, and "rooted" critical loops, as found in the shield region. We define rooted loops as closed critical lines that are attached to the critical line structure by means of unstable critical line. We obtain the rooted loops in the global phase diagrams of the polymer mixture solutions within the framework of a model that combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory, and we present the influence of the chain length of long molecules on the rooted critical loops. We present the results in the density-density and the temperature (T)-pressure (P) planes in detail.     

A finite-size scaling study of a model of globular proteins

Grand canonical Monte Carlo simulations are used to explore the metastable fluid-fluid coexistence curve of the modified Lennard-Jones model of globular proteins of ten Wolde and Frenkel [Science, 277, 1975 (1997)]. Using both mixed-field finite-size scaling and histogram-reweighting methods, the joint distribution of density and energy fluctuations is analyzed at coexistence to accurately determine the critical-point parameters. The subcritical coexistence region is explored using the recently developed hyper parallel tempering Monte Carlo simulation method along with histogram reweighting to obtain the density distributions. The phase diagram for the metastable fluid-fluid coexistence curve is calculated in close proximity to the critical point, a region previously unattained by simulations.