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.     

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.     

Fluid phase stability and equilibrium calculations in binary mixtures: Part II: Application to single-point calculations and the construction of phase diagrams

The methodology presented in Part I of this work is applied to a large number of pressure–temperature flash calculations, and to the automated construction of constant temperature pressure–composition phase diagrams, and constant pressure temperature–composition phase diagrams for binary mixtures modeled with an augmented van der Waals equation of state. An automated prototype implementation of the algorithm is developed for this purpose. We follow the classification of Scott and van Konynenburg [R.L. Scott, P.H. van Konynenburg, Discuss. Faraday Soc. 49 (1970) 87] and present phase diagrams corresponding to non-azeotropic mixtures of the five main types of fluid phase behavior (I–V), studying in detail representative diagrams at constant pressure and constant temperature. Special attention is given to the solution of numerically problematic equilibrium regions, such as those close to three-phase equilibria where metastable and unstable critical points can also be found. Of the order of 10⁴ flash calculations at varying temperatures and pressures, and for different intermolecular parameters of the components in the mixture, have been carried out. The algorithm provides the correct stable equilibrium state for all of the points considered. Despite the fact that our implementation is not optimised for performance, we find that the algorithm identifies the stable solution in difficult regions of the phase space without any penalty in terms of computational time, when compared to simpler regions.     

Liquid mixtures of xenon with fluorinated species: xenon + sulfur hexafluoride

The vapor-liquid equilibrium of binary mixtures of xenon + SF6 has been measured at nine temperatures from 235.34 to 295.79 K and pressures up to 6.5 MPa. The mixture critical line is found to be continuous between the critical points of the pure components, and hence, the system can be classified as type I phase behavior in the scheme of van Konynenburg and Scott. The excess Gibbs free energies have been calculated, and the experimental results have been interpreted using the statistical associating fluid theory for potentials of variable range (SAFT-VR). Additionally, the SAFT-VR equation has been used to model other systems involving SF6 and alkanes, illustrating the predictability of the approach and further demonstrating the transferability of parameters between binary mixtures involving alkanes and xenon.     

Critical lines for an unequal size of molecules in a binary gas-liquid mixture around the van Laar point using the combination of the Tompa model and the van der Waals equation

We combine the modified Tompa model with the van der Waals equation to study critical lines for an unequal size of molecules in a binary gas-liquid mixture around the van Laar point. The van Laar point is coined by Meijer and it is the only point at which the mathematical double point curve is stable. It is the intersection of the tricritical point and the double critical end point. We calculate the critical lines as a function of χ(1) and χ(2), the density of type I molecules and the density of type II molecules for various values of the system parameters; hence the global phase diagrams are presented and discussed in the density-density plane. We also investigate the connectivity of critical lines at the van Laar point and its vicinity and discuss these connections according to the Scott and van Konynenburg classifications. It is also found that the critical lines and phase behavior are extremely sensitive to small modifications in the system parameters.     

Bulk and interfacial wetting behavior of binary mixtures induced by associating between unlike-pair molecules

The statistical associating fluid theory of Wertheim is applied to describe binary mixtures with associating between unlike-pair molecules. The phase behavior of this binary mixture would fall into five different types (I, II, III, V, and VI) of the classification scheme of van Konynenburg and Scott by varying the associating strength and the energy parameters. Both interfacial wetting behavior and wetting transitions are carefully examined in all the vapor-liquid-liquid (gamma-beta-alpha) three-phase-coexisting regions of the binary mixtures. The global wetting behavior and wetting transitions are delineated by scanning the parameter space. In certain regions, the middle beta phase exhibits interfacial phase transitions sequentially, nonwetting --> partial-wetting --> nonwetting, at the interface separating lower alpha and upper gamma phases along with increasing temperature.     

The shapes of critical loci of binary fluid mixtures on the p–T plane

The relations between the shapes of the critical loci of binary fluid mixtures and the positions of the critical points of their component fluids on the p–T plane were considered theoretically. The consideration was carried out for vapor–liquid phase equilibria in the model systems without liquid–liquid equilibria. We focused only the relations between the shapes and the tangent of the straight lines connecting the critical points of the component fluids on the p–T plane, and so the effects of the distance between the critical points were out of the scope of this work. The changes in the shapes of the critical loci were classified logically into three patterns. Literature survey has shown that the two patterns exist in the experimental results for several types of mixtures. The shapes of the critical loci of the binary fluid mixtures on the p–T plane are closely related to the relative positions between the critical points of their component fluids.     

Thermodynamic equilibrium of adsorbed phases

The types of phase equilibrium behavior for adsorbed binary mixtures that can be predicted by an equation of state (EOS) based on the lattice gas theory are investigated. The equilibrium conditions were obtained by solving the isofugacity equations between adsorbed phases. It is observed that the investigated EOS can predict complex behavior for adsorbed phases such as the existence of azeotropes, and retrograde and double retrograde phase transition phenomena, that are analogous to those found in bulk phase equilibrium. Furthermore, it was possible to find systems that presented phase equilibrium between two dense adsorbed phases, analogously to liquid–liquid equilibrium for bulk phases. Experimental data would be necessary to confirm the types of adsorbed phase behavior predicted by the calculations presented.     

Modeling the phase behavior of H2S+n-alkane binary mixtures using the SAFT-VR+D approach

A statistical associating fluid theory for potential of variable range has been recently developed to model dipolar fluids (SAFT-VR+D) [Zhao and McCabe, J. Chem. Phys. 2006, 125, 104504]. The SAFT-VR+D equation explicitly accounts for dipolar interactions and their effect on the thermodynamics and structure of a fluid by using the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. In this work, we apply the SAFT-VR+D approach to real mixtures of dipolar fluids. In particular, we examine the high-pressure phase diagram of hydrogen sulfide+n-alkane binary mixtures. Hydrogen sulfide is modeled as an associating spherical molecule with four off-center sites to mimic hydrogen bonding and an embedded dipole moment (micro) to describe the polarity of H2S. The n-alkane molecules are modeled as spherical segments tangentially bonded together to form chains of length m, as in the original SAFT-VR approach. By using simple Lorentz-Berthelot combining rules, the theoretical predictions from the SAFT-VR+D equation are found to be in excellent overall agreement with experimental data. In particular, the theory is able to accurately describe the different types of phase behavior observed for these mixtures as the molecular weight of the alkane is varied: type III phase behavior, according to the scheme of classification by Scott and Konynenburg, for the H2S+methane system, type IIA (with the presence of azeotropy) for the H2S+ethane and+propane mixtures; and type I phase behavior for mixtures of H2S and longer n-alkanes up to n-decane. The theory is also able to predict in a qualitative manner the solubility of hydrogen sulfide in heavy n-alkanes.     

Phase equilibria and critical phenomena in the rubidium nitrate-water-acetonitrile system

Phase equilibria and critical phenomena were studied from -5 to 120°C in the rubidium nitrate-water-acetonitrile system, in which the liquid binary subsystem is characterized by liquid-liquid phase separation with an upper critical solution point (UCSP), using a visual polythermal method. We found that rubidium nitrate has a salting out effect on water-acetonitrile solutions and causes them to demix at any temperature in the specified range. Acetonitrile distribution coefficients between aqueous and organic monotectic phases were calculated for various temperatures. The minimum value was observed for 20.0°C. Six isothermal phase diagrams of the system were plotted to verify a fragment of the global scheme of the topological transformation of phase diagrams for salt-binary solvent ternary systems with salting out. The salting out effects of potassium, rubidium, and cesium nitrates on water-acetonitrile mixtures were comparatively analyzed.     

Thermal Analysis of Solid-Solid Interactions in Binary Mixtures of Alkylcyclohexanes Using DSC

Differential scanning calorimetry (DSC) was used to construct phase diagrams of binary mixtures of alkylcyclohexanes and to characterize metastable phases formed in the binary mixtures. The experimentally measured liquidus curves were compared to the liquidus curves calculated using ideal solution theory. The measured phase diagrams of pentadecylcyclohexane/nonadecylcyclohexane and octadecylcyclohexane/nonadecylcyclohexane binary mixtures are consistent with theoretical phase diagrams constructed based on the assumption that these mixtures form eutectic systems. It was also observed that a metastable phase formed in some binary mixtures of pentadecylcyclohexane/nonadecylcyclohexane under fast cooling conditions. It is hypothesized that this metastable phase recrystallizes into the eutectic phase upon heating. This revised version was published online in July 2006 with corrections to the Cover Date.     

Systematic investigation of the global phase behavior of polymer-solvent systems in the density-density plane

The phase behavior of fluid mixtures is understood by the critical lines in fluid-gas diagrams. We investigated the critical lines of polymer-solvent systems at the mathematical double point, where two critical lines meet and exchange branches, and its environment within the framework of a model that combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory. The critical lines are expressed as a function of x₁ and x₂, the density of type 1 polymer molecules and the density of type 2 polymer molecules, respectively; in this way global phase diagrams are presented and discussed in the density-density plane. Density-density plots are preferable when studying the differences in behavior of different classes, since they enable us to follow the connectivities in a systematic way. In this study the connectivity of critical lines at the mathematical double point and its around is investigated in detail. We also discuss the topology of the critical lines according to the Sadus classification scheme for ternary mixtures.     

Phase behavior of binary symmetric mixtures in pillared slit-like pores: a density functional approach

Density functional approach is applied to study the phase behavior of symmetric binary Lennard-Jones(12,6) mixtures in pillared slit-like pores. Our focus is in the evaluation of the first-order phase transitions in adsorbed phases and lines delimiting mixed and demixed adsorbed phases. The scenario of phase changes is sensitive to the pore width, to the energy of fluid-solid interaction, the amount, and the length of the pillars. Quantitative trends and qualitative changes of the phase diagrams topology are examined depending on the values of these parameters. The presence of pillars provides additional excluded volume effects, besides the confinement due to the pore walls. The effects of attraction between fluid species and pillars counteract this additional confinement. We have observed that both the increasing surface pillar density and the augmenting strength of fluid-solid interactions can qualitatively change the phase diagrams topology for the model with sufficiently strong trends for demixing. If the length of pillars is sufficiently large comparing to the pore width at low temperatures, we observe additional phase transitions of the first and second order due to the symmetry breaking of the distribution of chain segments and fluid species with respect to the slit-like pore center. Re-entrant symmetry changes and additional critical points then are observed.     

Topological transformation of phase diagrams in KBr–оxyethylated surfactant–water pseudo-ternary systems

A scheme was developed to explain the transformation of phase diagrams for KBr–oxyethylated surfactant–water systems in response to varying temperature. This scheme was shown to correspond with the respective scheme for salt–binary solvent systems. The surfactant structure was shown to have an effect on the temperature ranges of existence of a liquid–liquid two-phase equilibrium field and the positions of critical points. The elucidated trends serve as the basis for selecting components and optimizing parameters of surfactant- involving extraction processes.     

Automated calculation of complete Pxy and Txy diagrams for binary systems

An algorithm for the calculation of global phase equilibrium diagrams has been recently developed [M. Cismondi, M.L. Michelsen, Global phase equilibrium calculations: critical lines, critical end points and liquid–liquid–vapour equilibrium in binary mixtures, J. Supercrit. Fluids 39 (2007) 287–295]. It integrates the calculation of critical lines, liquid–liquid–vapour (LLV) lines and critical end points, and was implemented in the software program GPEC: global phase equilibrium calculations [M. Cismondi, D.N. Nuñez, M.S. Zabaloy, E.A. Brignole, M.L. Michelsen, J.M. Mollerup, GPEC: a program for global phase equilibrium calculations in binary systems, in: Proceedings of the CD-ROM EQUIFASE 2006, Morelia, Michoacán, Mexico, October 21–25, 2006; www.gpec.plapiqui.edu.ar]. In this work we present the methods and computational strategy for the automated calculation of complete Pxy and Txy diagrams in binary systems. Being constructed from the points given by the global phase diagram at a specified temperature or pressure, their calculation does not require the implementation of stability analysis.     

Phase equilibria and critical phenomena in the cesium nitrate–water–pyridine ternary system

The solubilities of components, phase equilibria, and critical phenomena in the cesium nitrate–water–pyridine ternary system are studied in the 5–100°C temperature range by the visual–polythermal method. Cesium nitrate is found to exhibit a salting-out effect at temperatures above 79.9°C causing phase separation in homogeneous water–pyridine solutions. The temperature of formation of the critical monotectic tie line (79.9°C) and the compositions of solutions corresponding to the liquid–liquid critical points at three temperatures are determined. The pyridine distribution coefficients between the aqueous and organic phases of the monotectic state at 85.0, 90.0, and 100.0°C are calculated. Their values demonstrate that salting-out of pyridine from aqueous solutions by cesium nitrate increases at higher temperatures. The plotted isotherms of phase diagrams confirm the fragment of the scheme of topological transformation of the phase diagrams of salt–binary solvent ternary systems with salting-in and salting-out phenomena.     

Thermodynamic aspects of phase equilibrium in binary water–organic solvent mixtures

It is shown that the boundary curves of liquid equilibria in binary systems characterize the temperature–concentration boundary of the existence of homogeneous mixtures whose formation is not accompanied by changes in the Gibbs energy of the system and are a combination of two branches that do not convert into each other but intersect at the temperature of homogenization of a mixture of critical composition. The phase diagrams of a number of water–organic solvent systems are analyzed to determine the thermodynamic particularities of the latter.

     

Phase diagrams of binary crystalline-crystalline polymer blends

A thermodynamically self-consistent theory has been developed to establish binary phase diagrams for two-crystalline polymer blends by taking into consideration all interactions including amorphous-amorphous, crystal-amorphous, amorphous-crystal, and crystal-crystal interactions. The present theory basically involves combination of the Flory-Huggins free energy for amorphous-amorphous isotropic mixing and the Landau free energy of polymer solidification (e.g., crystallization) of the crystalline constituents. The self-consistent solution via minimization of the free energy of the mixture affords determination of eutectic, peritectic, and azeotrope phase diagrams involving various coexistence regions such as liquid-liquid, liquid-solid, and solid-solid coexistence regions bound by liquidus and solidus lines. To validate the present theory, the predicted eutectic phase diagrams have been compared with the reported experimental binary phase diagrams of blends such as polyethylene fractions as well as polycaprolactone/trioxane mixtures.     

A simple statistical mechanical theory for the mutual solubility of fluid mixtures of water and organic solvents under high pressure

A simple statistical mechanical theory is presented to explain phase diagrams of fluid mixtures with both a lower critical solution temperature and an upper critical solution temperature under pressure. By postulating a temperature dependence for the interaction free energy parameter of the constituent molecules and a pressure dependence for the excess volume, phase diagrams with both lower critical solution temperature, and upper critical solution temperature and their pressure dependence can be reproduced by quadratic surfaces in temperature-concentration-pressure space. The topological aspects of the observed phase diagrams in this space have been related to our theoretical model, and the thermodynamical meaning of the topologies has been interpreted based on our model. Experimental data for the mutual solubility of water and 2-butanol under pressure and that of water and 3-methylpyridine with added salts have been analyzed quantitatively and theoretical parameters are determined.     

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.