Phase Behavior Of Binary Mixtures Research Articles

Surface and smectic layering transitions in binary mixtures of parallel hard rods

The surface phase behavior of binary mixtures of colloidal hard rods in contact with a solid substrate (hard wall) is studied, with special emphasis on the region of the phase diagram that includes the smectic A phase. The colloidal rods are modeled as hard cylinders of the same diameter and different lengths, in the approximation of perfect alignment. A fundamental-measure density functional is used to obtain equilibrium density profiles and thermodynamic properties such as surface tensions and adsorption coefficients. The bulk phase diagram exhibits nematic-smectic and smectic-smectic demixing, with smectic phases having different compositions; in some cases they are microfractionated. The calculated surface phase diagram of the wall-nematic interface shows a very rich phase behavior, including layering transitions and complete wetting at high pressures, whereby an infinitely thick smectic film grows at the wall via an infinite sequence of stepwise first-order layering transitions. For lower pressures complete wetting also obtains, but here the smectic film grows in a continuous fashion. Finally, at very low pressures, the wall-nematic interface exhibits critical adsorption by the smectic phase, due to the second-order character of the bulk nematic-smectic transition.

Modeling the phase behavior in binary mixtures involving blowing agents and thermoplastic resins

AbstractThe thermophysical properties of mixtures of thermoplastic resins and blowing agents, together with the knowledge of the solubilities of these components, are the basis for the manufacturing of plastic foams. In this work, the solubilities of blowing agents trichlorofluoromethane, dichlorodifluoromethane, chlorodifluoromehane, and 1,2‐dichloro‐1,1,2,2‐tetrafluoroethane in thermoplastic resins poly(styrene), high density poly(ethylene), low density poly(ethylene), poly(propylene), poly(vinyl chloride), poly(carbonate) and poly(propylene oxide) were modeled by using the Perturbed Chain‐Statistical Associating Fluid Theory (PC‐SAFT) and the Sánchez‐Lacombe equations of state (EoS), fitting a single temperature‐dependent binary interaction parameter. PC‐SAFT is a theoretically based equation of state with three pure component parameters that describe efficiently the thermodynamics of complex systems. Earlier works with this EoS have already predicted the phase coexistence properties of various refrigerants and higher order alkane series compounds, along with their mixtures. The pure component parameters for the blowing agents were obtained by regression of vapor pressure and liquid density data, while the pure component parameters for the thermoplastic resins were obtained by regression of pure liquid PVT data. The parameter estimation was performed by using a modified maximum likelihood method. The solubility results obtained with both EoS have been compared; the results from PC‐SAFT showed a higher accuracy in terms of solubility pressure deviations. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

Liquid Crystal Phase Transitions in Systems of Colloidal Platelets with Bimodal Shape Distribution

We have studied a system of polydisperse, charged colloidal gibbsite platelets with a bimodal distribution in the particle aspect ratio. We observe a density inversion of the coexisting isotropic and nematic phases as well as a three-phase equilibrium involving a lower density nematic phase, an isotropic phase of intermediate density, and a higher density columnar phase. To relate these phenomena to the bimodality of the shape distribution, we have calculated the liquid crystal phase behavior of binary mixtures of thick and thin hard platelets for various thickness ratios. The predictions are based on the Onsager-Parsons theory for the isotropic-nematic (I-N) transition combined with a modified Lennard-Jones-Devonshire cell theory for the columnar (C) state. For sufficiently large thickness ratios, the phase diagram features an I-N density inversion and triphasic I-N-C equilibrium, in agreement with experiment. The density inversion can be attributed to a marked shape fractionation among the coexisting phases with the thick species accumulating in the isotropic phase. At high concentrations, the theory predicts a coexistence between two columnar phases with distinctly different concentrations. In experiment, however, the demixing transition is pre-empted by a transition to a kinetically arrested, glassy state with structural features resembling a columnar phase.

Clustering in nondemixing mixtures of repulsive particles

Using classical density functional theory (DFT), we investigate the phase behavior of binary mixtures, in which the interactions between all particles are described by ultrasoft, repulsive potentials. In the pure case, one of the species, species 2, forms clusters, and freezes into a cluster crystal at sufficiently high density, while the other, species 1, does not cluster and remains liquid at all densities of interest. For some mixtures, DFT predicts two instabilities in the liquid with respect to modulations of differing periodicities. One instability results from the cluster-crystal forming tendency of species 2. In concentrated species 2 mixtures, we find species 1 clusters in response to species 2 cluster formation, eventually freezing either on, or between the species 2 lattice sites. The second instability arises when the interaction between unlike species is either more favorable, or less favorable, than the interaction between like species; when less favorable, the particles form a highly delocalized cluster crystal. We examine the structure of the liquid and crystal phases. In addition, we explore the effect of the cross-interaction potential on the structure of the cluster crystal.

An improved perturbed hard-sphere equation of state

The Carnahan–Starling–Patel–Teja (CSPT) equation of state was revisited to improve the fitting accuracy of vapour–liquid equilibrium data of pure fluid substances. By setting the pseudo-critical compressibility factor and the correction coefficient in the attractive parameter as the temperature-dependent variables, the fitting accuracies of the vapour pressures and the saturated liquid-phase densities from the new CSPT increased significantly compared with the Patel–Teja equation of state (PT) and the Peng–Robinson equation of state (PR) and the original CSPT model. The new CSPT combined with temperature-dependent functions was applied to the vapour–liquid equilibrium data available for 45 pure substances. The results indicate that the new CSPT model can accurately reproduce the experimental vapour–liquid equilibria in the whole temperature and pressure range. The successful calculations of the PVT in the critical region suggest the new CSPT has wide applicability. The new CSPT model is also superior to PR and the original CSPT for calculating the phase behaviour of binary mixtures.

Tuning the Interaction Parameter for the Soave−Redlich−Kwong Equation of State Using the Critical End Points

In the petroleum industry, to solve problems such as the design of the catalytic cracking of heavy oil, correct knowledge of the phase behavior is essential. As a benchmark where the number of degrees of freedom for binary mixtures is zero, the critical end points can represent the type of phase behavior of the binary mixtures according to van Konynenburg and Scott’s classification scheme (van Konynenburg, P. H. and Scott, R. L.Philos. Trans. R. Soc. London A 1980, 298, 495−540). Calculating the phase behavior of binary mixtures using interaction parameters evaluated by other methods can cause wrong determinations of the type of phase behavior. The critical end points were employed to fit the interaction parameters for binary mixtures in the critical state at high pressure. The molar Gibbs energy of mixing was evaluated to locate the ranges of values for the interaction parameters where exploration for the critical end point would not fail. The phase behavior at the critical end point is rather complex. B...

A New Continuous Method for Performing Rapid Phase Equilibrium Measurements on Binary Mixtures Containing CO2 or H2O at High Pressures and Temperatures

Apart from paying a deserved tribute to Professor Schneider, a new synthetic dynamic method for rapid determination of phase boundaries at high pressures and temperatures is presented. This device is based on the change in the Flame Ionization Detector signal given by a small amount of sample taken by a capillary fiber from an equilibrium cell through which a mixture of known composition is continuously flowing. To validate the method, the phase boundaries for the system acetone + CO2 are measured at (0.2 and 0.7) acetone mole fraction and at (350 to 380) K. We also measured the phase boundaries for the system ethanol + H2O at compositions ranging from (0.05 to 0.4) ethanol mole fraction and temperatures up to 600 K. The results agree well with literature data, showing the feasibility of this method to measure the phase behavior of binary mixtures containing CO2 and H2O at extreme conditions.

A new crossover sine model based on trigonometric model and its application to the crossover lattice equation of state

In this study, a new crossover sine model (CSM) n was developed from a trigonometric model [M. E. Fisher, S. Zinn, and P. J. Upton, Phys. Rev. B 59, 14533 (1999)]. The trigonometric model is a parametric formulation model that is used to represent the thermodynamic variables near a critical point. Although there are other crossover models based on this trigonometric model, such as the CSM and the analytical sine model, which is an analytic formulation of the CSM, the new sine model (NSM) employs a different approach from these two models in terms of the connections between the parametric variables of the trigonometric model and thermodynamic variables. In order to test the performance of the NSM, the crossover lattice equation of state [M. S. Shin, Y. Lee, and H. Kim, J. Chem. Thermodyn. 40, 174 (2008)] was applied using the NSM for correlations of various pure fluids and fluid mixtures. The results showed that over a wide range of states, the crossover lattice fluid (xLF)/NSM yields the saturated properties of pure fluids and the phase behavior of binary mixtures more accurately than the original lattice equation of state. Moreover, a comparison with the crossover lattice equation of state using the CSM (xLF/CSM) showed that the new model presents good correlation results that are comparable to the xLF/CSM.

Limiting conditions for the critical pressure step point behavior in the Global Phase Diagram of binary mixtures composed by spherical molecules of equal sizes

Although many complex phase diagrams have been clearly systematized by means of the Global Phase Diagram (GPD) approach, no previous analysis has been devoted to establishing the limiting conditions of the critical pressure step point (CPSP) behavior for the case of binary mixtures. The CPSP mechanism implies a stationary inflection in the critical pressure of a mixture which can be observed along the PT projection of the gas–liquid critical line, although in ranges where (usually) a single critical phase exists. Due to this latter reason the CPSP cannot be detected using a phase stability analysis approach, which is the common tool used to delimiting mechanisms of phase behavior, but by clear geometric singularities of other key properties of fluid mixtures, such as the enthalpy. The scope of this work is to characterize the influence of the CPSP mechanism on the topology of phase diagrams over the whole range where the quoted mechanism exists and persists, in order to elucidate some gaps that still exist regarding the global phase behavior of binary mixtures. Accordingly, two new parametric regions of the GPD are described in this contribution, namely the goblet and the crown regions, where the effect of the CPSP on the fluid phase behavior can be clearly observed in systems that exhibit negative deviation from ideal behavior (mainly Type I and V systems) and in mixtures that are in the vicinity of the shield region.

Many-fluid Onsager density functional theories for orientational ordering in mixtures of anisotropic hard-body fluids

The extension of Onsager's second-virial theory [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for the orientational ordering of hard rods to mixtures of nonspherical hard bodies with finite length-to-breadth ratios is examined using the decoupling approximations of Parsons [Phys. Rev. A 19, 1225 (1979)] and Lee [J. Chem. Phys. 86, 6567 (1987); 89, 7036 (1988)]. Invariably the extension of the Parsons-Lee (PL) theory to mixtures has in the past involved a van der Waals one-fluid treatment in which the properties of the mixture are approximated by those of a reference one-component hard-sphere fluid with an effective diameter which depends on the composition of the mixture and the molecular parameters of the various components; commonly this is achieved by equating the molecular volumes of the effective hard sphere and of the components in the mixture and is referred to as the PL theory of mixtures. It is well known that a one-fluid treatment is not the most appropriate for the description of the thermodynamic properties of isotropic fluids, and inadequacies are often rectified with a many-fluid (MF) theory. Here, we examine MF theories which are developed from the virial theorem and the virial expansion of the Helmholtz free energy of anisotropic fluid mixtures. The use of the decoupling approximation of the pair distribution function at the level of a multicomponent hard-sphere reference system leads to our MF Parsons (MFP) theory of anisotropic mixtures. Alternatively the mapping of the virial coefficients of the hard-body mixtures onto those of equivalent hard-sphere systems leads to our MF Lee (MFL) theory. The description of the isotropic-nematic phase behavior of binary mixtures of hard Gaussian overlap particles is used to assess the adequacy of the four different theories, namely, the original second-virial theory of Onsager, the usual PL one-fluid theory, and the MF theories based on the Lee (MFL) and Parsons (MFP) approaches. A comparison with the simulation data for the mixtures studied by Zhou et al. [J. Chem. Phys. 120, 1832 (2004)] suggests that the Parsons MF description (MFP) provides the most accurate representation of the properties of the isotropic-nematic ordering transition and density (pressure) dependence of the order parameters.

Phase behaviour of binary mixtures involving tristearin, stearyl stearate and stearic acid: thermodynamic study and BAM observation at the air–water interface and AFM analysis of LB films

The binary mixtures involving tristearin (TS), stearyl stearate (SS) and stearic acid (SA) were studied by surface pressure–area ( π– A) measurements and by Brewster angle microscopy (BAM), at the air–water interface, and the Langmuir–Blodgett (LB) monolayers, transferred onto mica substrates, were analysed by AFM. The thermodynamic analysis indicated miscibility in the whole composition range for the system SA/TS, and partial miscibility for systems SA/SS and TS/SS. This behaviour was further confirmed by BAM observation and AFM analysis of LB films. The AFM imaging of collapsed monolayers revealed domains with a multilayered structure varying with system and composition. The layers thickness determined by cross section analysis are consistent with estimated molecular lengths and conformations proposed for the molecules, assuming nearly perpendicular or tilted orientations of the hydrocarbon chains to the interface.

A New Model System for Diffusion NMR Studies of Concentrated Monodisperse and Bidisperse Colloids

A method to prepare monodisperse and simultaneously NMR-visible and fluorescent colloidal particles is described, and a systematic approach to obtain spectrally resolved diffusion coefficient for every component in a monodisperse colloidal suspension is presented. We also prepared bidisperse colloidal suspensions, where each colloid component has a distinct NMR spectral signature, and obtained the diffusion coefficients of both colloid species simultaneously in concentrated colloidal suspensions, with volume fractions between 20 and 50%. The colloidal model system developed in this work enables the study of colloidal phase behavior in binary mixtures for different number and size ratios.

Detection of lipid phase coexistence and lipid interactions in sphingomyelin/cholesterol membranes by ATR-FTIR spectroscopy

The phase behavior of binary mixtures of egg sphingomyelin and cholesterol has been inspected by attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy in the amide I′ band reion of the spectrum. Because cholesterol does not have any major absorption bands in this region, effects seen in the spectra of mixtures of sphingomyelin and cholesterol can be attributed to the change in the lipid phase and to the interaction with cholesterol. It is shown that the temperature dependence of the overall bandwidth of the amide I′ band displays a phase-specific behavior. In addition, it is observed that the amide I′ band for a sample exhibiting phase coexistence can be described by a linear combination of the spectra of the individual lipid phases. Description of changes in the amide I′ band shape and by that the study of possible hydrogen bonding interactions of sphingomyelin with cholesterol was assisted by the use of curve fitting. It turns out that the presence of hydrogen bonding between hydroxyl group of cholesterol and carbonyl group of sphingomyelin is obscured by the complexity of different possible hydrogen bonding and coupling between the N–H (N–D) and the C O group vibrations.

Phase behaviour of binary mixtures of colloidal charged spheres

Abstract As a step towards the modelling of binary metal alloys we here report on the shape of the phase boundary of two deionized charged sphere colloidal suspensions as a function of mixing ratio and particle density. Their size ratios are r = 0.68 and r = 0.56. Both aqueous suspensions of polystyrene copolymer spheres crystallize in a body-centred cubic structure. Interesting differences in the shape of the phase boundary are observed. In the first case a peaked increase of crystal stability was observed for a mixing ratio of p = 0.2–0.3, which gives the fraction of small spheres. Also in the second case the stability of the crystalline phase is larger than expected for an ideal solid solution but over a more extended range of small p. In addition at p = 0.7–0.8 we find a pronounced suppression of crystallization and furthermore some indications of a precipitation of one species at p = 0.9. While the first phase diagram resembles that of a solid solution with possibly the onset of compound formation, the second more resembles a eutectic.

Binary Mixtures of Hard Rods: A Short Account

Results of recent calculations aimed at predicting the liquid-crystalline phase behavior of binary mixtures of hard spherocylinders are shortly reviewed. These calculations have been made by adopting a simple, re-summed second-virial Onsager-type theory, and include, among the usual isotropic and nematic phases, smectic phases too. The paradigmatic hard spherocylinders with diameter D and length of the cylindrical part equal to 5D have been taken as reference component, to which hard spherocylinders of different geometry are added. The liquid-crystalline phase diagram of the bidisperse mixtures so generated have been traced in all range of composition as a function of pressure. Various phenomena, such as strong demixing, presence of triple, critical and azeotropic points, and smectic phases with different symmetries, have been observed.

Phase separation of model adsorbates in random matrices

The liquid-liquid phase behavior of binary mixtures in random pores is investigated with non-additive hard spheres using both ROZ (Replica Ornstein-Zernike) integral equations and cavity biased grand canonical Monte Carlo simulations. The critical densities of the coexistence phase envelopes are determined as function of the non-additivity parameter Delta, varying from Delta = 0.2, 0.4, 0.6, up to 0.8. The matrix is made of quenched hard spheres. Its porosity is varied to ascertain the effects of confinement, with packing densities rho(0) ranging from 0.1, 0.3, to 0.5. To obtain fiduciary results from ROZ, we use the accurate ZSEP closure relation proposed earlier with and without thermodynamic consistency. The ZSEP closure is known to enforce the zero-separation theorems via special adjustable parameters in the bridge function. Two versions of this closure are used to assess their accuracies (vis-à-vis the Monte Carlo data): first ZSEP-T, namely, the ZSEP closure with added thermodynamic consistency (the Gibbs-Duhem relation); and second purely ZSEP without adding thermodynamic consistency. It is found that both closures give correct qualitative trend, with errors of ZSEP falling within 8-9%, while ZSEP-T, being more accurate, to within 1-2%. As non-additivity is increased, both versions become more accurate. The critical density rho(c) is found to decrease with decreasing porosity. In addition, rho(c) also decreases with increasing Delta, in a non-monotone fashion.

Phase behavior of binary mixture of 1-dodecyl-3-methylimidazolium bromide and water revealed by differential scanning calorimetry and polarized optical microscopy

Phase behavior of aqueous mixture of imidazolium ionic liquid, 1-dodecyl-3-methylimidazolium bromide, was investigated by means of differential scanning calorimetry and polarized optical microscopy. The mixture forms two types of lyotropic liquid-crystalline gels, one is composed of lamellar phase and the other is of hexagonal phase. T – X phase diagram of the mixture was constructed, which defines the regions of various phases appearing in this mixture.

Properties and Thermal Phase Behaviour of Binary Mixtures of Homologues of Unsymmetrically Substituted Phenyl Benzoates

Sixteen liquid crystalline esters of the type 4-(n-CnH2n+1O)C6H4COOC6H4X-4 have been investigated for their thermal phase behaviour. These compounds constitute four homologous series that differ from each other by the substituent X. The latter varies between CH3O, CH3, CN, and NO2. The number (n) of carbon varies, within a homologous series, between 6, 8, 14, and 16. All possible binary mixtures made from any two homologues that cover the whole composition range were prepared and characterized for their mesophase behaviour by differential scanning calorimetry (DSC) and polarizing light microscopy. Twenty four phase diagrams for the various binary combinations were constructed (i) to investigate the dependence of the phase behaviour of mixed systems upon differences in the length of the alkoxy group, (ii) to determine the eutectic composition, and its phase transitions, in each system. Each eutectic system of the binary mixtures (I6/In)X was investigated for its birefringence dependency on temperature via measurement of its refractive index as a function of temperature. The estimated orientational order parameter S for each system was used to examine the effect of the differences in chain length of alkoxy group on its optical properties.

Phase behavior of binary mixture of asphaltene + solvent and ternary mixture of asphaltene + solvent + precipitant

Asphaltene precipitation is a perennial problem in producing and refining crude oils. To study asphaltene precipitation, it is useful to model the solubility of asphaltenes in petroleum fluids as a function of temperature and liquid-phase composition. In this work a polymer solution model is used for asphaltene precipitation in two cases. In the first case a binary mixture is considered which consists of asphaltene as a polymer component and crude oil as the solvent. In the second case ap ternary mixture is considered which consists of asphaltene as a polymer component and crude oil as the solvent and a precipitant as the third component. The phase diagrams and phase stability limits obtained for a sample of crude oil with four different precipitants are presented.

Phase behaviour of binary mixtures of LC compounds of different molecular structure and comparable molecular length: I. 4-(4′-Substituted phenylazo)phenyl-4″-alkoxybenzoates and 4-(4′-substituted phenyl carbonyloxy)phenyl-4″-alkoxybenzoates

Phase diagrams were constructed for the various binary systems made from compounds of structurally different mesogens; one component is from the five homologous series 4-(4′-substituted phenylazo)phenyl-4″-alkoxybenzoates ( I a–e) and the other from the similarly substituted homologous series 4-(4′-substituted phenyl carbonyloxy)phenyl-4″-alkoxy benzoates ( II a–e). Transition temperatures of all mixtures prepared were measured by differential scanning calorimetry and identified by polarized light microscopy. Polarity and polarizability of the investigated compounds could be varied by changing the substituent X (CH 3O, CH 3, Cl, CN and NO 2), which covers a wide range of polarity, and the alkoxy-chain length, which varied between 6, 8, 14, or 16 carbons.