Miscibility Boundary Research Articles

What does the NRTL model look like? Determination of boundaries for different fluid phase equilibrium regions

AbstractThe adequate correlation of experimental phase equilibrium data by using any thermodynamic model represents a key point for the rigorous design of the chemical processes. However, this data correlation process remains a challenging problem, due to the high nonlinearity of the models used and the consequent problems of convergence. The present work analyzes the nonrandom two‐liquids mode (NRTL) model to check the relation between the values of the binary interaction parameters and the corresponding phase equilibria that the NRTL model can or cannot reproduce. Additionally, in the case of the LLE, empirical equations have been established as a function of the nonrandomness parameter, to model the trajectory of the different miscibility boundaries observed. These functions can be used as constraints in the experimental data correlation procedure to reduce the search space and guarantee the consistency of the obtained binary interaction parameters with the experimental behavior of the system under study.

Determination of the equilibrium miscibility gap in the Pd–Rh alloy system using metal nanopowders obtained by decomposition of coordination compounds

The Pd–Rh phase diagram has been reinvestigated in the subsolidus region using X-ray diffraction, scanning and transmission electron microscopy. The true equilibrium at the miscibility boundary was achieved with the two-way approach. Nanosized powders of metastable solid solutions and two-phase palladium–rhodium mixtures were used to shorten the time required to equilibrate the system. The initial samples were prepared by decomposition of coordination compounds [Pd(NH3)2Cl2], [Rh(NH3)5Cl]Cl2, [Pd(NH3)4]3[Rh(NO2)6]2 and [Pd(NH3)4][Rh(NH3)(NO2)5].The obtained phase diagram exhibits miscibility gap wider than generally accepted with the critical point of solubility at 58at.% Rh and 820°C.

Photochemical control of membrane raft organization

Controllable membrane phase separation through the action of a synthetic photoresponsive amphiphile is reported. We studied multi-component giant vesicles formed from a ternary lipid mixture of saturated and unsaturated phospholipid and cholesterol together with the photoresponsive amphiphile. A change in the conformation of the photoresponsive amphiphile can switch membrane lateral segregation in a reversible manner. Cis-isomerization induces lateral phase separation in one-phase membranes or produces additional lateral domains in two-phase membranes. Membranes that are close to miscibility boundary show high photo-responsiveness. This is the first report on the reversible control of membrane lateral segregation triggered by a conformational change in a membrane-constituting molecule. These findings may lead to new methods for controlling membrane self-organization such as raft engineering.

Key role of entropy in nanoparticle dispersion: polystyrene-nanoparticle/linear-polystyrene nanocomposites as a model system

Dilution of contact, hard sphere-like, nanoparticle-nanoparticle interactions upon mixing plays a key role in explaining nanoparticle dispersion in athermal all-polymer nanocomposites, as illustrated for polystyrene-nanoparticle/linear-polystyrene blends as a model system.

Phase diagram and entropic interaction parameter of athermal all‐polymer nanocomposites

AbstractAn entropic model is introduced for the prediction of the χ interaction parameter and phase diagram of athermal all‐polymer nanocomposites (chemically identical polymer‐nanoparticle/linear‐polymer blends). According to this model, dilution of contact (hard sphere‐like) nanoparticle/nanoparticle interactions upon mixing plays a key role in explaining the miscibility behavior of athermal all‐polymer nanocomposites in the presence of unfavorable chain expansion (or contraction) effects. The new model is valid both for the cases of chain stretching and chain contraction and provides an appropriate capture of entropy changes accompanying the mixing of chemically identical nanoparticles and polymers. A good agreement was found between predicted χ interaction parameter (χcal = −2.3 × 10−3) and reported small angle neutron scattering (SANS) experimental data ($\bar \chi _{\exp } $ ∼ −2 × 10−3) for 211 kDa cross‐linked poly(styrene) (PS)‐nanoparticles dissolved in 473 kDa deuterated linear‐PS. In addition, the miscibility boundary calculated from the model for PS‐nanoparticle/linear‐PS nanocomposites (ϕ1 = 0.02) compared very favorably to that experimentally found. For this system, the spinodal line in the polymer radius of gyration (Rg) versus nanoparticle radius (a) phase diagram was found to follow the simple scaling law: $R_{\rm g}^{{\rm sp}} \approx 0.27a^{3/2} $, $R_{\rm g}^{{\rm sp}} $ being the polymer radius of gyration at which the second derivative of the free energy of mixing vanishes. Finally, the model has been employed for the prediction of the entropic χ interaction parameter, the miscibility behavior, and the melting point depression of athermal poly(ethylene) (PE)‐nanoparticle/linear‐PE nanocomposites using recent chain dimension data from Monte Carlo (MC) simulations, where chain stretching or chain contraction effects were observed depending on nanoparticle size. Copyright © 2007 John Wiley & Sons, Ltd.

Elastomer particle morphology in ternary blends of maleated and non-maleated ethylene-based elastomers with polyamides: Role of elastomer phase miscibility

The elastomer particle morphology in ternary blends of maleated and non-maleated ethylene-based elastomers with polyamides has been examined. The elastomers used include an ethylene/propylene copolymer, EPR, with a maleic anhydride (MA) grafted version, EPR- g-MA, and an ethylene/1-octene copolymer, EOR, with maleated versions EOR- g-MA- X% where X is 0.35, 1.6 or 2.5. The polyamides used were nylon 6 and an amorphous polyamide, Zytel 330 from DuPont. The morphology development was explored from both thermodynamic and kinetic points of view where the former refers to miscibility of the elastomers and the latter might include the ratio of the elastomers, the matrix type, the order of mixing, mixing intensity, i.e. the extruder type, and graft structure, etc. Both sources influence the morphology developed. For ternary blends with EPR- g-MA/EPR, the morphology (particle size and distribution) seems to be well controlled via the level of maleation in the rubber phase. The two polyamides generate comparable rubber particle sizes at the same of MA level. For ternary blends with EOR- g-MA/EOR, the morphology strongly depends on the level of MA; the rubber particle size, in general, is much smaller in nylon 6 blends than in Zytel 330 blends. Morphology of ternary blends with EOR- g-MA/EOR is much more complex than that of blends with EPR- g-MA/EPR due to the co-existence of miscibility limits and the kinetic factors. Miscibility of maleated EOR elastomers is examined via transmission electron microscopy (TEM) using a special staining technique; a miscibility boundary, as revealed by TEM, occurs around Δ(%MA)=0.9−1.25 MA%. If the two elastomers are miscible, a unimodal particle size distribution always appears in blends regardless of the kinetic factors; however, if immiscibility prevails, either a unimodal or bimodal particle size distribution may develop depending on the ratio of the elastomers and the matrix type. The order of mixing and the mixing intensity do not seem to change the modality of the size distribution.

Effect of monomer sequence on miscibility in statistical copolymer blends and estimation of segmental χ parameters from their miscibility

AbstractMiscibility in statistical AB/AB copolymers was investigated from the viewpoint of the copolymer sequence effect based on the Balazs theory. The AB copolymers used were poly[(p‐chlorostyrene)‐co‐(hexyl methacrylate)], poly(styrene‐co‐HMA) and poly[(methyl methacrylate)‐co‐HMA]. Miscibility in the former two systems displayed deviation from the Flory–Huggins theory extended to statistical copolymers, and such behavior was interpreted as the sequence effect based on the Balazs theory. From calculations of the probabilities, Z, of interactions between triads, changes in Z for AAA/BBB, AAA/BBA, AAA/ABA, AAB/BBB and BAB/BBB were remarkable around the miscibility boundaries. In order to obtain insight into the miscibility behavior, we related the interaction parameters for the triads, i.e. χAAA/BBA = χAAA/ABA, χAAB/BBB = χBAB/BBB, and χAAB/BBA = χBAB/BBA = χAAB/ABA = χBAB/ABA. Using the above treatment, the χ parameters were estimated from the experimental miscibility data. Reproducibility in miscibility was good for all of the systems. In addition, the parameters were comparable to those obtained by using the Cantow–Schulz assumption. Copyright © 2004 Society of Chemical Industry

Separation of Liquid Phases in Giant Vesicles of Ternary Mixtures of Phospholipids and Cholesterol

We use fluorescence microscopy to directly observe liquid phases in giant unilamellar vesicles. We find that a long list of ternary mixtures of high melting temperature (saturated) lipids, low melting temperature (usually unsaturated) lipids, and cholesterol produce liquid domains. For one model mixture in particular, DPPC/DOPC/Chol, we have mapped phase boundaries for the full ternary system. For this mixture we observe two coexisting liquid phases over a wide range of lipid composition and temperature, with one phase rich in the unsaturated lipid and the other rich in the saturated lipid and cholesterol. We find a simple relationship between chain melting temperature and miscibility transition temperature that holds for both phosphatidylcholine and sphingomyelin lipids. We experimentally cross miscibility boundaries both by changing temperature and by the depletion of cholesterol with β-cyclodextrin. Liquid domains in vesicles exhibit interesting behavior: they collide and coalesce, can finger into stripes, and can bulge out of the vesicle. To date, we have not observed macroscopic separation of liquid phases in only binary lipid mixtures.

Determination of the composition and molar volume of H 2O-CO 2 fluid inclusions by microthermometry

H 2O-CO 2 fluid inclusions are common in nature but their accurate analysis by microthermometry has been hindered by insufficient characterisation of the fluid properties along the solvus (high temperature miscibility boundary) of the system. Thus some of the previous methods of calculating fluid inclusion composition ( x) and molar volume ( V) have relied on notoriously unreliable optical estimates of phase volume fractions. Although the T-V-x properties of the solvus can be modelled thermodynamically from equations of state, a review shows that none of the published equations are accurate enough to be useful in fluid inclusion microthermometry. Therefore, the available experimental data have been used to construct a new V-x diagram, contoured for phase transition temperatures and phase volume fractions. This diagram allows the bulk composition and molar volume of individual fluid inclusions to be determined accurately from two microthermometric measurements: the temperature of partial homogenisation of the carbonic phases (in the presence of excess aqueous liquid), and the temperature of total homogenisation.

Long-wavelength photodiodes based on Ga1−x InxAsySb1−y wit composition near the miscibility boundary

The possibility of using liquid-phase epitaxy to obtain Ga1−xInxAsySb1−y solid solutions isoperiodic with GaSb near the miscibility boundary is investigated. The effect of crystallographic orientation of the substrate on the composition of the solid solutions grown in this way is examined, and the indium concentration is observed to grow from 0.215 to 0.238 in the Ga1−xInxAsySb1−y solid phase in the series of substrate orientations (100), (111)A, (111)B. A change in the composition of the solid solution leads to a shift of the long-wavelength edge of the spectral distribution of the photosensitivity. The use of a GaSb (111)B substrate made it possible, without lowering the epitaxy temperature, to increase the indium content in the solid phase to 23.8% and to create long-wavelength photodiodes with spectral photosensitivity threshold λth=2.55 µm. The primary characteristics of such photodiodes are described, along with aspects of their fabrication. The proposed fabrication technique shows potential for building optoelectronic devices (lasers, LED’s, photodiodes) based on Ga1−xInxAsySb1−y solid solutions with red boundary as high as 2.7 µm.

Undercooling, Liquid Separation and Solidification of Cu-Co Alloys

Large undercooling can induce not only various solidification pathways, but also a precursor reaction, or liquid separation. This paper deals with the latter effect of undercooling using examples of the Cu-Co system which has a flattened liquidus. Bulk Cu-Co alloys (about 7 mm in diameter) at compositions ranging from 10 to 100 wt % Co were highly undercooled using a fluxing technique. Except for compositions above 90 wt % Co, liquid separation was directly observed as undercooling exceeded a critical value depending on the composition. It was also confirmed by a microstructural transition from dendrites to droplets above the critical undercooling. Finally, calculations of the metastable miscibility boundary were made to analyze the experimental results.

Direct determination of the metastable liquid miscibility gap in undercooled Cu–Co alloys

Bulk Cu–Co alloys at compositions ranging from 10 to 80 wt.% Co were highly undercooled using a melt fluxing technique. The metastable liquid separation boundary has been directly determined from the measured temperature-time profiles. It was also calculated using a subregular solution model. The critical point of the miscibility gap was found to be about 80 K below the liquidus. A droplet-shaped microstructure was observed for all solidified specimens (Cu–10 to 80 wt.% Co), when the melts were undercooled into the metastable miscibility boundary.

The marangoni effect and enhanced oil recovery Part 1. Porous media studies

AbstractThe use of partitionable solutes, e.g., aliphatic alcohols, to enhance the recovery of trapped oil in reservoir rock, has been simulated using a ballotini‐packed column initially flooded with kerosene, and subsequently lowered to an irreducible value by a water drive. Introduction of a “slug” of an alcohol effected an increased recovery, with n‐propanol and sec‐butanol giving the highest yields. Previous workers attributed such increased recovery to the formation of a “soluble front”, in which both oil and connate water are completely dissolved. However, we obtained similar recoveries using slugs with initial compositions lying on the miscibility boundary, which could not form soluble fronts. It was therefore concluded that Marangoni‐induced oscillation of the trapped drops is the more likely explanation of the enhanced recovery.

PHASE BEHAVIORS IN BLENDS OF POLY(VINYL METHYL ETHER) AND POLY(STYRENE-CO-BUTADIENE)

The dependence of miscibility on temperature for blends of poly(vinyl methyl ether) (PVME) and styrene-butadiene random copolymer (SBR) was studied. The binary interaction energy densities of the blends could be evaluated from the observed cloud point curves. With a simple approach based on the mean-field theory for blends of a homopolymer with a random copolymer, the miscibility boundary could be determined as a function of composition of the copolymer. The predicted miscibility region for the given polymer pairs was compatible with the experimental results. © 1997 Elsevier Science Ltd

Miscibility of poly(ε‐caprolactone), a semicrystalline polymer, with amorphous poly(styrene‐4‐hydroxystyrene) copolymers

AbstractThe miscibility of poly(ε caprolactone) (PCL) with poly(styrene‐co‐4‐hydroxystyrene) (PHS) copolymers was investigated as a function of comonomer composition experimentally and with calculations by two models; the binary interaction model and the association model. PCL was found to be completely miscible with PHS copolymers containing 5 or more mole percent of 4‐hydroxystyrene (HS) comonomer units for the entire range of blend compositions. Segmental interaction densities, Bijs, were determined by the analysis of the equilibrium melting point depression and by the application of the binary interaction model. By correlating the segmental interaction energy densities with the binary interaction model, thermodynamic miscibility is for comonomer composition over five mole percent of 4‐hydroxystyrene, which is in agreement with the experimental phase behavior. Application of the association model for specific interactions to blends also predicts the experimental miscibility boundary and phase behavior for all the PHS copolymers/PCL blends. © 1995 John Wiley & Sons, Inc.

Phase behavior of blends of styrene/maleic anhydride copolymers

AbstractThe phase behavior of blends of styrene/maleic anhydride copolymers (SMA) with styrene/methyl methacrylate copolymers (SMMA), styrene/acrylonitrile copolymers (SAN), tetramethyl bisphenol‐A polycarbonate (TMPC), and poly(2,6‐dimethyl‐1,4‐phenylene oxide) (PPO) have been determined. Tentative binary interaction energies were evaluated from mapping the copolymer composition miscibility boundaries using the Flory–Huggins theory combined with the binary interaction model. Data on phase‐separation temperatures were too sparse for these systems to obtain refined estimates using the Sanchez–Lacombe theory. A negative interaction energy was obtained for the MA/AN pair; however, the MA unit showed strong repulsive interactions with all other monomer units examined here. © 1994 John Wiley & Sons, Inc.

Estimation of interaction energies by the critical molecular weight method: 1. Blends with polycarbonates

AbstractThe interaction energies between PS, Pα‐MS, and PMMA with several bisphenol‐A‐based polycarbonates were quantitatively determined from oligomer/oligomer, oligomer/homopolymer, and homopolymer/copolymer blends. Interaction energies were calculated from the Flory‐Huggins theory and the Sanchez‐Lacombe equation of state theory using experimental cloud points or miscibility boundaries. Alkyl addition to the phenyl rings of polycarbonate is favorable for miscibility with polystyrene whereas halogenation of the bisphenol connector unit is favorable for miscibility with poly(methyl methacrylate). Interaction energies are quantitatively ranked and described qualitatively in terms of changes in the electronic charge distribution of the polymer repeat units as calculated by SYBYL software. © 1994 John Wiley & Sons, Inc.

Estimation of interaction energies by the critical molecular weight method: 2. Blends with polysulfones

AbstractThe interaction energies between PS, Pα‐MS, and PMMA, as well as acrylonitrile and maleic anhydride units, with a series of polysulfones were quantitatively determined from oligomer/oligomer, oligomer/homopolymer, and homopolymer/copolymer blends. Interaction energies were calculated from the Flory‐Huggins theory and the Sanchez‐Lacombe equation of state theory using experimental cloud points or miscibility boundaries. Alkyl addition to the phenyl rings of polysulfone is favorable for miscibility with polystyrene whereas halogenation of the bisphenol connector unit favors miscibility with poly(methyl methacrylate). Interaction energies are quantitatively ranked and described qualitatively in terms of changes in the electronic charge distribution of the polymer repeat units as calculated by SYBYL software. © 1994 John Wiley & Sons, Inc.

Interaction energies for blends based on glycidyl methacrylate copolymers

The phase behaviour of blends of glycidyl methacrylate/methyl methacrylate (GMA/MMA) copolymers with styrene/acrylonitrile (SAN) copolymers and of GMA/styrene copolymers with tetramethyl polycarbonate and poly(2,6-dimethyl-1,4-phenylene oxide) has been determined and analysed using two theoretical approaches. Binary interaction densities for repeat-unit pairs were evaluated from the lower critical solution temperature type phase behaviour using the lattice-fluid theory of Sanchez and Lacombe and from copolymer composition miscibility boundaries using the Flory-Huggins theory. For the GMA/MMA-SAN system the interaction energies obtained by the two approaches agree quite well with each other and with independent information obtained by the critical molecular-weight method.

Hydrogen bonding in polymer systems involving poly(p-vinylphenol). 1. Binary blends with poly(ethyl methacrylate-co-methyl methacrylate)

An association model extended to ternary systems has been applied to poly(ethyl methacrylate) (PEMA)/poly(methyl methacrylate) (PMMA)/poly(p-vinylphenol) (PVPh) blends. In this ternary blend, PVPh is miscible with PMMA and PEMA, while the last two polymers are immiscible with each other. Using model parameters previously determined for binary PMMA/PVPh and PEMA/PVPh blends, the spinodal curve of the ternary system at 165 o C has been predicted and found to be very sensitive to the values of the solubility parameters employed. FTIR measurements were conducted in order to obtain an indication of the miscibility boundaries in the ternary diagram