Liquid-liquid phase equilibria for some polystyrene-methylcyclohexane mixtures

Liquid-liquid cloud point diagrams of solutions of nearly monodisperse samples of polystyrene (PS), and binary mixtures of nearly monodisperse PS’s, both in methylcyclohexane (MCH), were determined for several polymer molecular weights (M_w) at 0.1 MPa. The bimodal mixtures (PS[M_w(1),ρ(1)] + PS[M_w(2),ρ(2)], M_w(1)=90×10³ g/mol, M_w(2)=13×10³ g/mol, 5.78 × 10³ g/mol, and 2.2 × 10³ g/mol, ρ=1.06) were prepared constraining 〈M_w〉=38.6×10³ g/mol, ρ=M_w/M_n is the polydispersity index. In each case the cloud point curves (CPC’s) for the bimodal mixtures are strongly skewed, lying well above CPC for 〈M_w〉 when φ<φ_CRITICAL, and below CPC for 〈M_w〉 when φ>φ_CRITICAL; φ is volume fraction polymer in the polymer/solvent mixture. The experimental results are discussed in the context of empirical and mean-field representations.     

Liquid-liquid equilibria of polymer solutions: a closed miscibility loop phase behavior

In the phase behavior of binary polymer/solvent mixtures, a lower critical solution temperature (LCST) and hour-glass shaped and closed miscibility loop phase behavior are encountered. The closed miscibility loop phase behavior may be mainly due to highly oriented interactions such as hydrogen bonding. The purpose of this study is to describe closed miscibility loop phase behavior in the liquid-liquid equilibria of polymer solutions. To consider highly oriented interactions (or specific interactions), we employed a secondary lattice concept as a perturbation term.     

Liquid-liquid phase separation in multicomponent polymer solutions

Summary In conformity with a prediction byTompa, polymer solutions were found which, in a limited range of concentrations and temperatures, separate into three liquid phases. This was demonstrated with solutions in diphenylether of two polyethylene fractions with narrow molecular weight distributions, which represented the closest possible approximations of ternary systems. The phenomenon takes place exactly under the conditions indicated byTompa on the basis of theFlory-Huggins free enthalpy of mixing function.

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Zusammenfassung In Übereinstimmung mit einer Voraussage vonTompa ließen sich polymere Lösungen finden, die sich in einen begrenzten Bereich von Konzentration und Temperature in drei flüssige Phasen trennen. Dies wurde an Lösungen von zwei Polyäthylenfraktionen mit schmaler M-G-Verteilung in Diphenyläther gezeigt, die die engste mögliche Annäherung an ternäre Systeme repräsentieren. Das Phänomen tritt exakt unter den Bedingungen auf, dieTompa auf Grundlage derFlory-Hugginsschen Freien Mischungsenthalpie angegeben hat.

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With 9 figures in 26 details and 3 tables     

Liquid-liquid equilibria of polymer solutions: Applicability of extended Redlich-Kister expansion

We developed a simple and improved expression for the Helmholtz energy of mixing which uses a Taylor series of an exponential function based on extending the Redlich-Kister expansion. This model incorporates the chain-length dependence of polymers and specific interactions such as hydrogen bonds. The proposed model can accurately predict most phase diagrams of various binary polymer solutions including upper critical solution temperature (UCST), lower critical solution temperature (LSCT), both UCST and LCST, and closed miscibility loops. Our model fits experimental data of the complex phase behavior of polymer solutions well.     

Phase equilibria in polymer solutions

A theoretical study of phase equilibria in multicomponent polymer solutions is presented. The treatment is based on the virial expansion of the osmotic pressure. A program for the numerical determination of phase diagrams is worked out and applied to the polystyrene-cyclohexane system. The present approach is compared with the Flory-Huggins theory of polymer solutions, which is shown to represent a special class of approximations in the present treatment.     

Membrane equilibria in concentrated polymer solutions

Membrane equilibria in concentrated polymer solutions are investigated. A three-component system (solvent, a polymer and an arbitrary solute) is considered. Starting with the virial expansion of the osmotic pressure, the Gibbs-Duhem equation for the system is integrated and the chemical potentials of the different components are evaluated. From the latter the equilibrium conditions are derived for a variety of experimental situations. The treatment is extended to the study of partition equilibria in gels, using a concentrated polymer solution as a model for the gel.     

Liquid-liquid equilibria for ternary acetonitrile-ethanol-saturated hydrocarbon and acetonitrile-1-propanol-saturated hydrocarbon mixtures

Isothermal vapour-liquid equilibrium data for acetonitrile-1-propanol at 45° C were measured by use of a recirculating still. The liquid-liquid equilibria of (acetonitrile-etha-nol)-(n-hexane or n-heptane or n-octane) and those of (acetonitrile-1-propanol)-(cyclohexane or n-hexane or n-heptane) were obtained from measurements of tie-lines. The experimental results were compared with those calculated from the UNIQUAC associated-solution model.     

乙腈-水的液液、固液相平衡和过量Gibbs自由能

测制了xCH~3CN+(1-x)H~2O的液液、固液平衡相图, 此系液液分层的简单低共熔混合物类相图。低共熔点温度为227.44K, 组成x=0.955。最高临界溶解温度为271.0K, 临界组成x=0.35, 临界指数n=2.64。两液相与冰的平衡温度为263.07K。计算出体系在263.07K的过量Gibbs自由能G~m^E, 液液分层时G~m^E的最大值为1174J·mol^-^1。     

Influence of solid surface on equilibria in polymer mixtures

The influence of solid disperse particles (aerosil) on phase equilibria in ternary (polymer-polymer-solvent) and binary (polymer-polymer) systems has been investigated using adsorption and gas chromatography techniques. The change in position and shape of the binodal for the ternary systems has been established. The region of thermodynamic compatibility of two polymers in a common solvent is broadened due to the selective adsorption of high molecular weight fraction of one of the polymers, this effect being dependent on the amount of solid particles introduced into the system. For binary systems, the thermodynamic interaction parameters χ₂₃ have been determined and increasing thermodynamic stability of the mixture in the presence of the solid phase has been discovered. The complicated dependences of the interaction parameters on mixture composition are connected with differences in selectivity of adsorption for various compositions. It is supposed that increased thermodynamic stability of a mixture of two incompatible polymers in the presence of solid is due to the transition of both polymers into adsorption and border layers.     

Liquid-liquid phase equilibria of aqueous two-phase systems containing salts and polyethylene glycol

Liquid-liquid phase equilibria of the ternary systems: (a) polyethylene glycol - ammonium sulfate- water and (b) polyethylene glycol - sodium carbonate -water have been determined experimentally at 15°, 25°, 35° and 45°C and for two different molecular weights of the polymer (Avg. M.W. 1000 and 2000). Details of the glass cell and of the equilibration and analytical procedures used are described. Equilibrium data along with phase diagrams are presented. Finally the effect of temperature and of the molecular weight of the polymer are also discussed.     

Equations for describing liquid-vapor phase equilibria in binary mixtures

Three forms of equations for describing experimental data on liquid and vapor pressures, depending on temperature and composition at phase equilibria in binary mixtures, are proposed and evaluated. It is determined that the form of equation depends on the relationship between the temperature of a mixture and the critical temperatures of the components of the mixture. Exact data on the phase equilibria in nitrogenoxygen, nitrogen-argon, and oxygen-argon mixtures [1] are approximated to assess the effectiveness of the equations’ forms. It is found that the equations also allow us to determine the phase composition at a given temperature and pressure and temperatures of phases at a given pressure and composition.     

Liquid-liquid equilibria and theta temperatures in homopolymer-solvent solutions from a perturbed hard-sphere-chain equation of state

The perturbed hard-sphere-chain (PHSC) equation of state is used to calculate liquid-liquid equilibria of binary nonpolar solvent/homopolymer systems exhibiting both an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST). Systems studied include polyisobutylene, polyethylene, and polystyrene solutions. Equation-of-state parameters of homopolymers are obtained by regressing the pressure-volume-temperature data of polymer melts. In polymer solutions, however, theory overestimates the equation-of-state effect which causes the LCST at elevated temperature. To correct the overestimated equation-of-state effect, an empirical adjustable parameter is introduced into the perturbation term of the PHSC equation of state. An entropy parameter is also introduced into the Helmholtz energy of the mixture to correlate quantitatively the dependence of critical temperatures on polymer molecular weight. For systems exhibiting a LCST, two adjustable parameters are required to obtain quantitative agreement of theoretical critical temperatures with experiment as a function of polymer molecular weight. For systems exhibiting both an UCST and a LCST, three adjustable parameters may be necessary. The need for so many empirical binary parameters is probably due to the oversimplified perturbation term which is based on the mean-field assumption. © 1996 John Wiley & Sons, Inc.     

On phase equilibria,interfacial tension and phase growth in ternary polymer blends

A gradient squared free energy functional of the Landau-Ginzburg type is combined with Flory-Huggins theory to calculate minimum domain sizes, concentration profiles and interfacial tensions in ternary polymer blends. The dynamic equations governing spinodal decomposition are linearized to show that the minimum size for growth is identical to the thermodynamic minimum on phase volume. It is shown that unseparated, third components are enriched at the interface, reduce interfacial tension, increase stability and increase the minimum domain sizes. Enrichment of the third component at the interface causes concentrations at the major components to lie outside their binodal limits at a distance from the interface. Although the effects are most pronounced when the third component is a compatibilizer, the general phenomena remain true even when the third component is relatively incompatible. Generalizations to blends of N components are presented, and a robust method for calculating multicomponent phase diagrams is described.     

Vapor-liquid equilibria of polymer solutions determined by molecular mechanics

A method of calculating interaction parameters used in phase equilibrium calculations was extended for predicting solvent activities of polymer solutions. A pair of interaction parameters are determined by calculating interaction energies between all pairs of molecules in the solution of interest with a molecular mechanics method called the consistent force field (CFF). The conformational space of a pair of molecules is sampled with a Monte Carlo algorithm followed by energy minimizations. The method is used to calculate solvent activities for the diethylketone/polypropylene system, giving results in good agreement with experimental values. In addition, solvent activities are predicted for the diethylketone/polyethylenesystem for which no experimental data are available. The method is fully predictive, as no fitting to experimental phase-equilibrium data is carried out.     

Dynamics of phase separation and critical phenomena in polymer mixtures

The phenomenological mean-field theory for statics and dynamics of polymer mixtures is described, generalizing the approaches of Flory-Huggins, Cahn-Hilliard and de Gennes. Predictions are made for critical behavior, spinodal decomposition and homogeneous nucleation. The validity of the mean-field approximations is discussed with Ginzburg criteria. The results of the theory are compared to computer simulations and recent experiments.Invited talk delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschu\ Polymerphysik, Kaiserslautern, 12–14 March 1986, and at the Gordon Research Conference on Polymer Physics, Andover, New Hampshire, 14–18 July 1986.The author is grateful to Dieter W. Heermann, Alla Sariban, Harry L. Frisch, Josef JÄckie and Thomas Schichtel for their fruitful collaboration on this research described in this review. He thanks them and Arthur BaumgÄrtner for allowing to present partially unpublished material, and for stimulating discussions. Furthermore the author has benefitted from discussions with P. G. de Gennes, P. Pincus, H. Sillescu and G. R. Strobl. This research is supported in part by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 41.     

Particle-induced phase separation in mixed polymer solutions

The influence of added colloidal particles on the phase separation of mixed aqueous polymer solutions is investigated. Two types of particles (polystyrene latex or silica) and different combinations of segregating polymers (dextran of varying molar mass combined with poly(ethylene oxide) (PEO) of varying molar mass, or Ucon, a copolymer of ethylene oxide and propylene oxide) were used. All systems displayed particle-induced instability effects, but the extent of the effect varied strongly between the various combinations and with the amount of added salt. Very large instability effects were seen in certain mixtures. Two mechanisms, both relying on the adsorption of at least one of the polymers to the particle surface, seem to operate. Close to the cloud-point curve of the particle-free polymer1/polymer2/water mixture, adsorption of PEO or Ucon to the particles gives rise to a capillary-induced phase separation. Close to the dextran/water axis of the phase diagram, the adsorbing polymer gives rise to a surface modification of the particles, which then interacts repulsively with the surrounding dextran solution.