Equilibria Of Polymer Solutions Research Articles

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.

Group contribution method for group contribution method for estimation of vapor liquid equilibria in polymer solutions

This study introduces a specified group-contribution method for predicting the phase equilibria in polymer solutions. The method is based on a modified double lattice model developed previously. The proposed model includes a combinatorial energy contribution that is responsible for the revised Flory-Huggins entropy of mixing, the van der Waals energy contribution from dispersion, a polar force and specific energy contribution. Using the group-interaction parameters obtained from data reduction, the solvent activities for a large variety of mixtures of polymers and solvents over a wide range of temperatures can be predicted with good accuracy. This method is simple but provides improved predictions compared to those of the other group contribution methods.

Prediction of vapor–liquid and liquid–liquid equilibria for polymer systems: Comparison of activity coefficient models

A large number of equations of state and activity coefficient models capable of describing phase equilibria in polymer solutions are available today, but only a few of these models have been applied to different systems. It is therefore useful to investigate the performance of existing thermodynamic models for complex polymer solutions which have not yet been widely studied. The present work studies the application of several activity coefficient models [P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, New York, NY, 1953; T. Oishi, J.M. Prausnitz, Estimation of solvent activities in polymer solutions using a group-contribution method, Ind. Eng. Chem. Process Design Dev. 17 (1978) 333; H.S. Elbro, A. Fredenslund, P. Rasmussen, A new simple equation for the prediction of solvent activities in polymer solutions, Macromolecules 23 (1990) 4707; G.M. Kontogeorgis, A. Fredenslund, D. Tassios, Simple activity coefficient model for the prediction of solvent activities in polymer solutions, Ind. Eng. Chem. Res. 32 (1993) 362; C. Chen, A segment-based local composition model for the Gibbs energy of polymer solutions, Fluid Phase Equilib. 83 (1993) 301; A. Vetere, Rules for predicting vapor–liquid equilibria of amorphous polymer solutions using a modified Flory–Huggins equation, Fluid Phase Equilib. 97 (1994) 43; C. Qian, S.J. Mumby, B.E. Eichinger, Phase diagrams of binary polymer solutions and blends, Macromolecules 24 (1991) 1655; Y.C. Bae, J.J. Shim, D.S. Soane, J.M. Prausnitz, Representation of vapor–liquid and liquid–liquid equilibria for binary systems containing polymers: applicability of an extended Flory–Huggins equation, J. Appl. Polym. Sci. 47 (1993) 1193; G. Bogdanic, J. Vidal, A segmental interaction model for liquid–liquid equilibrium calculations for polymer solutions, Fluid Phase Equilibria 173 (2000) 241] and activity coefficient from equations of state [F. Chen, A. Fredenslund, P. Rasmussen, Group-contribution Flory equation of state for vapor–liquid equilibria en mixtures with polymers, Ind. Eng. Chem. Res. 29 (1990) 875; M.S. High, R.P. Danner, Application of the group contribution lattice—fluids EOS to polymer solutions, AIChE J. 36 (1990) 1625]. The evaluation of these models was carried out both at infinite dilution and at finite concentrations and the results compared to experimental data. Furthermore, liquid–liquid equilibrium predictions for binary polymer solutions using six activity coefficient models are compared in this work. The parameters were estimated for all the models to achieve the best possible representation of the reported experimental equilibrium behavior.

Intra- and Intermolecular Hydrogen-Bonding Model and Its Application to 2-Alkoxyethanol Systems

Intramolecular hydrogen bonding is known to be responsible for unusual phase behaviors such as liquid−liquid equilibria in polymer solutions and protein folding in biological systems. Results of experimental intra- and interbonded fraction data and molecular simulation have been interpreted using lattice statistics and perturbation theories. So far, however, few quantitative comparisons are reported with physical properties and phase equilibrium data of real systems. In this study, a more general derivation of statistics was developed for intra- and interbonding contributions based on Veytsman statistics, which was incorporated in physical contributions of a nonrandom lattice fluid theory to obtain a free energy model for real systems. The proposed model was applied to vapor pressures and densities of pure 2-alkoxyethanols and intra- and interbonded mole fractions and phase equilibria of 2-alkoxyethanol containing mixtures. Calculated results were found in close agreement with property data in the constraint of correlating inter- and intrabonded mole fractions, and deviations of calculated results with data were found similar to those without an intrabonding consideration.

A new model and extension of Wong–Sandler mixing rule for prediction of (vapour + liquid) equilibrium of polymer solutions using EOS/ GE

The cubic equation of state (CEOS) is a powerful method for calculation of (vapour + liquid) equilibrium (VLE) in polymer solutions. Using CEOS for both the vapour and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EOS approach. However, the traditional mixing rules are not appropriate to extend the CEOS to non-ideal mixtures such as polymer solutions. Several authors have applied the EOS/ G E approach to predict (vapour + liquid) equilibria in polymer solutions, however, incorporating an appropriate excess Gibbs free energy for the new mixing rule is a major step. In this research, the NRTL-NRF model was extended in terms of volume fraction of polymer and solvent (instead of mole fraction), then equilibrium calculations were carried out using PRSV EOS and Wong–Sandler mixing rules. Using the adjustable parameters as a function of solution temperature, the NRTL-NRF model can be used as a predictive model. In comparison with NRTL model, the results of the new NRTL-NRF model show better accuracy.

Liquid-liquid phase equilibria in polymer solutions and polymer mixtures

The pressure dependence of liquid-liquid equilibria in weakly interacting binary macromolecular systems (homopolymer solutions and blends) will be discussed. The common origin of the separate high-temperature/low-temperature and high-pressure/low-pressure branches of demixing curves will be demonstrated by extending the study into the region of metastable liquid states including the undercooled, overheated and stretched states (i.e. states at negative pressures). The seemingly different response of the UCST-branch of solutions and blends when pressurized (pressure induced mixing for most polymer solutions, pressure induced demixing for most blends) will be explained in terms of the location of a hypercritical point found either at positive (most solutions) or negative pressure (most blends). Further, it is shown that the pressure dependence of demixing of homopolymer solutions and blends may be described using a master-curve' which, however, is sometimes partly masked by degradation or by vapour-liquid and/or solid-liquid phase transitions. Experimental results demonstrating the extension of liquid-liquid phase boundary curves into the metastable regions will be presented, and the existence of solubility islands in the vicinity of the hypercritical points discussed.

Phase equilibria of polymer solutions: modified perturbed hard-sphere-chain equation-of-state

We modified the perturbed hard-sphere-chain (PHSC) equation-of-state by introducing Chapman's equation into the bonding term of the reference equation. The proposed model successfully predicts the vapor/liquid equilibria (VLE) of pure fluids with three characteristic parameters obtained for each substance. We also extended the modified PHSC equation-of-state to describe the liquid/liquid equilibria (LLE) of polymer solutions. Characteristic parameters obtained from the pure substances were directly used to predict the LLE of polymer solutions. The calculated coexistence curves using the proposed model agree remarkably well with the experimental data.

Predicting liquid–liquid transitions in polymer solutions using the GCLF equation of state

Group contribution lattice fluid equation of state (GCLF-EOS) have been extended and used to calculate phase equilibria in polymer solutions. Group parameters for three group contributions and nine new group contributions have been calculated. Saturation vapor pressure for pure solvent and weight fraction activity coefficients in polymer solutions have been calculated and the agreement obtained with experimental data indicated the accuracy of the parameters. A combining rule consisting a pair interaction parameter with temperature dependency was proposed. The area method was used with GCLF-EOS to obtain phase diagram for liquid equilibrium (LLE) of polymer solutions. The method was able to predict both lower critical solution temperature (LCST) and upper critical solution temperature (UCST).

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 equilibria of polymer solutions: a closed miscibility loop phase behavior

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

Liquid–liquid equilibria in polymer solutions at negative pressure

Properties of liquids under tension (i.e. at negative pressure) are discussed together with methods of producing negative pressure. That established, the pressure dependence of liquid–liquid demixing in certain polymer–solvent solutions, including demixing at negative pressure is described.

Predicting Specific Volumes of Pure Polymers and VLE of Polymer Solutions by Group-Contribution Lattice Theory

A generalized group-contribution (GC) scheme with an equation of state (EOS) presented previously by the present authors was extended to the prediction of specific volumes of pure polymers and vapor–liquid equilibria of polymer solutions. The GC-EOS requires only two parameters, representing group size and interaction between groups. A unique feature of the approach is that a single set of group information can be applied to predict both the configurational properties of pure polymers and mixtures in general. The approach was illustratively applied to the prediction of the density of pure polymers, vapor pressures of organic solvents, and phase equilibria of their polymer solutions.

Improvement of predictive accuracy of the UNIFAC model for vapor-liquid equilibria of polymer solutions

Improvement of predictive accuracy of the UNIFAC model for vapor-liquid equilibria of polymer solutions

A new mixing rule for cubic equations of state and its application to vapor-liquid equilibria of polymer solutions

A new mixing rule for cubic equations of state and its application to vapor-liquid equilibria of polymer solutions

Prediction of vapor-liquid equilibria in polymer solutions using EOS-group contribution model consistent with the second virial coefficient condition

Prediction of vapor-liquid equilibria in polymer solutions using EOS-group contribution model consistent with the second virial coefficient condition

An early look at macromolecular crowding

Interest in the interaction between proteins and polysaccharides in semidilute systems developed in the late 1950's and early 1960's both in the field of matrix biology and in the construction of new separation techniques. The author gives an account of how his work in the 50's on the characterization of a connective tissue polysaccharide, hyaluronan, led him into studies on polysaccharide networks, sieve effects, molecular exclusion, a theory of gel filtration, solubility of proteins and chemical equilibria in polymer solutions, water and protein homeostatis in vivo, and ordered convectional flow in concentrated polymer systems.

Measurement and correlation of vapor-liquid equilibria in polymer solutions containing polystyrene with polymer ASOG

A gas chromatographic method is used to measure the activities of solvents which have a range of finite concentrations in polymer solutions. Experimental data are presented for 8 binary solvent/polystyrene systems at 393.15 and 423.15 K. The polymer ASOG is proposed to be correlated with the activities of solvents in polymer solutions, and consists of the original ASOG and the empirical modification of free volume. For 8 binary solvent/polystyrene systems containing nonpolar and moderately polar solvents, the polymer ASOG was successful to correlate with experimental data within the range of 1% error.

Prediction of Vapor-Liquid Equilibria in Polymer Solutions Using an Equation Of State/Excess Gibbs Free Energy Model

A new mixing rule has been developed, which is coupled with a translated and modified version of the Peng-Robinson equation of state (EoS) and the entropic-FV activity coefficient model. The resulting EoS/GE model is applied to the correlation and prediction of vapor-liquid equilibria (VLE) in solvent/polymer mixtures, after appropriate modification of the cubic EoS to describe the volumetric behavior of the pure polymer. The model yields very good correlation of experimental equilibrium pressures in concentrated polymer solutions, but more importantly, successful predictions of the same data are obtained. A comparison with other EoS-based models applicable to the prediction of VLE in polymer solutions is also presented.

Isotope and pressure dependence of liquid-liquid equilibria in polymer solutions. 5. Measurements of solute and solvent isotope effects in polystyrene-acetone and polystyrene-methylcyclopentane. 6. A continuous polydisperse thermodynamic interpretation of demixing measurements in polystyrene-acetone and polystyrene-methylcyclopentane solutions

Cloud and spinodal loci have been obtained as functions of pressure (P), temperature (T), polymer molecular weight (MW), polymer fraction, and H/D substitution on solute (z D ) or solvent (y D ), for acetone-polystyrene and methylcyclopentane-polystyrene solutions. A light scattering technique was employed. The isotope effects and their pressure dependences are large. An increase in pressure, an increase in H/D ratio in the solvent (or decrease in the polymer H/D ratio), or a decrease in polymer molecular weight increases the region of miscibility. The solutions show both upper and lower branches, which, for acetone, join at a hypercritical point. The cloud point diagrams are highly distorted in the hypercritical region but smooth as one moves away by appropriately varying pressure, H/D ratio, or solute molecular weight. In the vicinity of the multiple critical point, hypercritical distortion for polystyrene/ (CH 3 ) 2 CO solutions causes a highly unusual homogeneous one-phase «hole» in the (T, W ps ) cloud point diagram. This «extra» one-phase region appears close to the hypercritical point, and just inside the two-phase region which forms immediately after the system collapses into the «hourglass» configuration. The effect is not seen in (CD 3 ) 2 CO or mixed (CH 3 ) 2 CO/(CD 3 ) 2 CO solutions, but those solutions also show marked distortion in the (T, W ps ) plane. H/D substitutions (on either polymer or solvent) cause large differences in cloud point and spinodal temperatures, especially in the vicinity of the hypercritical point. Isotope shifts as large as 40 K were observed on the cloud points of the polystyrene/acetone system. A mean-field formalism to interpret cloud point and spinodal data on liquid-liquid demixing of polymer-solvent solutions exhibiting both upper and lower consolute branches and hypercritical points is developed. The dependence of the phase equilibria on pressure, temperature, segment number, polydispersity, and H/D substitution of either or both solvent and polymer are explicitly considered. Calculations of cloud and shadow curves are reported. The method is based on a Flory-Huggins type continuous thermodynamic representation of free energies in polydisperse polymer solutions due to Ratzsch and co-workers. The computer algorithm PHASEEQ r written in QUICKBASIC r has been coded for the case of Schulz-Flory segment distribution functions. Calculations interpreting demising data for polystyrene/acetone and polystyrene/methylcyclopentane solutions over wide ranges of pressure, concentration, molecular weight, and H/D substitution are reported. The isotope effects, which are large, are discusaed using Bigeleisen-Van Hook-Wolfsberg condensed phase isotope effect theory. Along the critical line multidimensional classical or nonclassical scaling equations permit economical representation of the data. The scaling approach is developed and compared with the mean-field based interpretation

Equations of state and activity coefficient models for vapor‐liquid equilibria of polymer solutions

AbstractFour noncubic equations of state, (EOS) and five activity coefficient models are applied to binary polymer and solvent solutions. Solvent activities at intermediate concentrations and equilibrium pressures are predicted with the perturbed‐soft‐chain theory (PSCT), group‐perturbed‐soft‐chain theory, (GPSCT), group‐contribution‐lattice fluid (GCLF) EOS, GC‐Flory EOS, UNIFAC‐FV, entropic‐FV and GK‐FV models, “new” UNIFAC, and modified Flory‐Huggins model. Free‐volume activity coefficient models (UNIFAC‐FV, entropic‐FV) are simpler and, when applied to polymer solutions, more accurate than the EOS. Activity coefficient models are restricted to low‐pressure calculations and require accurate values of pure‐component volumes. Mixture parameters for activity coefficient models and GC‐Flory EOS have been previously evaluated from experimental vapor‐liquid equilibrium data for mixtures with only low‐molecular‐weight compounds. The GC‐Flory EOS, though more complicated than activity coefficient models, provides equally good or in some cases better predictions. The application of GC‐Flory EOS developed as an activity coefficient model is restricted to low‐pressure calculations. On the other hand, PSCT and GCLF developed as “true” EOS provide reliable equilibrium predictions using mixture parameters evaluated solely from pure‐component properties together with standard mixing and combining rules. PSCT EOS performs generally better than GCLF EOS for polymer solutions considered in this study.