Phase Equilibria Of Polymer Solutions Research Articles

A novel approach for estimation of solvent activity in polymer solutions using genetic programming

In this paper, genetic programming (GP) as a novel approach for the explicit modeling the phase equilibria of polymer solutions is presented. The objective of this study is to develop robust model based on experimental data for prediction of solvent activity in polymer/solvent mixtures. Molecular weight, density, chemical structures of polymer and solvent, and concentration of polymer solution were considered as input parameters of the model. Activity of solvent is considered as output parameter of the model. Some statistical parameters were calculated in order to investigate the reliability of model. The results showed very well agreement with the experimental data with an average error of less than 3%.

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.

Thermodynamics of Phase Equilibria of Polymer Solutions

Thermodynamics of Phase Equilibria of Polymer Solutions

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.

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).

A modified NRTL equation for the calculation of phase equilibrium of polymer solutions

A local composition model based on the lattice theory, which is a modified non-random two-liquid (NRTL) equation, is developed for the representation of the Helmholtz free energy of polymer solutions. A simple temperature dependence of the model parameters is introduced to account for the oriented interactions without changing the general formulation of the free energy of mixing. The model provides a flexible thermodynamic framework for both correlating and predicting the phase equilibrium of polymer solutions. Special attention is paid to the representation of phase behavior of homologous polymer solutions and systems with or without oriented interactions.

Quasilattice equation of state for phase equilibria of polymer solutions.

An equation of state (EOS) recently proposed by the present authors based on the nonrandom lattice fluid theory was applied to correlate phase equilibrium properties of polymer solutions. The EOS requires only two molecular parameters for pure r-mers and one additional interaction energy parameter for binary systems. The molecular parameters for 12 common polymers and the binary interaction energy parameters for 17 common binary polymer solutions are presented. We found that the EOS describes quantitatively well the solvent activities and heats of mixing of various polymer solutions. The results obtained with the EOS is compared with the results obtained by such models as the random lattice model (Okada and Nose, 1981a, b), Flory theory (Flory, 1970) and the EOSs proposed by Sanchez and Lacombe (1976) and Panayiotou and Vera (1982) and UNIFAC-FV model (Oishi and Prausnitz, 1978). We believe that the result obtained to date demonstrated that the EOS can be a useful tool for practical phase equilibrium calculations of polymer solutions.

Phase equilibria in polymer solutions. Block-algebra, simultaneous flash algorithm coupled with SAFT equation of state, applied to single-stage supercritical antisolvent fractionation of polyethylene

A robust but rigorous flash algorithm allows for simulating multicomponent two-phase equilibria in supercritical asymmetric solutions that contain very large and very small components, such as polymers and supercritical solvents or monomers. The approach is to solve simultaneously all the equilibrium and material balance equations using a Newton iterative procedure in the framework of block algebra. The SAFT equation of state is used to estimate the required thermodynamic properties. This approach is illustrated with an example of single-stage fractionation of polyethylene with supercritical ethylene and 1-hethylene. The calculated solvent capacities and selectivities are related to ethylene concentration, pressure, and temperature

The chain length dependence of the chemical potentials of macromolecular systems at zero density: Exact calculations and Monte Carlo simulations

In a previous paper we illustrated a Monte Carlo method to calculate the incremental chemical potential between polymer chains of length ν and ν+1 at all densities. In this document we present a statistical mechanics model that allows for its quantitative evaluation as a function of chain length and temperature for macromolecular systems at zero density. Through this approach the incremental chemical potential at zero density is shown to be a strong function of chain length at low temperatures, but becomes chain length independent even for short chains (ν≥3) at higher temperatures. The temperature where the chemical potential becomes essentially chain length independent is a definition of the Boyle transition for finite chain length polymers, and we show that this transition temperature has a well defined chain length dependence. Chain dimensions and incremental entropies associated with chain segments are also found to decrease significantly when the temperature is reduced below this θ temperature thus proving that chain segments are localized in the vicinity of other segments in the collapsed state. The consequences of these results on the modeling of the phase equilibria of polymer solutions are also examined.

Affinity Partitioning and Its Potential in Biotechnology

Abstract The affinity partitioning technique and its applications to biotechnological separations are reviewed. In spite of the great potential for large-scale continuous processing and the wide success in laboratory separations offered by the technique, relatively few reports of biotechnological applications have been made. This underutilization is attributed in part to the lack of design criteria for establishing and optimizing partitioning systems. A first step toward developing a thermodynamically based design model for affinity partitioning, based on the incorporation of a Gibbs energy model for phase equilibria in polymer solutions into a separate theory accounting for the affinity effect, is presented.

Polydispersity Effects on the Demixing Behavior of Poly(Vinyl Methyl Ether)/Polystyrene Blends

Abstract Phase equilibrium calculations for solutions or mixtures of synthetic polymers become considerably more difficult when there is polydispersity of the polymers. To simplify the calculations, polydispersity is often neglected in the calculations or accounted for in a summary way only, and often only relatively simple free energy relations are applied. For example, Halary et al. published experimental demixing data on poly(vinyl methyl ether)/polystyrene blends. In evaluating the data the following assumptions were made: 1) the minimum of the demixing curve equals the critical point, 2) the X-parameter is independent of concentration and molecular weight, 3) the polydispersity may be roughly taken into account by using the formulas for monodisperse polymers and using the weight-average molecular weight. Continuous thermodynamics proves to be a suitable method to overcome the difficulties caused by polydispersity. Therefore, this method permits one to obtain detailed information on the phase equilibria in polymer solutions and in polymer blends in a relatively easy way. To show this, the data of Halary et al. are reanalyzed by means of continuous thermodynamics. In this way, more profound knowledge may be obtained from the experimental material, e.g., a more precise determination of the critical point and a more correct location of the spinodal.

Phase equilibria of polymer solutions by group contribution. 1. Vapor-liquid equilibria

Le modele de prevision a la forme d'une equation d'etat de phase liquide et est une extension du travail de Prigogine, Patterson et Flory

Phase Equilibria in polymer solutions by group contribution

A new group contribution method for predicting phase equilibria in polymer solutions is introduced. Results on vapor-liquid equilibria, liquid-liquid equilibria and compatibility of polymer blends are presented and ideas for future developments are suggested.

Phase equilibrium of polymer solutions in static conditions and in a flow regime

The results of investigation of the phase equilibrium of systems with upper and lower critical dissolution temperatures and also crystalline phase separation in static and dynamic conditions are presented. The role of the hydrodynamic field is considered in relation to the rate of shear, concentration and surface energy of the components.

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.

Absolute prediction of upper and lower critical solution temperatures in polymer solutions from corresponding states theory: a semi-empirical approach

Application of the corresponding states theory to phase equilibria in polymer solutions as formulated by both Flory and Patterson has been shown to provide only a qualitative description of the systems studied. A more quantitative agreement between theory and experiment can be obtained if the solvent temperature reduction parameter T☆1 is selected using a semi-empirical method which is embodied in the equation T☆1/K =–17 491 + 74.774 Tc–61.085 × 10–3T2c where Tc is the solvent critical temperature. This modified approach leads to an absolute prediction of lower critical solution temperatures from measurements of only upper critical solution temperatures, and vice versa, although the latter is less accurate. The limitations of the method are discussed and alternative procedures for data analysis are examined, none of which appears to be an improvement.

Phase equilibria in polymer solutions

AbstractA new semiempirical equation is presented for the Gibbs energy of mixing for solutions of polymers in single and mixed solvents. The equation contains two adjustable parameters per binary mixture and can readily be extended to multicomponent systems without additional parameters. The new expression gives a very good representation of the properties of a variety of polymer solutions including those in which there are strong specific interactions such as hydrogen bonding. Parameters are determined from binary vapor pressure data.A graphical method based on the new equation is given for predicting solubility limits in ternary systems containing one polymer and a mixed solvent. Only binary data are used. The method is demonstrated by comparisons of predicted solubility behavior with new experimental data taken on systems composed of polystyrene and the following mixed solvents: acetone‐toluene, acetone‐benzene, methanol‐benzene, methanol‐ethyl acetate, and acetone‐methylcyclo‐hexane.