Liquid Equilibria of Polymer Solutions

An excellent discussion of the thermodynamics of LLE systems has been given by Sorensen and Arlt (1979,1980) and Sorensen et al. (1979). The following section is adapted from these references. Consider a binary liquid mixture of + n2 moles at fixed temperature and pressure. The necessary and sufficient condition for equilibrium is that the total Gibbs free energy of mixing, AG, for the mixture is a minimum with respect to all possible changes 

According to Equation (2F-1), a liquid mixture with a total volume fraction p2 between p2 and 02M W H split into two liquid phases with binodal compositions p2 and p2. The Gibbs energy for the mixture will thus lie on the solid line between p2 and 2 instead of lying on the hypothetical dashed curve predicted by the model. The solid line is a tangent touching the predicted curve at the binodal compositions. 

is a minimum, a differential change of composition occurring at equilibrium at fixed pressure and temperature will not produce any change in AG. 

For binary equilibria, potential false solutions may be detected by checking the sign of d2 AG)/d p22 n whole composition range between zero and one (Sorensen and Arlt, 1979). 

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Chapter 3 contains the recommended predictive and correlative procedures for the specific volume of pure polymer liquids and the calculation of the vapor liquid equilibria of polymer solutions. These methods have been tested and evaluated with the data bases included in this Handbook. 

Fortunately, the polydispersity of polymers does not significantly affect the vapor-liquid equilibrium of polymer solutions since the polymer remains entirely in the condensed phase. Polydispersity becomes important in the liquid-liquid equilibria of polymer solutions where the... 

Wang, L.S. Ahlers, J. Gmehling, J. Development of a universal group contribution equation of state. 4. Prediction of vapor-liquid equilibria of polymer solutions with the volume translated group contribution equation of state. Ind. Eng. Chem. Res. 2003, 42, 6205-6211. 

Kontogeorgis, G. M., Fredenslund, A., Economou, I. G., and Tassios, D. P., 1994a. Equations of state and activity coefficient models for vapor-liquid equilibria of polymer solutions. AIChEJ., 40 1711-1727. 

Wang, W., Tree, D.A., and High, M.S., A comparison of lattice-fluid models for the calculation of the liquid-liquid equilibria of polymer solutions. Fluid Phase Equilibria, 114, 47-62, 1996. a) Novenario, C.R., Caruthers, J.M., and Chao, K.-C., VLE of polymer+solvent mixtures by the chain-of-rotators EoS, Ind. Eng. Chem. Res., 21, 1033, 1998. b) Saraiva, A., Bogdanic, G., and Fredenslund, Aa., Revision of the GC-Flory EoS for phase equilibria calculations in mixtures with polymers. 2. Prediction of LLE for polymer solutions, Ind. Eng. Chem. Res., 34, 1835, 1995. 

Comparison of the Performance of the Simplified against the Original PC-SAFT in Predicting Vapor-Liquid Equilibria of Polymer Solutions (Ar,y = 0 in All Cases)... 

Bogdanic, G., Fredenslund, A. Revision of the Group-Contribution Flory Equation of State for Phase Equilibria Calculations in Mixtures with Polymers. 1. Prediction of Vapor-Liquid Equilibria for Polymer Solutions. Ind. Eng. Chem. Res. 1994,33 1331-1340. 

Holten-Andersen, J. Rasmussen, P. Fredenslund, A., "Phase Equilibria of Polymer Solutions by Group-Contribution Part 1. Vapor-Liquid Equilibria," Ind. Eng. Chem. Res., 26, 1382 (1987). 

Kalospiros, N. S., and Tassios, D. P., 1995. Prediction of vapor-liquid equilibria in polymer solutions using an equation of state/excess Gibb.s free energy model. Ind. Eng. Chem. Res., 34 2117-2124. 

These three approaches have found widespread application to a large variety of systems and equilibria types ranging from vapor-liquid equilibria for binary and multicomponent polymer solutions, blends, and copolymers, liquid-liquid equilibria for polymer solutions and blends, solid-liquid-liquid equilibria, and solubility of gases in polymers, to mention only a few. In some cases, the results are purely predictive in others interaction parameters are required and the models are capable of correlating (describing) the experimental information. In Section 16.7, we attempt to summarize and comparatively discuss the performance of these three approaches. We attempt there, for reasons of completion, to discuss the performance of a few other (mostly) predictive models such as the group-contribution lattice fluid and the group-contribution Flory equations of state, which are not extensively discussed separately. 

Since then. Dr. WoWfarth s main research has been related to polymer systems. Currently, his research topics are molecular thermodynamics, continuous thermodynamics, phase equilibria in polymer mixtures and solutions, polymers in supercritical fluids, PVT behavior and eqnations of state, and sorption properties of polymers, about which Ik has published approxiniately 100 original papers. He has written the books Vapor-Liquid Equilibria ofBinary Polymer Solutions, CRC Handbook of Thermodynamic Data of Copolymer Solutions, and CRC Handbook ofThermocfynamic Data of Aqueous Polymer Solutions. 

SCH Schultze, J.D., Zhou, Z., and Springer, J., Gas sorption in poly(butylene terephthalate). A critical test of the influence of gas Asta,Angew. Makromol. Chem., 185-186, 265, 1991. 1991SZY Szydlowski, J. and van Hook, W.A., Isotope and pressure effects on hquid-liquid equilibria in polymer solutions. H/D solvent isotope effects in acetone-polystyrene solutions. Macromolecules, 24, 4883, 1991. 

Liquid-Liquid Phase Equilibria of Polymer Solutions... 

LUS Luszczyk, M., Rebelo, L.P.N., and van Hook, W.A., Isotope and pressure dependence of liquid-liquid equilibria in polymer solutions. 5. Measirrements of solute and solvent isotope effects. 6. A continuous polydisperse thermo namic interpretation of demixing measirrements in polystyrene-acetone and polystyrene-methylcyclopentane (exp. data by L.P.N. Rchclo), Macromolecules, 28, 745, 1995. 

Fig. 6 and the remarks made about it in 2.2.1. bring out the essential features of liquid-liquid equilibria in polymer solutions. Given the appropriate A G function for the system considered, the location of the miscibility gap is determined by the temperature. Introducing T on a third axis, we obtain the three-dimensional diagram in Fig. 50. Coexisting... 

Vetere, A., Rules for predicting vapor-liquid equilibria of amorphous polymer solutions using a modified Flory-Huggins equation. Fluid Phase Equilibria, 97, 43, 1994. 

Feng, W. et al.. Calculation of vapor-liquid equilibria of high concentrated polymer solution by a modified SAFT equation of state, presented at the 9th International Conference on Rroperties and Phase Equilibria for Product and Process Design, Kurashiki, Japan, May 20-25, 2001, 2001. 

Some implicit databases are provided within the Polymer Handbook by Schuld and Wolf or by Orwoll and in two papers prepared earlier by Orwoll. These four sources list tables of Flory s %-function and tables where enthalpy, entropy or volume changes, respectively, are given in the literature for a large number of polymer solutions. The tables of second virial coefficients of polymers in solution, which were prepared by Lechner and coworkers (also provided in die Polymer Handbook), are a valuable source for estimating the solvent activity in the dilute polymer solution. Bonner reviewed vapor-liquid equilibria in concentrated polymer solutions and listed tables containing temperature and concentration ranges of a certain number of polymer solutions." Two CRC-handbooks prepared by Barton list a larger number of fliermodynamic data of polymer solutions in form of polymer-solvent interaction or solubility parameters." ... 

Treating polymer solutions with distribution functions by continuous thermodynamics and procedures to measure and calculate liquid-liquid equilibria of such systems is reviewed in 1989RAE and 1990RAE. 

SA1 Sadeghi, R. and Shahebrahimi, Y., Vapor-liquid equilibria of aqueous polymer solutions from vapor-pressure osmometry and isopiestic measurements, J. Chem. Eng. Data, 56, 789, 2011. 

Wong, P.T.T., Mantsch, H.M., and Snyder, R.G., /. Chem. Phys., 47, 1316,1967. Yamakawa, H., Effects of pressure on conformer equilibria in liquid n-hexane. Modern Theory of Polymer Solutions, Harper and Row, New York, 1971. 

Tanbonliong, J.O. and Prausnitz, J.M., 1997. Vapor-Liquid Equilibria of Binary and Ternary Solutions Containing Polyvinylacetate as a Component. Polymer, 38 5775. 

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