Polymer vapor-liquid equilibrium

Figure 3. Polymer/solvent vapor-liquid equilibrium...

None of the experimental techniques described by Bonner, however, has been capable of providing reliable vapor-liquid equilibrium data at the combined extremes of elevated temperature and reduced pressure, conditions applicable to most commercial polymer-stripping operations. This problem has been addressed by Meyer and Blanks (1982), who developed a modified isopiestic technique that could be used when solubilities are low. Although the success of this new technique was demonstrated using just polyethylene with isobutane and propane, the idea shows considerable promise for obtaining data at unusual conditions of temperature and pressure. 

Many vapors of substances, such as those of certain metals, are mixtures of monomers and dimers and, possibly, of even higher polymers. This must be taken into account when the chemical potential of the substance in a condensed phase, either pure or a solution, is determined by a study of the vapor-liquid equilibrium. We choose to consider only the components in the condensed phase, and use the molecular mass of the monomer to determine the mole numbers. We designate the component whose chemical potential is to be determined by the subscript 1. The condition of equilibrium is then... 

The current state-of-the-art is such that there are no reliable methods of predicting liquid-liquid equilibria of polymer-solvent systems. Thus, the recommended procedures and computer programs included in this Handbook treat only vapor-liquid equilibrium. A discussion of the correlation of LLE data is included in Chapter 2. 

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... 

Orbey, N., and Sandler, S. I., 1994. Vapor liquid equilibrium of polymer solutions using a cubic equation of state. AlChE J., 40 1203-1209. 

Here, the transport rates depend on the partition coefficient Kfp only. The solute concentration in the membrane can often be related to the gas phase partial pressure using Henry s law or a similar equilibrium relationship. At higher pressures, vapor-liquid equilibrium or gas-polymer absorption data are necessary to determine the concentration gradient in the membrane. 

Figure 3.24 Comparison of the schematic P-T diagrams for small molecule systems with those for polymer-solvent systems (A), type-lll system for a small molecule system where the vapor-liquid equilibrium curves for two pure components end in their respective critical points,...

A critical need exists for consiractiou of a systematic, reliable data base for a wide number of gases in a wide number of polymers. Until this need is recognized and addressed in the same way that collection of vapor-liquid equilibrium data is accepted, membrane development will be reduced largely to an Edi-sonian" approach. 

Wen, H., Elhro, H. S., and Alessi, R, Polymer Solution Data Collection. I. Vapor-liquid equilibrium II. Solvent activity coefficients at infinite dilution III. Liquid-liquid equilibrium. Chemistry Data Series, Vol. 15, DECHEMA, Frankfurt am Main, 1992. 

Vapor-liquid equilibrium (VLE) data and gas solubilities for binary or ternary polymer solutions... 

SUR Surana, R.K., Danner, R.P., DeHaan, A.B., and Beckers, N., New technique to measure high-pressure and high-temperature polymer-solvent vapor-liquid equilibrium. Fluid Phase Equil., 139, 361, 1997. 

Solvent activities of polymer solutions have been measured for about 60 years now. However, the database for polymer solutions is still modest, in comparison with the enormous amount of data available for mixtures of low-molecular substances. Three explicit databases have been published in the literature up to now. The database prepared by Wen Hao et al. is summarized in two parts of the DECHEMA Chemistry Data Series. Danner and Higtf provided a database and some calculation methods on a floppy disk with their book. WoUfarth prepared the most complete data collection regarding vapor-liquid equilibrium data of polymer solutions. His annually updated electronic database is not commercially available however, personal requests can be made via his e-mail address given above. 

An up-to-date list of all polymer-solvent systems for which solvent activities or vapor pressures from vapor-liquid equilibrium measurements were published in the literature is provided in Appendix 4.4. A of this Subchapter 4.4 (please see below). 

In summary, investigations on vapor-liquid equilibrium of polymer solutions are the most important souree for obtaining solvent aetivities in polymer solutions. Therefore, emphasis is laid in this subehapter on the experimental methods, whieh use this equilibrium. 

The data reduction of vapor-pressure osmometry (VPO) follows to some extent the same relations as outlined above. However, from its basic principles, it is not an equilibrium method, since one measures the (very) small difference between the boiling point temperatures of the pure solvent drop and the polymer solution drop in a dynamic regime. This temperature difference is the starting point for determining solvent activities. There is an analogy to the boiling point elevation in thermodynamic equilibrium. Therefore, in the steady state period of the experiment, the following relation can be applied if one assumes that the steady state is sufficiently near the vapor-liquid equilibrium and linear non-equilibrium thermodynamics is valid ... 

Equation-of-state approaches are preferred concepts for a quantitative representation of polymer solution properties. They are able to correlate experimental VLE data over wide ranges of pressure and temperature and allow for physically meaningful extrapolation of experimental data into unmeasured regions of interest for application. Based on the experience of the author about the application of the COR equation-of-state model to many polymer-solvent systems, it is possible, for example, to measure some vapor pressures at temperatures between 50 and 100 C and concentrations between 50 and 80 wt% polymer by isopiestic sorption together with some infinite dilution data (limiting activity coefficients, Henry s constants) at temperatures between 100 and 200 C by IGC and then to calculate the complete vapor-liquid equilibrium region between room temperature and about 350 C, pressures between 0.1 mbar and 10 bar, and solvent concentration between the common polymer solution of about 75-95 wt% solvent and the ppm-region where the final solvent and/or monomer devolatilization process takes place. Equivalent results can be obtained with any other comparable equation of state model like PHC, SAFT, PHSC, etc. 

Wen Hao, H. S. Elbro, P. Alessi, Polymer Solution Data Collection, Ptl Vapor-Liquid Equilibrium, Pt.2 Solvent Activity Coefficients at Infinite Dilution, Pt. 3 Liquid-Liquid Equilibrium, DECHEMA Chemistry Data Series, Vol. XIV, Pts. 1,2+3, DECHEMA, FrankfUrt/M., 1992. 

Investigations on vapor-liquid equilibrium of polymer solutions can be made by various methods ... 

VAPOR-LIQUID EQUILIBRIUM (VLE) DATA OF AQUEOUS POLYMER SOLUTIONS... 

SER Se, R.A.G. and Aznar, M., Vapor-liquid equilibrium of polymer -t- solvent systems Experimental data and thermodynamic modeling, Polymer, 48, 5646, 2007. 

There are about 850 newly published referenees containing about 150 new vapor-liquid equilibrium data sets and some new tables containing classical Henry s coefficients, about 600 new liquid-liquid equilibrium data sets and some new high-pressure fluid phase equilibrium data, 10 new enthalpic data sets, 20 new data sets describing PVT-properties of polymers, and 120 new data sets with densities or excess volumes. There are also new results on second osmotic virial coefficients of about 45 polymers in aqueous solution. So, in comparison to the original handbook, the new supplementary volume contains even a larger amoimt of data and will be a useful as well as necessary completion of the origirral handbook. 

As pointed out above, dynamic vapor-liquid equilibrium measurement methods are not very suitable for concentrated polymer solutions, especially due to their heavy foaming behavior. For dilute polymer solutions, however, there is continuing application of ebulliometry as an absolute method for the direct determination of the number-average molecular mass M . Dedicated differential ebulliometers allow the determination of values up to an order of 100,000 g/mol. EbuUiometry as a method for molar mass determination was recently reviewed by Cooper, Glover, and Mays and Hadjichristidis. ... 

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