Phase equilibria of polymer solutions

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). 

J. Holten Andersen, "Group Contribution Model for Phase Equilibria of Polymer Solutions", Ph.D. Thesis., Instituttet for Kemilndustrl, Technical University of Denmark, 1985. 

Many databases (some available in computer form) and reliable GC methods are available for estimating many pure polymer properties and phase equilibria of polymer solutions such as densities, solubility parameters, glass and melting temperatures, and solvent activity coefficients. 

The scattered intensity of light due to concentration flucmations, extrapolated to zero-scattering angle, is inversely proportional to the second derivative of AG . Thus, it can be used to determine the location of a spinodal, i.e., the spinodal temperature, T for the given mixmre. As Eq. 2.32 indicates, LS makes it possible to determine also the second virial coefficient (A2) and from it the binary interaction parameter ix )- However, this technique is applicable only to homogenous systems, i.e., at temperatures T for those having UCST. As mentioned in Sect. 2.S.2.2, the LS methods has been used primarily to study the phase equilibria of polymer solutions. 

Liquid-Liquid Phase Equilibria of Polymer Solutions... 

High-pressure fluid-phase equilibria can only be modeled using equations of state. However, the equation of state models contain adjustable binary interaction parameters that have to be fitted to data. Small variations in these parameters in general have a large influence on the predicted phase equilibria. The most promising models for high-pressure phase equilibria of polymer solutions are the SAFT and the PC-SAFT ones. 

In this section the theory of phase equilibria of polymer solutions is discussed as it is a simple practical illustration of the Flory-Huggins theory and can be extended to explain the principles behind the fractionation techniques which are used with polymer solutions. Finally the technique of gel-permeation chromatography, which is now widely used in polymer laboratories, is described in detail. 

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... 

Sorensen, E. L., Phase Equilibria for Polymer Solutions, M.S. Thesis, Technical University of Denmark, (1988). 

Many properties of pure polymers (and of polymer solutions) can be estimated with group contributions (GC). Examples of properties for which (GC) methods have been developed are the density, the solubility parameter, the melting and glass transition temperatures, as well as the surface tension. Phase equilibria for polymer solutions and blends can also be estimated with GC methods, as we discuss in Section 16.4 and 16.5. Here we review the GC principle, and in the following sections we discuss estimation methods for the density and the solubility parameter. These two properties are relevant for many thermodynamic models used for polymers, e.g., the Hansen and Flory-Hug-gins models discussed in Section 16.3 and the free-volume activity coefficient models discussed in Section 16.4. 

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. 

Phase Behavior of Polymer Systems in High Pressure Fluids The basic description and definitions of the different phenomena associated with phase equilibria in polymer solutions are described in Section 25.2.5. Topics such as construction and interpretation of binary... 

EHR Ehrlich, P. and Kurpen, J.J., Phase equilibria of polymer-solvent systems at high pressiue near their critical loci, polyethylene with n-alkanes, J. Polym. Sci. Part A, 1, 3217, 1963. 1965ALL Allen, G. and Baker, C.H., Lower critical solution phenomena in polymer-solvent systems,... 

Since polymers have no vapor pressure and as a consequence the vapor phase does not contain polymer, the equilibrium conditions for low-pressure vapor-Uquid equilibria of polymer solutions as given by Eq. (20) are only applicable to the solvent s as in Eq. (24), or in a case where the weight fraction of polymer is used as a composition variable as in Eq. (25), where f2s is the weight fraction based activity coefficient of the solvent. 

In this section are briefly reviewed some technical problems of the simulation of dense many-chain systems, such as the sampling of intensive variables such as chemical potential, pressure etc., but also entropy, which are not straightforward to obtain as averages of simple quantities. Some of the standard recipes developed for computer simulation of condensed phases in general have difficulties here, due to the fact that the primary unit, the polymer chain, is already a large object and not a point particle. But knowledge of quantities such as the chemical potentials are necessary, e.g., for a study of phase equilibria in polymer solutions. ... 

Unfortunately these refinements do not lead to significant improvements in the agreement between the theory and experimental observations, but even so the Flory-Huggins theory can be applied with some success to studies of phase equilibria in polymer solutions and it goes some way towards explaining other phenomena. 

Chen, C.-C.., 1993, A Segment Based Local Composition Model for the Gibbs Energy of Polymer solutions. Fluid Phase Equilibria, 83, 301. 

Figure 11 shows the phase boundary concentration data for aqueous Na salt xanthan [78], fd-virus [24], and TMV [23] with added salt. In all these systems, Ci and cA are very low at low added salt concentration Cs or ionic strength I, and increase with Cs or I. Since such low phase boundary concentrations are not usually observed for neutral liquid-crystalline polymer solutions, it is apparent that polyion electrostatic interactions play an important role in the phase equilibria of these systems. 

Kamide K, In Thermodynamics of Polymer Solutions. Phase Equilibria and Critical Phenomena, Jenkins AD (ed.), Elsevier, Amsterdam, 1990. 

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. 

Chapter 4 describes the polymer data bases. This chapter is organized into sections discussing the experimental methods available for measuring the thermodynamic data of polymer solutions with an overview of the advantages and disadvantages of each method. The next section, Data Reduction Methods, describes how the experimental measurements from these experiments can be used to calculate the activity coefficients that are necessary for phase equilibria calculations. Finally, a summary of all the systems that are available on the data diskettes is provided. A user can scan this section or use the computer program POLYDATA to find if data are available for a particular system. 

Data are available for equilibrium pressure-volume-temperature of pure polymer liquids, solvent activity coefficients at infinite dilution, solvent activity coefficients at finite concentrations, and liquid-liquid phase equilibria of binary and ternary polymer solutions. 

Conio, G. Corazza, P. Bianchi, E. Tealdi, A. Ciferri, A. Phase equilibria of cellulose in N,N-dimethylacetamide/lithium chloride solutions. J. Polym. Sci. Polym. Lett. 1984, 22 (5), 273-277. 

The correlation and prediction of phase equilibria of solutions containing polar and hydrogen bonding solvents and polymers... 

Zhong, C. et al.. Improvement of predictive accuracy of the UNIEAC model for VLE of polymer solutions, Eluid Phase Equilibria, 123, 97, 1996. 

Zhong, C. and Masuoka, H., A new mixing rule for cubic equations of state and its application to vapor-liqnid eqnUibria of polymer solutions. Fluid Phase Equilibria, 123, 59, 1996. 

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