Multicomponent polymer solutions

Koningsveld, R. Staverman, A. J., "Liquid-Liquid Phase Separation in Multicomponent Polymer Solutions. I. Statement of the Problem and Description of Methods of Calculation," J. Polym. Sci., Part A-2, 6, 305 (1968). 

Koningsveld, R. Chermin, H. A. G. Gordon, M., "Liquid-Liquid Phase Separation in Multicomponent Polymer Solutions. VIII. Stability Limits and Consolute States in Quasi-Ternary Mixtures," Proc. Roy. Soc., Ser. A, 319, 331 (1970). 

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. 

Other multicomponent polymer solutions of interest consist of chemically different polymers dissolved in a solvent or a single polymer in a mixture of different solvents. Their phase equilibrium behavior is important in relation to many practical problems, but it is much more complex and difficult to tinalyze and predict than that of quasi-binary systems. 

Multi-phase equilibria reflect very sensitively the dependence of AG on its variables. Precise data on them, especially those on the phase compositions, therefore, should be useful for strict testing of any proposed expressions for AG of multicomponent solutions. It is clear now that whatever approach may be used, it cannot be self-contained unless taking into account the dependence of g (or the corresponding factors) on /(P) in the concentrated regime as well as in the dilute one. However, this fact does not seem to be well recognized by current workers who are interested in the phase equilibrium of multicomponent polymer solutions. 

Koningsveld, R. Phase relationships and fractionation in multicomponent polymer solutions. Pure Appl. Chem. 20, 271 (1969). 

Koningsveld.R., Kteintjens,L.A., Shultz, A. R. Liquid-liquid phase separation in multicomponent polymer solutions. IX. Concentration-depe ent pair interaction parameter from critical miscibility data on the system polystyrene-cyclohexane. J. Polymer Sd. A 2,8,1261 (1970). 

Koningsveld R (1967) On Liquid-Liquid Phase Relationships and Fractionation in Multicomponent Polymer Solutions. Thesis, Leiden Univ. 

For the calculation of the stability of a multicomponent polymer solution (spinodal line and critical solution points), the stability theory can be applied [42]. One possible consequence of the poiydispersity, especially if the distribution function is bimodal, is the appearance of tri-critical solution points [2]. Suggestions for the phase equilibrium calculations of such systems can be found in the literature [2, 39, 43). 

Koningsveld Staverman, 1968, hquid-liquid phase separation in multicomponent polymer solutions. 2. critical state,/. Polym. Set, Part A, Vol. 6, No. 2, PP. 325-347 Konowalow, 1903, The critical area of solutions and the appearance of opalescence, Ann. Physik., Vol. 10, No. 2, PP. 360-392... 

K03 Koningsveld, R. and Staverman, A.J., Liquid-liqnid phase separation in multicomponent polymer solutions IV. Coexistence cnrves, Kolloid-Z. Z. Polym., 218, 114,... 

RE1 Rehage, G. and Koningsveld, R., Liquid-liquid phase separation in multicomponent polymer solutions VI. Some errors introduced by the binary approximation, J. Polym. Sci., Polym. Lett, 6, 421, 1968. 

GOR Gordon, M., Chermin, H.A.G., and Koningsveld, R., Liquid-liquid phase seapration in multicomponent polymer solutions. VII. Relations for the spinodal and critical loci. Macromolecules, 2, 207, 1969. 

BOR Borchard, W. and Rehage, G., Critical phenomena in multicomponent polymer solutions, Chem. Ser., 99, 42, 1971. 

J. R. Krahn and T. P. Lodge. Spatial heterogeneity of solvent dynamics in multicomponent polymer solutions. J. Phys. Chem., 99 (1995), 8338-8348. 

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