Solubility Behavior of Polymers

If we denote the force of attraction between the molecules of one material A by Faa, that between the molecules of another material B by Fbb, and represent that between one A and one B molecule as Fab, then the system will be compatible and a solution will result if Fab Fbb and Fab Faa- On the other hand, if Faa or Fbb Fab, the system will be incompatible and the molecules will separate, forming two phases. In the absence of any specific interaction (e.g., hydrogen 

A measure of the intermolecular attraction forces in a material is provided by the cohesive energy. Approximately, this equals the heat of vaporization (for liquids) or sublimation (for solids) per mol. The cohesive energy density in the liquid state is thus AEyfV, in which AE-o is the molar energy of vaporization and V is the molar volume of the liquid. The square root of this cohesive energy density is known as the solubility parameter (d), that is, 

If the vapor behaves approximately like an ideal gas, Eq. (3.108) can be written as 

Problem 3.15 Calculate an estimate of the solubility parameter for water at 25°C from its heat of vaporization at the same temperature, given by 

Hildebrand (Hildebrand et al, 1970) first used the solubility parameter approach for calculating estimates of the enthalpy of mixing, AHmix, for mixtures of liquids. The equation employed (for derivation see Appendix 3.1) is 

A necessary reqnirement for solution and blending compatibility is a negative or zero Gibbs free energy change (AGmix) when the solution or blend components are mixed, that is, 

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Since most methods of molecular characterization involve analysis of polymers in dilute solution, it is advantageous to introduce the relevant theories for polymers in solution before considering the individual methods of determination of molecular weight. Chapter 3 therefore deals with thermodynamics of polymer solutions and also considers the swelling and solubility behavior of polymers. 

Phase separation is frequently observed in polymer solutions and it is mainly due to their low entropy of mixing. At a state of equilibrium each species of the mixture is partitioned between two phases, namely, the supernatant (extremely dilute) and precipitated (moderately dilute) phases [78]. Theoretical models and experimental techniques have been developed to predict the solubility behavior of polymer solutions, polymer blends, and other related systems [79, 80]. Simple theories only permit a rather qualitative description of this phenomenon [78]. Refined and improved theoretical and semiempirical models allow a more accurate prediction of the demixing phenomena and related thermodynamic properties [57, 81]. 

The advantage of the activated displacement polymerization is the facile incorporation of different and unconventional structural units in the polymer backbone. Most of the heteroarylene activated polyethers prepared by this route are soluble in many organic solvents. The solubility behavior of new polyethers is shown in Table 8. In contrast to many polyphenylenequi-noxalines, poly(aryl ether phenylquinoxalines) prepared by the quionoxaline activated displacement reaction are soluble in NMP. Solubility in NMP is important since it is frequently used for polymer processing in the microelectronics industry [27]. 

Charlesby, A. and Pinner, S. H., "Analysis of the Solubility Behavior of Irradiated Polyethylene and Other Polymers", Proc. R. Soc., 1959, A249, 367-386. 

Solvent viscosity vs, concentration plots for cellulose dissolved in TFA-CH2CI2 (70/30, v/v) do not exhibit a maximum (1I,S1) in contrast to the typicid behavior of polymer liquid crystal solutions. This same behavior is exhibited by other cellulose-solvent systems (52,fiQ). Conio et al. (59) si gest that due to the close proximity of the cholesteric mesophase to its solubility limit, it is only observed in a metastable condition. 

Koros, W. J. (1985). Simplified analysis of gas/polymer selective solubility behavior, J. Polym. Sci. Polym. Phys. Ed. 23, 1611. 

We have described the phase behavior of polymer-solvent-cosolvent mixtures where the cosolvent generally increases the solubility of the polymer... 

Tager, A. A. Kolmakova, L. K. Solubility parameter, its evaluation methods, connection with polymers solubility. High-Molecular Compounds. A, 1980, 22(3), 483 96. Lee, H. -R. Lee, Y. -D. Solubility behavior of an organic soluble polyimide. J. Appl. 

As will be evident from the examples cited below, the S-S theory for multicomponent systems has been successful in describing thermodynamics (e.g., phase equilibria, CED, solubility) and PVT behavior of polymer mixtures with gases, liquids, or solids. For binary systems, Eqs. (6.49) and (6.51) might be written as... 

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