Polymer solution theory solubility characterization

The great advantage of the solubility parameter model is in its simplicity, convenience, and predictive ability. The stability of polymer mixtures can be predicted from a knowledge of the solubility parameters and hydrogen-bonding tendencies of the components. The predictions are not always very accurate, however, because the model is so oversimplified. Some examples have been given in the preceding section. More sophisticated solution theories are not predictive. They contain parameters that can only be determined by analysis of particular mixtures, and it is not possible to characterize individual components a priori. The solubility parameter scheme is therefore the model that is most often applied in practice. 

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. 

The thermodynamic behavior of fluids near critical points is drastically different from the critical behavior implied by classical equations of state. This difference is caused by long-range fluctuations of the order parameter associated with the critical phase transition. In one-component fluids near the vapor-liquid critical point the order parameter may be identified with the density or in incompressible liquid mixtures near the consolute point with the concentration. To account for the effects of the critical fluctuations in practice, a crossover theory has been developed to bridge the gap between nonclassical critical behavior asymptotically close to the critical point and classical behavior further away from the critical point. We shall demonstrate how this theory can be used to incorporate the effects of critical fluctuations into classical cubic equations of state like the van der Waals equation. Furthermore, we shall show how the crossover theory can be applied to represent the thermodynamic properties of one-component fluids as well as phase-equilibria properties of liquid mixtures including closed solubility loops. We shall also consider crossover critical phenomena in complex fluids, such as solutions of electrolytes and polymer solutions. When the structure of a complex fluid is characterized by a nanoscopic or mesoscopic length scale which is comparable to the size of the critical fluctuations, a specific sharp and even nonmonotonic crossover from classical behavior to asymptotic critical behavior is observed. In polymer solutions the crossover temperature corresponds to a state where the correlation length is equal to the radius of gyration of the polymer molecules. A... 

More fundamental treatments of polymer solubility go back to the lattice theory developed independently and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by %, the Flory-Huggins interaction parameter, which is related to solubility parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubility criterion is x A 0.5. 

As it has been shown above, a macromolecular coil in solution fractal dimension is defined by two groups of factors polymer-solvent interactions and macromolecular coil elements between themselves. As an approximation, the first from the indicated factors can be characterized by the difference of polymer 6 and solvent 6 solubility parameters A8= 6 6j [16]. As to the second group of factors, then a parameters number exists, influencing on value in some way chain rigidity, bulk side groups availability, hydrogen bond and so on. Since at present the strict theory of polymer regular solutions has not still developed, then analytical relationships... 

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