Polymer solutions, theories

To recapitulate, the Flory version of the Prigogine free-volume or corresponding-states polymer solution theory requires three pure-component parameters (p, v, T ) for each component of the solution and one binary parameter (p ) for each pair of components. 

Many further developments can be expected in the use of corresponding-states polymer solution theory in engineering practice. However, the reliability and versatility of this method is now well demonstrated for engineering use. 

A summary of the results obtained from GPC/DV on the first day and the third day after solution preparation is shown in Table II. For Red Oak and RO PO, the number average molecular weight decreased by approximately 6% from the first day to the third day. However, the intrinsic viscosities increased. According to traditional polymer solution theory (42), the product of intrinsic viscosity and molecular weight yields the hydrodynamic volume specifically, it has been shown that the molecular weight that... 

In so doing, we shall not discuss the possible biophysical significance of some of the data and considerations presented below. Instead, emphasis will be put on the illustration of experimental results of primary interest from the viewpoint of polymer solution theory and on the existing possibilities for their molecular interpretation. It is hoped that this review will draw attention to the new aspects one encounters in solution studies of nonrandomly coiled macromolecules. 

The major theories developed to predict phase separation and biomolecule partitioning in aqueous two-phase systems are mostly extensions of the widely known polymer solution theories of Flory and Huggins and the osmotic virial expansion. 

Ploehn and Russel s (1988) SCF, clearly show different characteristics for the adsorbed layer. Further progress depends on the evolution of accurate polymer solution theories as well as more extensive comparisons of solution and adsorption data with theoretical predictions. 

To address the hmitations of ancestral polymer solution theories, recent work has studied specific molecular models - the tangent hard-sphere chain model of a polymer molecule - in high detail, and has developed a generalized Rory theory (Dickman and Hall (1986) Yethiraj and Hall, 1991). The justification for this simplification is the van der Waals model of solution thermodynamics, see Section 4.1, p. 61 attractive interactions that stabilize the liquid at low pressure are considered to have weak structural effects, and are included finally at the level of first-order perturbation theory. The packing problems remaining are attacked on the basis of a hard-core model reference system. 

In polymer science, the ideal form of the thermodynamic equations is preserved and the nonideality of polymer solutions is incorporated in the virial coefficients. At low concentrations, the effects of the cl terms in any of the equations will be very small, and the data are expected to be linear with intercepts which yield values of and slopes which arc measures of the second virial coefficient of the polymer solution. Theories of poly mer solutions can be judged by their success in predicting nonideality. This means predictions of second virial coefficients in practice, because this is the coefficient that can be measured most accurately. Note in this connection that the intercept of a straight line can usually be determined with more accuracy than the slope. Thus many experiments which are accurate enough for reasonable average molecular weights do not yield reliable virial coefficients. Many more data points and much more care is needed if the experiment is intended to produce a reliable slope and consequent measure of the second virial coefficient. 

Corresponding reduced potentials for an isotropic phase are the familiar expressions from polymer solution theory ... 

As we have mentioned before, the theory of polymer solutions has started with the lattice modek The abnormal properties of high pol3uner solutions were attributed after all to the big difference in sizes of solvent and solute polymer molecules. They may te understood by comparing the results of the zeroth order approximate polymer solution theory with those of regular solution theory. Pol5nner solutions are characterized by the volume concentrations [Pg.246]

Kurata, M. Some recent aspects in polymer solution theory. Pure Appl. Chem. 12, 587 (1966). 

Applications of polymer solution theory to the studies of the dissolution of humic acids and of their extraction from soils suffer most because interactions betvi een each pair of components must be known (criterion 4, p. 343). Unfractionated humic and fulvic acids and humic substances in the soil are parts of multicomponent systems, and interactions between the different components are unknown. 

The closest approach to successful applications of polymer solution theory to humic substances was made by Chiou et al. (1983) when studying the binding of small organic chemicals by soils. They considered the soil sorbent substances to be amorphous macromolecular humic substances, and they adapted the Flory-Huggins theory to a study of the sorbate species solubilized in the amorphous macromolecules. 

In the above considerations, the hydrophobic portions of both the membrane polymer and the small molecules that enter the membrane are expected to interact in the hydrophobic microphases in the membrane. It therefore becomes useful to find a numerical measure of the miscibility of these hydrophobic portions of molecules. In the case of complete molecules, both small and polymeric, the solubility parameter concept has been useful in the past. This concept is related to the enthalpy change which occurs on mixing in regular solution theory as developed by Hildebrand and coworkers (10) and as used for polymer solution theory by Flory (11). The Hildebrand solubility parameter is a measure of the attraction between molecules of the same kind, including dispersion forces, polar forces, and hydrogen bonding... 

In dilute solutions using a solvent system good for all blocks, there is little intermolecular interaction, and the behavior of block polymers approaches that of homopolymers or random copolymers. Conventional dilute polymer solution theory may be applied with moderate success, as in osmometry and viscoraetry, provided that the block composition is taken into account. Some complicating features may arise because of the possibility of intramolecular block separation, for example, prevention of a random coil configuration, which is usually assumed in some conventional treatments (87). 

A rough rule of thumb in polymer solution theory is... 

More recent polymer solution theories (41, 42) recognize the importance of the free volume dissimilarity of the solute and polymer. This effect, first introduced in theories of solution by Prigogine and collaborators (43), has important thermodynamic consequences. Flory and collaborators (42) now suggest that (In ax )n0ncomb be composed of two terms, an equation of state and a contact interaction contribution. The newly defined parameter, denoted x. becomes... 

The mixing effects described above are readily interpreted in terms of polymer solution theory, and apply when the separation between the approaching surfaces is alrout one to two adsorbed layer thicknesses. At closer approach is it likely that both mixing and elastic compression occurs. The following equation was derived by Napper for the free energy of the interaction involving both effects ... 

The role of asphaltene deposition in miscible flooding processes is also examined. Experimental data together with coupled equation of state models and Flory-Huggins polymer solution theory have been used to illustrate the effect of various parameters such as solvent type, solvent/oll ratio and pressure on the amount of asphaltene precipitation during addition of solvents to heavy oil. 

Asphaltenes in crude oil are large, bulky molecules which behave like polymer molecules. Thus, liquid-liquid polymer solution theories are used to... 

In order to apply Flory-Huggins polymer solution theory to asphaltene-crude oil solutions, it is necessary to treat the crude as a mixture of two liquid phases, the first phase is pure asphaltene liquid phase which acts as a solute and the second phase as the remaining components of crude oil which acts as a solvent phase. 

A thermodynamic model based on Flory-Huggins polymer-solution theory was developed and coupled with Equation of State model to predict the amount of asphaltene precipitation. The model prediction shows close agreement with the experimental data after regression of asphaltene properties such as molar volume, solubility parameter and molecular weight. The model, however, fails to account for the effect of large changes in the solubility parameters of the oil-solvent mixtures. 

In practice, AX/c is plotted against the concentration of the polymer solutions used and this plot extrapolated to c O to give an intercept of 1 /M . The slope of these plots relates to deviations from ideal behaviour but no explicit significance can be attached to the magnitude of A in relation to polymer solution theories. 

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