Polymer solution theory, application

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. 

Although the remainder of this contribution will discuss suspensions only, much of the theory and experimental approaches are applicable to emulsions as well (see [2] for a review). Some other colloidal systems are treated elsewhere in this volume. Polymer solutions are an important class—see section C2.1. For surfactant micelles, see section C2.3. The special properties of certain particles at the lower end of the colloidal size range are discussed in section C2.17. 

To illustrate the application of corresponding-states theory to polymer solution calculations, we consider two cases of sol-vent/polymer vapor-liquid equilibria. The first case we consider is that of the chloroform/polystyrene solution. The second is that of benzene/polyethylene oxide. 

Gee and Orr have pointed out that the deviations from theory of the heat of dilution and of the entropy of dilution are to some extent mutually compensating. Hence the theoretical expression for the free energy affords a considerably better working approximation than either Eq. (29) for the heat of dilution or Eq. (28) for the configurational entropy of dilution. One must not overlook the fact that, in spite of its shortcomings, the theory as given here is a vast improvement over classical ideal solution theory in applications to polymer solutions. 

The viscosity of polymer solutions has been considered theoretically by Flory,130 but although this theory has been applied to cellulose esters,131 no applications have yet been made in the case of the starch components. Theoretical predictions of the effect, on [17], of branching in a polymer molecule have been made,132 and this may be of importance with regard to the viscometric behavior of amylopectin. 

Although many thermodynamic theories for the description of polymer solutions are known, there is still no full understanding of these systems and quite often, one needs application of empirical rules and conclusions by analogy. As a rough guide, some solvents and non-solvents are indicated in Table 2.6 (Sect. 2.2.5) for various polymers. However, not all combinations of solvent and nonsolvent lead to efficient purification of a polymer via dissolution and reprecipitation, and trial experiments are required therefore. 

Maron, S. H., Nakajima, N. A theory of the thermodynamic behavior of non electrolyte solutions. II. Application to the system benzene-rubber. J. Polymer Sci. 40, 59-71... 

Mukherji, B., and W. Prins Applicability of polymer network theories to gels obtained by crosslinking a polymer in solution. J. Polymer Sci., Pt. A 2, 4367 (1964). 

Two theoretical approaches for calculating NMR chemical shift of polymers and its application to structural characterization have been described. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are in the calculation by combining quantum chemistry and statistical mechanics. This approach has been applied to polymer systems in the solution, amorphous and solid states. Another approach is to employ the tight-binding molecular orbital theory to describe the NMR chemical shift and electronic structure of infinite polymer chains with periodic structure. This approach has been applied to polymer systems in the solid state. These approaches have been successfully applied to structural characterization of polymers... 

There already exists a substantial literature devoted to the estimation of various material properties with the help of additive structual increments (Reid et. al, 1987, Van Krevelen, 1990). The regular solution theory in combination with additive structural increments has a wide application for estimating the relative solubilities of organic substances in polymers and the solubility of polymers in various solvents (Barton, 1983) and will be described later in this chapter. When estimating partition coefficient values, one is quickly confronted with this method s application limits, particularly with polar and non-polar structures, for example the partitioning of substances between polyolefins and alcohol (Baner and Piringer, 1991). 

In this chapter we will mostly focus on the application of molecular dynamics simulation technique to understand solvation process in polymers. The organization of this chapter is as follow. In the first few sections the thermodynamics and statistical mechanics of solvation are introduced. In this regards, Flory s theory of polymer solutions has been compared with the classical solution methods for interpretation of experimental data. Very dilute solution of gases in polymers and the methods of calculation of chemical potentials, and hence calculation of Henry s law constants and sorption isotherms of gases in polymers are discussed in Section 11.6.1. The solution of polymers in solvents, solvent effect on equilibrium and dynamics of polymer-size change in solutions, and the solvation structures are described, with the main emphasis on molecular dynamics simulation method to obtain understanding of solvation of nonpolar polymers in nonpolar solvents and that of polar polymers in polar solvents, in Section 11.6.2. Finally, the dynamics of solvation with a short review of the experimental, theoretical, and simulation methods are explained in Section 11.7. 

Chemical process rate equations involve the quantity related to concentration fluctuations as a kinetic parameter called chemical relaxation. The stochastic theory of chemical kinetics investigates concentration fluctuations (Malyshev, 2005). For diffusion of polymers, flows through porous media, and the description liquid helium, Fick s and Fourier s laws are generally not applicable, since these laws are based on linear flow-force relations. A general formalism with the aim to go beyond the linear flow-force relations is the extended nonequilibrium thermodynamics. Polymer solutions are highly relevant systems for analyses beyond the local equilibrium theory. 

Regular solution theory, the solubility parameter, and the three-dimensional solubility parameters are commonly used in the paints and coatings industry to predict the miscibility of pigments and solvents in polymers. In some applications quantitative predictions have been obtained. Generally, however, the results are only qualitative since entropic effects are not considered, and it is clear that entropic effects are extremely important in polymer solutions. Because of their limited usefulness, a method using solubility parameters is not given in this Handbook. Nevertheless, this approach is still of some use since solubility parameters are reported for a number of groups that are not treated by the more sophisticated models. 

The application of McMillan-Mayer theory to high polymer solutions was first made by B. H. ZiMM. J. Chem. Phys. 14, 104 (1946). 

A brief review is presented of the theories describing transport processes in binary solutions of an amorphous, uncross-linked polymer and low molecular weight solutes. At present, there exists no theory capable of describing diffusion in polymer-solute systems over the entire concentration range. No general theory has been formulated to describe diffusional transport under conditions where viscoelastic effects are important. However, methods have been developed to anticipate conditions under which anomalous effects can be expected (2-2). This brief review is limited to the theories applicable for concentrated polymer solutions under conditions where the classical diffusion theory holds. 

The SAFT equation of state was proposed by Radosz, Gubbins, Jackson, and Chapman and is a model derived based on the perturbation theory of Weirtheim. SAFT is a noncubic equation with separate terms for the various effects (dispersion, polar, chain, hydrogen bonding). SAFT has already found extensive application in both polymer and oil industry, where different capabilities of the model have been exploited. In the oil industry, it is used for describing the complex multiphase equilibria of hydrogen bonding multicomponent systems, e.g., water-oil-alcohols (glycols). Several recent reviews of the SAFT equation of state are available, all of which present results for polymer solutions. 

Qian, C., Mumby, S.J., and Eichinger, B.E., Application of the theory of phase diagrams to binary polymer solutions and blends, Polym. Preprints, 31, 621, 1990. 

It will be observed even for the limited data in Table 3.1 that entropies of dilution (as indicated by ip) are highly variable from one polymer-solvent system to another and from one solvent to another for the same polymer depending on the geometrical character of the solvent. This is contrary to the theory developed from consideration of lattice arrangements according to which Ip should be approximately and nearly independent of the system. It may be noted that theories of polymer solutions fail to take into account the specific geometrical character of the solvent in relation to the polymer segment. This is a serious deficiency which must be borne in mind in applications of these theories. 

Various theories have been proposed which take into account the effects of aggregation on the viscosities of polymer solutions (2). These theories generally require a detailed knowledge of the mechanism and energetics of association. Further, they are considered applicable only to moderately concentrated solutions. 

---