Dilute Polymer Solutions Definitions

In this section we will define several quantities which are convenient for the discussion of the viscoelasticity of dilute polymer solutions. As mentioned above, the two quantities G and G — o)t s related to the complex modulus as functions of to, are the measurable quantities. In order to make comparisons with theory, one has to extrapolate these quantities to infinite dilution, i.e., 

In terms of existing molecular theories, the longest relaxation time is related to the viscosity as follows, 

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Definitions of Terms Relating to Individual Macromolecules, Their Assemblies, and Dilute Polymer Solutions... 

Definitions of terms relating to individual macromolecules, their assemblies, and dilute polymer solutions (lUPAC Recommendations 1988), PureAppl. Chem. 61, 211-241 (1989). Reprinted as Chapter 3, this edition. 

The set of constitutive equations for the dilute polymer solution consists of the definition of the stress tensor (6.16), which is expressed in terms of the second-order moments of co-ordinates, and the set of relaxation equations (2.39) for the moments. The usage of a special notation for the ratio, namely... 

For dilute polymer solutions the following definitions are well known... 

Rudin and Strathdee (1974) remarked that the equations presented for the viscosity of dilute polymer solutions were valid approximately up to the critical concentration. This leads to a more general definition of a concentrated polymer solution, viz. a solution for which c > ccr. 

The relaxation spectrum may include a term corresponding to x = 0. This may be expressed as t) on the first line of Eq. (1.10) and gives rise to an additional term icot] x in Eq. (1.11). Ordinary solvents, usually of low molecular weights, are Newtonian fluids which have only one mechanism corresponding to t = 0 with rj m = t]s, where % is the viscosity. It is customary to describe the viscoelastic behavior of dilute polymer solutions with G ((o) — icoris instead of G (w) This corresponds to the exclusion of a term tjs d (t) from the definition of H (t) which is assumed to be the contribution of the solvent with viscosity ris. 

Definitions of terms relating to individual macromolecules, their assemblies, and dilute polymer solutions... 

The subject of this chapter represents one of the most diverse areas in soft matter science. Colloidal materials are systems in which small droplets or particles of one material are dispersed in a continuous phase of another material. This definition is deliberately broad as colloidal systems span an extremely wide range of materials, from solid particles suspended in aqueous solution, to droplets of moisture in the air, and foams, and can even be extended to include granular materials like sand. Colloidal science is a subject that is particularly relevant in our everyday lives because it plays an important role in the manufacture of numerous everyday substances. Many of the foods we eat can be described as colloids. Creamy foods, like mayonnaise, sauces, or ice cream, contain tiny droplets of fat dispersed in an aqueous medium food can be foams (liked whipped cream), and it can be a solid sponge (like bread or cake). Personal care products like face creams and toothpastes are colloidal systems, as are household paints and inks. Even the dilute polymer solutions discussed in Chapter 4 can be considered colloids. 

Figure 7.10 Radius of gyration (Rg) - definition, examples and typical values. Radii of gyration can be experimentally obtained from light scattering measurements of dilute polymer solutions. Polymer molecules dissolved in good solvents have a much greater Rg than they would In the dry state...

Intrinsic viscosity (rj) is the viscosity of an infinitely diluted polymer solution. It is a measure of the hydrodynamic volume occupied by a macromolecule, which is closely related to the size and conformation of the chain, but is independent of concentration of macromolecule. In dilute solutions, by definition, the polymer chains are separated and there is negligible interaction between them. Therefore, the (rj) of polymer in solution depends only on the dimension and the molecular weight of polymer chain. Experimentally determined values of the relative and specific polymer viscosities were used to calculate it, according to Huggins [53] and Kraemer [64] equations given by... 

The formulation of the hydrodynamic constant theta and the definition of the Theta Point, where excluded volume effects are neutrahzed. These results were particularly important, because they allow a rational interpretation of physical measurements of dilute polymer solutions. 

Since this chapter is concerned with block copolymers in dilute solution, it is useful to include a definition of the dilute regime for polymer solutions in the Introduction. This regime extends up to a volume fraction above which swollen coils overlap (de Gennes 1979) ... 

It is difficult to give an exact definition of the terms "dilute" and "concentrated". Usually there is a gradual transition from the behaviour of dilute to that of concentrated solutions, and the concentration range of this transition depends on a number of parameters. As a rule of thumb, however, a polymer solution maybe called concentrated if the solute concentration exceeds 5% by weight. 

It was concluded that definition of asphaltenes based only on solubility is not a satisfactory criterion and that the behavior of asphaltenes in chromatographic separations is incompatible with such structures where the polymer units are interconnected predominantly by a-bonds. The asphaltenes are a complex state of aggregation best represented by the stacked cluster structure (micelle), which, however, cannot explain some of the GPC behavior of very dilute asphaltene solutions. 

Any formal definition of a gel has been avoided, because its formulation would be difficult on the basis of external properties. By any criterion, a 1 % aqueous solution of agar does form a gel when it is cooled from 95 to 20°, whereas a 1 % solution of sucrose does not but properties may be so continuous between these extremes that any dividing line would be arbitrary. Most of this Chapter is concerned with fairly permanent network structures formed from polymer solutions. As a definition of gels, this description is incomplete. Some cellulose gels, and pastes of gelatinized, starch granules, would be excluded, because they are formed by limited dispersion of solids. In other words, an arbitrary choice will be made to focus on those gels that are dilute with respect to polymer, because the information available about them at the molecular level is more precise than for others. 

Klein (1980 1982) has performed the most definitive experiments to date on the distance dependence of the steric interactions of polymer coated macroscopic surfaces. Monodisperse polystyrene, of molecular weight 1 x 10 or 6 X 10 , was adsorbed onto the mica plates by incubation of the plates with a very dilute solution (ca 7 x 10 g dm ) of the polymer in cyclohexane at 24 C. The polymer solution (save for ca 1 cm between the plates) was then replaced by pure cyclohexane. 

Definition of terms relating to individual macromolecules, their assemblies, and dilute solution.This document includes the recommended definitions for molecular weight, molecular weight averages, distribution functions, radius of gyration, end-to-end-distance vector, the Flory-Huggins-Staverman theory, solution viscosity, scattering of radiation by polymers and polymer solutions, fractionation, separation techniques, and so on. The document on dispersity is an important extension of this recommendation. 

Adsorption equilibria for polymers out of concentrated solutions as function of concentration frequently exhibit very pronounced maxima (Fig. 12). These unusual curves can be accounted for if one assumes that the adsorbed species are in aggregation equilibrium in the solution, depending upon the amount of surface area per unit volume of solution. Hence one expects that the adsorption equilibrium out of concentrated polymer solution may not only be approached with "infinite slowness but is also a function of the system characteristics, and the definition of reproducible conditions contains many more variables than one is used to from the more common work with dilute solution. This complexity is particularly awkward when one deals with the important case of competitive adsorption of polymers out of concentrated multicomponent solutions, a common phenomenon in many industrial processes, such as paint adhesion, corrosion prevention, lubrication, especially wear prevention, etc. 

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