Semi-Dilute and Concentrated Polymer Solutions

Polymer-polymer interactions are neglected in the foregoing sections. This is justified for very dilute solutions. Because a polymer molecule contains mostly solvent in its coil, the molecules start to overlap at a relatively low concentration. At that concentration, the separation distances between the coils approach the dimensions of the coils themselves. A solution in which the polymer coils overlap is referred to as a nonconnected network. Taking 4/3( / g) as the coil volume, the concentration c (in mol monomer dm ), at which the nonconnected network starts to form is given by 

FIGURE 12.7 Polymer solutions, (a) dilute, (b) onset of a nonconnecting network, and (c) semi-dilute solution. The dashed circles in (a) and (b) indicate the size of the polymer molecules and in (c) the blob size. 

In a random walk conformation, the average segment density Pp g varies with whereas for a swollen coil, pp is proportional to At c the average segment concentration in solution equals that in an individual coil and, hence, Ce and c Ap° The formation of a nonconnected network is accompanied by sudden changes in physical-chemical properties of the system, for instance, an abrupt increase in the viscosity. 

At even higher concentrations, where the volume fractions of polymer and solvent are comparable, the size of the blob reduces to that of the length of a polymer segment Then, the conformation of the polymer chains can be described again by a random walk. Hence, concentrated polymer solutions (and polymer melts) are always at 0 conditions. 

---

Jamieson, A. M., Simha, R., Newtonian viscosity of dilute, semi-dilute and concentrated polymer solutions. Chapter 1, in Polymer Physics From Suspensions to Nanocomposites and Beyond, Utracki L. A. and Jamieson A. M., Editors, J. Wiley Sons, New York (2010). 

J. Klein, The onset of entangled behavior in semi-dilute and concentrated polymer solutions, Macromolecules 11(5), 852 (1978). 

These classical molecular theories may be used to illustrate good agreement with the experimental findings when describing the two extremes of concentration ideally dilute and concentrated polymer solutions (or polymer melts). However, when they are used in the semi-dilute range, they lead to unsatisfactory results. 

Dynamic scattering can also provide information about relaxation modes of polymers at higher values of the wavevector q ( 7 >1). Equation (8.164) can be generalized to higher wavevectors and to semi-dilute and concentrated solutions by noticing that the decay of the... 

The aim of the theories developed for polymer solutions has been to explain experimental observations such as deviations from Raoult s law and the molecular weight dependence of solubility at any given temperature. Indeed, it is necessary to account for the phase diagram for polymer solutions in general. The more recent theories deal with semi-dilute and concentrated solutions. No single theory currently explains ail the experimental observations for polymer solutions. Some of the more significant are [8-16] ... 

In a good solvent, c whereas in a theta solvent, c It is often more convenient to use the polymer volume fraction, 0, rather than concentration, because then for a polymer in the absence of solvent, 0 = 1. Using 0, two concentration regimes can be distinguished from the dilute regime. If the coils are overlapped, i.e. 0 > 0, where 0 is the overlap volume fraction, but there is still not much polymer in solution, 0 < 1, then the solution is said to be semi-dilute. However, if 0 > 0 and 0 1, the solution is concentrated. Polymer chains in dilute, semi-dilute and concentrated solutions are sketched in Fig. 2.13. 

Low temperature The polymer is in a good solution state and possesses the shape of an expanded coil. At low concentration, the polymer molecule has no contact with other molecules (single polymer chain). If the diluted solution is irradiated, radicals were produced and some polymer chains react. Molecules with high molecular weight, mostly branched, are formed (Quemer et al. 2004). Irradiation of a higher-concentrated polymer solution (semi-diluted polymer solution with concentration above the overlap concentration ), results in a homogeneous macroscopic (bulky) gel. 

Therefore, if N 1, there has to be a rather broad range of concentrations (p < (f) < 1 (c < c < l/v) in which the coils are heavily entangled (f) < (f>), yet there is still little polymer in the solution (j> < 1). This type of polymer solution is known as semi-dilute, and is shown in Figure 4.7 c. Really concentrated solution corresponds to 1, when the volume fractions of the polymer and the solvent are comparable (Figure 4.7... 

Summarizing, we may conclude that reported sedimentation and diffusion data on semi-dilute solutions do not always lend support to the predictions of the Brochard-de Gennes blob theory. Certainly, this theory oversimplifies the complex hydrodynamic interactions involved in many-chain systems. Nonetheless we should not underestimate its merit that has sparked off many sedimentation and diffusion measurements on concentrated polymer solutions in recent years. 

The log-normal distribution of correlation times can be used to fit the relaxation data from concentrated polymer solutions. The data provide reasonable variations of the mean correlation times with concentration and temperature. Of the systems studied, PIPA-di was found to reorient much more rapidly than either PEA-di or PNBA-di. Relatively low energies of activation were found for PIPA-di in semi-dilute solution. These energies of activation increased with concentration and were similar for all three polymers until the highest concentration where the apparent energies of activation scaled with the glass transition temperature of the bulk polymers. 

The dynamics of moderately concentrated and entangled polymer solutions has been widely investigated using various techniques, a review can be found in Ref. (33). The most important features of these semi-dilute solutions can be described within a model based on the repta-tion" idea (34). ... 

---