Polymer solutions concentration regimes

This correlation is illustrated in Table I, which shows the fluorescence lifetime and frequency shift for the excimer excitation spectrum relative to that of the free solution. The first six values correspond to different polymer solution concentrations ranging from [Py-PEG-Py(8650)] = I x 10" to 4 X 10 M with added untagged PEG(22,000) of 0 and I x I0 M. In this regime, the tagged chains remain on the silica particle surfaces. All these... 

Another remarkable fact known experimentally is that D tends to merge with Dc as the solution approaches and enters the semi-dilute regime. This fact explains why QELS has recently replaced the time-consuming gradient method for routine D measurements on polymer solutions, concentrated as well as dilute. However, as far as the author is aware, no theoretical answer is given as yet to the important question of why D becomes indistinguishable from Dc as the solution crosses over the overlap concentration. This frustrating situation exemplifies our... 

For semi-dilute solutions, two regimes with different slopes are similarly obtained the powers of M, however, can be lower than 1.0 and 3.4. Furthermore, the transition region from the lower to the higher slope is broadened. The critical molar mass, Mc, for polymer solutions is found to be dependent on concentration (decreasing as c increases), although in some cases the variation appears to be very small [60,63]. 

Fig. 59. Incomplete screening of hydrodynamic interactions in semi-dilute polymer solutions. Presentation of different regimes which are passed with increasing concentration. A,C Unscreened and screened Zimm relaxation, respectively, B enhanced Rouse relaxation. (Reprinted with permission from [12]. Copyright 1987 Vieweg and Sohn Verlagsgemeinschaft, Wiesbaden)...

Fd h = 0) should increase as when the chain concentration increases. A very different picture is predicted in the case of adsorbing polymers [49]. The layer of adsorbed chains may be partially interpenetrated by free chains in the bulk and therefore the range and strength of the attraction are not determined by the solution concentration. Instead, they are rather sensitive to the coverage and thickness of the adsorbed chains which depend essentially on the solvent quality and on the mean chain length in the dilute regime. 

Here, A is the depletion layer thickness (assumed equal to the radius of gyration of the polymer, RG). H = r - 2a is the surface-to-surface particle separation, V ° is the molar volume of the solvent, and ji and ji are the solvent chemical potentials for the polymer solution and the pure solvent. It appears that the assumption A = RG is generally acceptable providing that the polymer solution is in the dilute concentration regime. At higher polymer concentrations, however, the value of A is reduced according to the relationship (Vincent, 1990) ... 

Summary The classical treatment of the physicochemical behavior of polymers is presented in such a way that the chapter will meet the requirements of a beginner in the study of polymeric systems in solution. This chapter is an introduction to the classical conformational and thermodynamic analysis of polymeric solutions where the different theories that describe these behaviors of polymers are analyzed. Owing to the importance of the basic knowledge of the solution properties of polymers, the description of the conformational and thermodynamic behavior of polymers is presented in a classical way. The basic concepts like theta condition, excluded volume, good and poor solvents, critical phenomena, concentration regime, cosolvent effect of polymers in binary solvents, preferential adsorption are analyzed in an intelligible way. The thermodynamic theory of association equilibria which is capable to describe quantitatively the preferential adsorption of polymers by polar binary solvents is also analyzed. 

Figure 5.3. Illustration of the five stable regimes (ideal dilute, swollen dilute, semi-dilute, marginal, and concentrated) and the phase separation region (hatched) for polymer solutions. The dependencies of the various cross-overs on N, p, and v are indicated.

The relative viscosities of polymer solutions are measured at different concentrations and a plot of the reduced viscosity versus concentration is made, in order to extrapolate to zero concentration. The concentration dependence of the viscosity of polymer solutions, in the dilute regime, may be expressed by several linear equations. For practical extrapolation to zero concentration, the most commonly employed are the Huggins equation ... 

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