Viscosity stretched-exponential behavior

There are broader exceptions to simple stretched-exponential behavior. These exceptions serve to test the generalization that stretched-exponential behavior is donfinant. For electrophoresis, as discussed in Chapter 3, a transition to power-law behavior with increasing P and E appears to correspond to the onset of nonlinear transport in which /i depends on the applied field. For the low-shear viscosity, the solufionfike-meltlike transition is sometimes seen as discussed in Section 9.10 and Chapter 11, this transition occurs simultaneously with the appearance of a light... 

From limited results, s(c) of sedimenting probes in a polymer matrix generally follows a stretched exponential in c. With a small matrix polymer, s(c) of a probe chain simply tracks the solution viscosity. In solutions of large matrix polymers, s and rj do not show the same concentration dependence. With probe spheres, 5(c) may track the solution viscosity or may show re-entrant behavior. The agreement of 5(c) with a stretched-exponential form is less outstanding when re-entrance is observed. The literature describes too few probe polymer pairs to be able to say if re-entrant behavior is common or rare. 

Finally, Lin and Phillies examined 20.4,80,620, and 1500 nm radius carboxyiate-modifled polystyrene spheres in solutions of 50 kDa and 1 MDa polyacrylic acid (10). They also measured the solution viscosity q. In 50 kDa PAA, q follows a stretched exponential in c. The 1 MDa PAA shows a viscometric transition, q changing from a stretched-exponential concentration dependence to a power-law concentration dependence at c 1.4 g/1 PAA. In 50 kDa PAA (Figure 9.3b), Dp c) for each probe size follows a stretched exponential in c. In 50 kDa PAA solutions. Dp and q are related by the Stokes-Einstein equation. In contrast, probes in 1 MDa PAA solutions do not show Stokes-Einsteinian behavior. As seen in Figure 9.4, with increasing c, Dpq/Dpoqo increases, and correspondingly r/, decreases, by four orders of magnitude. 

This chapter has made a systematic review of the published literature on the viscosity of nondilute polymer solutions. The primary conclusion here is that t](c, M) has a uniform behavior, namely that r] c, M) follows a stretched exponential in c and M, in all systems for r]/r]Q less than a few hundred, and in many systems up to extremely large q/r Q. In a considerable number of other systems, there is a transition viscosity rjt, above which r (c, M) follows a power law c. The location of the solutionlike-meltlike transition, when it occurs at all, has a characteristic viscosity rit is typically several hundred in dimensionless units. The transition is not identified by a characteristic concentration c+. In natural units, c [t]] for... 

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