Undiluted Polymers and Concentrated Solutions

The longitudinal bulk wave velocity has often been measured in polymers as a function of temperature at constant frequency. Because M and M are relatively 

Plot of a/i/2 against the logarithm of frequency in megahertz for solutions of seven poiystyrenes in toiuene at 30°C, c = 0.025 g/ml. Molecular weights, bottom to top 600,2000,4000, 10,000,20,400, 5 i, 000,97,000. (Cochran, Dunbar, North, and Pethrick. ) Reproduced, by permission, from Journal of the Chemical Society Faraday Transactions //. 

An example is shown in Fig. 18-17, where v and attenuation (= 8.686a) at 2 X 10 Hz are plotted against temperature for polyfvinyl acetate), as reported by Thurn and Wolf. Three zones of dispersion are apparent. The one at 93 C undoubtedly represents the primary transition from glasslike to rubberlike consistency, in which o drops by about 50% because of the virtual disappearance of the jG term in equation 13 as it becomes smaller than K by several orders of magnitude. But 

Bulk longitudinal wave velocity (o) and attenuation (a) at 2 X 10 Hz plotted against temperature for poly(vinyl acetate). (Thurn and Wolf. ) 

The secondary dispersions, at -10 and —85 , presumably can be attributed to side group rearrangements as are the P mechanisms and other secondary effects discussed in Chapter 15. But it is difficult to guess the relative roles of volume and shear deformations in these motions. In shear (torsion) measurements at about 10 Hz, Schmieder and Wolf found secondary maxima in tan 6 at —30 and -100°C. No certain identification of these respective mechanisms can be made, since maxima in a and tan 6 are not really equivalent, and the respective frequency ranges are very different. If the secondary maxima in Fig. 18-17 do correspond to the secondary shear maxima, the temperature dependence of the associated relaxation times must be quite high. 

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For undiluted polymers and concentrated solutions, there are two types of theories (a) the singlechain theories or reptation theories , in which one focuses on the motions of one polymer molecule in the fluid as it moves in some kind of mean field provided by the surrounding polymer molecules and (b) the network theories , in which one visualizes the fluid as a loosely joined network in which the network junctions have a distribution of lifetimes. The chain theories are similar in structure to the dilute solution theories, and one has to make some kinds of assumptions about how the surrounding molecules affect the hydrodynamic drag and the Brownian motion. The network theories are similar in structure to the kinetic theory of rubber elasticity, and one has to make some kinds of assumptions about the junction kinetics. 

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