Glassy systems viscoelastic functions

Viscoelastic Functions for Glassy Systems in the Frequency Domain 463... 

VISCOELASTIC FUNCTIONS FOR GLASSY SYSTEMS IN THE FREQUENCY DOMAIN... 

To show the effect of diluent o.n the detailed shapes of viscoelastic functions, it is convenient to employ corresponding-state plots as in Section C of Chapter 12. For the relaxation spectrum, we plot log H - log Tc/Mq against log t - log a o/kT). Of course, for a single polymer and its solutions the only variables are fo and c (which in the pure polymer becomes p). In Fig. 17-9, poly(vinyl acetate) is compared in this manner with its 50% solution in tri-m-cresyl phosphate. The values of log fo at 40°C for these two systems are 1.75 and -5.25, respectively—the diluent reduces the local friction coefficient by a factor of 10. The curves after reduction coincide at the bottom of the transition zone because this is fixed by the corresponding-state conditions, and are rather similar in shape throughout. However, the diluent causes the spectrum to rise somewhat more sharply from the theoretical slope of -5 at short times but at still shorter times it crosses the spectrum of the pure polymer, and its entrance into the glassy zone involves a broader maximum than the latter. 

The method of reduced variables as outlined in Section B above, including fitting the function flr(r) to the WLF equation, is appropriate for data in the transition, plateau, and terminal zones of time scale, with the provision that all contributions to the measured viscoelastic properties involve the same friction coefficient ftfand moreover that the internal structure of the system does not change with changing temperature. The latter restrictions are inherent in the development of Section A. In glassy and crystalline polymers, and in situations where two or more different classes of molecular motions with different temperature dependences are involved, some modifications in the treatment are necessary. 

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