Entropy theory structural relaxation times

This relation enables evaluating the fragility parameter Ks as well as the structural relaxation times r over the whole temperamre range To < T < Ta-Because T] depends on polymer microstructure and molar mass, Ap likewise exhibits the same dependence. Computations of Ks within the entropy theory have not been possible before. 

Figure 20. (a) Structural relaxation time i calculated from the generalized entropy theory for... 

The Kauzmann temperature plays an important role in the most widely applied phenomenological theories, namely the configurational entropy [100] and the free-volume theories [101,102]. In the entropy theory, the excess entropy ASex obtained from thermodynamic studies is related to the temperature dependence of the structural relaxation time xa. A similar relation is derived in the free-volume theory, connecting xa with the excess free volume AVex. In both cases, the excess quantity becomes zero at a distinguished temperature where, as a consequence, xa(T) diverges. Although consistent data analyses are sometimes possible, the predictive power of these phenomenological theories is limited. In particular, no predictions about the evolution of relaxation spectra are made. Essentially, they are theories for the temperature dependence of x.-jT) and r (T). 

In the free-volume model,/ becomes the dominant structural mode of the relaxation theories. The rearrangement of the cage structure requires diffusion, which is slowly being frozen out. As T approaches 7, p can no longer follow its equilibrium value, but becomes frozen at a value p>p. Since the variation in p no longer contributes to the heat capacity, decreases. The relevant contribution to arises from the communal entropy, which depends primarily on p and ceases to change. However, at temperatures above 7, the structure can equilibrate rapidly compared to the measurement time and both p and approach their equilibrium value. 

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