Tg Defined by the Structural Relaxation Time ts 1,000 sec

The structural- (or a-) relaxation time ts may be somewhat arbitrarily defined by the time when the ratio between the contribution of the glassy-relaxation process (G) to the relaxation modulus G(t) and the total contributed by all the entropic processes (R), G/R reaches 3. Physically, this means that G/R has decayed nearly by factor of e (2.72) from 10, which is the G/R ratio at the relaxation time t = t ) of the highest Rouse-Mooney mode when the temperature is at the glass transition point. At the same time, the contribution from the glassy component in such a state is still significant. The structmal-relaxation time defined this way is basically equivalent physically to that defined by  

The structural-relaxation time as given by Eq. (14.10) is also in close agreement with the a-relaxation time defined in a usual way the time at which the relaxation modulus reaches 10 dynes/cm (see Figs. 14.17 and 14.18). The structural-relaxation time defined by Eq. (14.10), besides reflecting the effect of the glassy relaxation on the bulk mechanical properties, has the virtue of following exactly the temperature dependence of the 

Using Eq. (14.9), the structural-relaxation time given by Eq. (14.10) may be rewritten as 

By analyzing the J t) line shape of sample A at the calorimetric Tg (97°C), the structural-relaxation time ts = 1,000 sec is obtained. In the literature, Ts reaching 100-1,000 sec has been used as the criterion for defining Tg. 30-32 In view of the ts value of sample A at its calorimetric Tg, ts = 1,000 sec is also used for defining the glass-transition points Tg of samples B and C, which will be used in the analyses and discussions of their results. As shown in Table 14.1, the thus defined Tg for samples A and C are consistent with the calorimetric values which are read from Fig. 14.12. Including at the thus defined Tg, the dynamic and structural quantities at different temperatures K, K, s and ts obtained by analyzing the Jp t) curves of sample A are listed in Table 14.2. 

For LIO, A5000, A2500, as the longest ts values extracted from the data of Inoue et al. are around 100-200 sec, their Tg values are determined by extrapolation using the best fit of the VTF equation to the available data. As shown in Table 14.1, these Tg values are consistent with the calorimetric values as closely as those of samples A, B and C are. In the case of AlOOO, the ts results at different temperatures are fitted to the VTF equation, from which the Tg point where ts = 1,000 sec is determined by interpolation. 

---