Analyses of J t , and in an Entanglement-Free System

As s increases in sample C, the time scale of the glassy-relaxation process becomes closer to those of the Rouse modes of motion and the steady-state compliance is predicted to decline according to Eq. (4.66). For sample C, 

Dividing a measured viscosity value by the product of pT/ poTb and rjp K = 10 ) jr]p K = 10 Aq = 0), a reduced viscosity value, denoted by r/R, is obtained. The rjR value, without the contribution of the internal viscosity and independent of the small change in modulus with temperature, is linearly proportional to K. Then, the K value at 134.1°C can be calculated by multipl3ung the K values at other temperatures by the ratio 

Calculated from the equations obtained by least-squares fittings to the values determined at different temperatures see the text. Values obtained from Table II of Ref. 12. 

The K values shown in Table 14.3 for sample C can be well fitted by the Vogel-Tammann-Fulcher (VTF) equation or the Williams-Landel-Ferry (WLF) equation.Prom the VTF equation with the parameters obtained from the fitting, the K values at 127.5 and 93.7gC are calculated and listed in Table 14.3, with the former also listed in Table 14.1. The result of K (andrs) at 93.7gC is used in sections 14.8 and 14.10.a where the structural relaxation time and the length scale at Tg are defined or studied. 

The G lo) spectra of LIO, A5000, and A2500 are quantitatively analyzed in terms of Eqs. (14.3)-(14.8) just as the Jp t) line shapes of sample C have been. The calculation of G u)) from a G t) functional form can be accurately carried out numerically according to the procedure described in Appendix 14.A. In the case of AlOOO, as the contribution of the Rouse modes of motion is negligible due to its very small molecular weight — about that of a single Rouse segment m = 850 — G lo) is analyzed in 

---