The Glass-Rubber Relaxation

Some examples of the analysis of the apparent activation energy Ea of blends can be found in the literature. When evolution of the Ea of liquid cis-polyisoprene/ trans-polyisoprene (CPI/TPI) blends was analyzed using the VFTH model [41], the Ea for pure TPI was observed to be higher than that of TPI/CPI blends. Moreover, as the concentration of TPI decreased, then the Ea also decreased this was ascribed to the fact that in glass-rubber relaxation the motion of molecules is governed by the crosslink density. As the decrease in TPI content caused a decrease in crosslink density, this in turn enhanced the motion of chains, and consequently less Ea was required to promote segmental cooperative movements. 

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Because G (T) is a decreasing function of temperature at the glass-rubber relaxation temperature, the following relationship at the peak maximum of tan 5 holds ... 

Owing to the fact that at the glass-rubber relaxation temperature the storage compliance function is an increasing function of temperature, the inequality... 

After smoothing the curve of figure P8.7.1 to avoid the contributions of the glass — rubber relaxation, one obtains by numerical integration ... 

The crystalline phase affects the viscoelastic dynamic functions describing the glass-rubber relaxation. For example, the location of this absorption in the relaxation spectrum is displaced with respect to that of the amorphous polymer and greatly broadened. Consequently, the perturbing effects of crystal entities in dynamic experiments propagate throughout the amorphous fraction. The empirical Boyer-Beaman law (32)... 

Figure 12,27 Variation of the complex relaxation modulus of poly(ethylene ter-ephthalate) with temperature, in the vicinity of the glass-rubber relaxation, for samples of various crystallinities obtained in isothermal crystallizations ( ) 46%, (<>) 40%, ( ), (V) 26%, ( ) 2-3%, and (O) 0%. (From Ref. 33.)...

Annealing promotes crystallite thickening at the expense of the crystalline-amorphous interphase and the amorphous phase. This process decreases the intensity of the glass-rubber relaxation and enhances that of the a relaxation if the crystalline polymer develops this absorption. 

Figure 12, Brillouin splittings Aw d vs, temperature near the glass-rubber relaxation for PMMA, 10,000 molecular-weight PS and 2100 molecular-weight polystyrene. The arrows indicate the value of T(g) determined uHth a differential scanning calorimeter.

Patterson, G. D., Bair, H. E., and Tonelli, A. E., Thermal behavior of atactic polystyrene above the glass-rubber relaxation, J. Polym. Sci. Polym. Symp. Ed, 54, 249-257 (1976). 

Stress relaxation modulus observed in tension E(t) of polyisobutylene at different temperatures in the region of the glass-rubber relaxation (Tg -atW). At -83 at short time. E(t) approaches asymptotically the modulus of the glass at -40 C at long time. E(t) approaches asymptotically the modulus of the rubber. The relaxation is centred in the region of -66. Note the immense reduction in (t) of over 3 decades in a temperature rise of 43 C this behaviour is typical of amorphous polymers at the glass-rubber relaxation. 

Jarry JP, Monnetie L (1979) Fluorescence depolarization study of the glass-rubber relaxation in a polyisoptene. Macromolecules 12(5) 927-932. doi 10.1021/ma60071a028... 

The plot of the influence of modifying the frequency of analysis / versus the reciprocal of the peak temperatures of E" or tan d, for all experiments at all frequencies, displays different behaviors for sub-T transitions and the glass-rubber relaxation, as shown in Figure 12.4. Typically, a linear behavior is found for sub-T transitions, which can be analyzed using an Arrhenius model (Eq. (12.7)), from which the apparent activation energy Ea can be obtained, as shown in Eq. (12.8), where Tq is a time reference scale (in seconds), and R is the ideal gas constant (8.31JK mor ). 

F re 12.S Miscibility of polymer blends by examination of the glass-rubber relaxation temperature. Hollow and full symbols differentiate initial (individual polymers) and final (polymer blend) situations. 

Table 12.2 Compositional rules based on the study of the glass-rubber relaxation temperature (Cp heat capacity obtained by differential scanning calorimetry a, k, and q are adjustable parameters).

It is apparent from the plots of log versus (T-Tg) shown in Fig. 5 that the rotational mobility of dipnant reflects the glass-rubber relaxation of the host matrix. The experimental data show little scatter in the fit provided by the WLF equation for temperatures... 

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