Glass-rubber relaxation

Dielectric measurements are carried out on PPOA and PPODG. The dielectric spectrum of PPOA in the bulk presents a prominent glass-rubber relaxation followed by a subglass absorption. The low-molecular-weight compound only exhibits a prominent glass-liquid absorption followed by a diffuse and weak subglass relaxation. This behaviour cannot be explained in terms of only intramolecular interactions, and therefore intermolecular interactions must play an important role in this process. 

In addition to the primary glass-rubber relaxation which follows the empirical shifts determined by Eq. (26), part of the recoverable compliance does not obey time-temperature superposition. The shortest time data at the lowest temperatures has a component which shifts according to the Arrhenius temperature dependence... 

In all the above three polymers only a single process is apparently observed in the time window for PCS (10-6 to 100 s). The shape of the relaxation function is independent of temperature. The temperature dependence of (r) follows the characteristic parameters observed for mechanical or dielectric studies of the primary (a) glass-rubber relaxation. Relaxation data obtained by many techniques is collected together in the classic monograph of McCrum, Read and Williams41. The data is presented in the form of transition maps where the frequencies of maximum loss are plotted logarithmically... 

Fig. 6. Transition map for PPG showing the primary glass-rubber relaxation (a process) and the secondary relaxation (J3 process)...

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.)...

Like other retardation processes, the strength of the mechanical glass-rubber relaxation can, in principle, be determined by means of the empirical Havriliak-Negami equation (34)... 

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 8, Transition map for PIB. The hypersonic result corir siderahly extends the available frequency range. The primary (P) glass-rubber relaxation line and secondary (S) relaxation line are from Ref. 22.

Usually the primary (P) glass-rubber relaxation cannot be resolved from the secondary relaxation at hypersonic frequencies. However, this is not always the case. The Brillouin frequencies Awd) and tan 8 for polypropylene glycol (PPG) (13) are plotted versus temperature in Figure 9. Two tempratures of maximum loss are observed. The higher temperature loss at 100 °G and a frequency of 4.40 GHz correlates very well with the primary glass-rubber relaxation line determined by dielectric relaxation at gigahertz frequencies (13), The lower temperature loss at 50°G and a frequency of 5.43 GHz correlates with an extension of the secondary transition line. The transition map is shown in Figure 10. 

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. 

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