Terminal Relaxation Time High Molecular Weight

Terminal Relaxation Time (High Molecular Weight) 

What is the terminal relaxation time of a linear polybutadiene with cis trans vinyl = 55 38 7 and nearly uniform molecular weight 347,000, at 25°C  

Equation 57a of Chapter 10 can be used to estimate the disengagement time tj of the Doi-Edwards theory. The microstructure is sufficiently close to that of the polybutadiene identified with footnote b in Table 12-III and footnote c in Table 13-1 to use the values of fo and G%) from those sources. The result is 11 

---

While all relaxation times depend on temperature and pressure, only the global motions (viscosity, terminal relaxation time, steady-state recoverable compliance) are functions of Af , (and to a lesser extent MWD). The glass transition temperature of rubbers is independent of molecular weight because chain ends for high polymers are too sparse to affect this bulk property (Figure 3.14 Bogoslovov et al., 2010). The behavior can be described by the empirical Fox-Hory equation (Fox and Flory, 1954) ... 

In the terminal zone where G and G" are proportional to co and co respectively, the viscoelastic properties are dominated by the longest relaxation times and these are determined by long-range motions in which a molecule of high molecular weight... 

The practical significance of the terminal relaxation time r in several qualitative aspects of behavior has already been mentioned in connection with equation 7 for polymers of low molecular weight. The same considerations apply to polymers of high molecular weight, where t (or Ta, in the framework of the tube model) and the other two viscoelastic constants ijo and Jg which characterize the terminal zone are even more important in the processing and use of polymeric materials. Rough estimates of these quantities can sometimes be made from the equations in Section C3 above for practical purposes. 

The model of Mead [23] includes only the terminal zone, and here the key difference from the models of Carrot and Guillet [51] and Leonardi et al. [52 ] is that the latter authors include the dependence of the terminal relaxation time on the molecular weight distribution. Leonardi et al [ 52 ] compare the predictions of their comprehensive model with those of Mead s model [23] and with experimental data. They conclude that Mead s approach is useftrl when the average molecular weight is high, i.e. when the and when the polydispersity index is... 

Highly entangled systems, especially those of narrow molecular weight distribution, are characterized by a set of relaxations at long times (terminal relaxations) which are more or less isolated from the more rapid processes. The modulus associated with the terminal processes is called the plateau modulus G°,. Because t]0 and depend on weighted averages over H(x), their values are controlled almost completely by the terminal processes. These experimental... 

The zero-shear-rate viscosity and recoverable compliance also change with dilution. For M > M (independent property of the polymer sample. The product G J° is in fact a measure of the polydispersity of relaxation times in the terminal zone [11]. It appears to be essentially universal for highly entangled linear polymers with narrow molecular weight distributions [49-51] ... 

Since the model only applies to the plateau and the terminal relaxations, other mechanisms, particularly the high frequency (short-time) Rouse modes, will pollute the curve of G t) and interfere with the MWD determination, as these do not depend on the molecular weight. 

---