Critical molecular weight for entanglement

Figure 20.9. Effect of molecular weight (MW) on viscosity of linear and branched polymer melts. Beyond a critical molecular weight for entanglements (MW ) viscosity (r o) increases rapidly for linear polymers as MW. ...

Fig. 37. Effect of the diluent molecular weight in blends with 1,800,000 molecular weight PS (X = 0.3) on craze fibril stability (e — ej. The samples were unfiltered and the strain rate used was 5 X 10 s Mc(as2Me) is the critical molecular weight for entanglement effects on the zero-shear-rate viscosity (From Ref. courtesy Macromolecules (ACS))...

The molecular weight of the trapped polyisoprene sequence must be higher than the critical molecular weight for entanglements of polyisoprene. 

Two other noteworthy physical properties result from the examination of the data. These are the critical molecular weight for entanglement and the molecular weight between entanglements. Table 10.2 shows that these values are about 9000 and 4000g/mol, respectively. For linear polymer melts, a factor of about 2 is a usual finding in polymer physics. 

FIGURE 21. The critical energy release rate Gc of PMMA as a function of molecular weight A/z. Mg is the critical molecular weight for entanglement. (From Reference 93.)... 

Now we assume that this linear relationship is valid up to M = Mq, where Mq is the critical molecular weight for entanglement introduced in Section 5.2.1. This implies that ... 

Similar values of G and can be obtained by fits of linear viscoelastic data [49]. Once G and Zj have been assigned, the value of the stretch relaxation time can be obtained from Zj i, since both of these time constants are controlled by the friction coefficient f. Since Tj i depends on the number of entanglements Zj to the second power, and Zj depends on Z to a higher power, 3.4, the values of and z j must converge as Z decreases. Pattamaprom and Larson [36] assume that the two time constants become equal at the critical molecular weight for entanglement Mq, which is aroimd twice M. With this assumption, one readily finds that... 

Here, Me is the critical molecular weight for entanglement of random branches, Mr is the molecular weight of the Kuhn segment, A is a constant determined by the chemical stracture of the chain and temperature, and B is a constant specific to the chemical structure. Equation [72] allows us to estimate Mb from the j/o data, M data (determined from SEC-LALS), and Mk data (determined from the characteristic ratio C ) given that the chains in the sample are randomly branched (no regular branches such as star branches) and that the values of A and B are known (which was the case for randomly branched polyesters examined in Reference 141). 

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