Tube Dilation or Dynamic Dilution

up to now, in our discussion of constraint release, we have assumed that for non-dilute concentrations of long chains, the reptation time of the long-chain component of a bidisperse melt is unaffected by relaxation of the other components (except for the factor of two correction predicted by double reptation). This is not always true. To take an extreme example, if a monodisperse polymer melt is diluted with a small-molecule solvent, entanglements will become less dense, and the plateau modulus will drop, thus increasing the tube diameter a as indicated by to Eq. 6.23  

Then the reptation time of the polymer will be reduced, as can be seen in the expression for the reptation time, Eq. 6.28  

28 shows that the reptation time is affected by the entanglement tube diameter a. In general, if tj) is the concentration of polymer in a polymer solution containing solvent, the plateau modulus decreases with decreasing (j) roughly as More generally, it has 

The two different regimes of constraint release obtained respectively at low and high values of the Graessley parameter are illustrated in Figs. 7.9 and 7.10 for binary blends of 1,4-polybutadiene. In Fig. 7.9, the two polymers have molecular weights = 36,800 and M = 168,000. Since Mf = 1543, and = M /M and Zj = Mj/M, we find that the Graessley parameter is G r = /Z = 0.008, and that for this blend, the long polymer 

the latter being obtained by a best fit. From Parkand Larson 

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