Entanglement renewal

Fig. 6. Proposed mechanism of entangled dynamics of a star polymer in a melt. Retractions as shown partially renew the tube, beginning with rapid retractions near the free end and much more rarely renewing deeper parts of the molecule...

Figure 17 The tube renewal concept an internal tube segment is lost when the attached entanglement disappears.

For weakly entangled polymers or long N-chains surrounded by shorter P-chains, a tube renewal time x shorter than Xc can be expected. If the two mechanisms are assumed to be independent of each other [17], the overall relaxation time x can be put as the harmonic average of the two times ... 

In a polydisperse sample, each N-chain is surrounded by chains of different lengths. Therefore, the constraint release time x. varies according to the reptation time of the passing chain. Some entanglements can be considered as permanent (P N), while others will disappear quickly (Ptime distribution will affect the tube renewal time and consequently the overall relaxation time of each chain. 

The simplest case for testing the tube renewal models is to isolate a long N-chain in a matrix of shorter entangled P-chains. A chain can be viewed as isolated from similar N-chains when the volume fraction N in the blend is such as NNtube renewal time is expected to scale as ... 

Nevertheless, a value of a = -2 does not guarantee the presence of an entangled regime when H = Af as pointed out in previous section. Studying chain diffusion in a crosslinked matrix helps avoid the tube-renewal factor, the presence of permanent topological constraints is assured, and an independent measure of the diffusion coefficient for the free chain can be obtained but mechanisms in addition to reptation could still appear, i.e., fluctuations of network Junctions. 

The fundamental assumptions revisited A renewed theoretical questioning of the founding assumptions of the reptation model has accompanied these more recent studies at molecular scales. The concept of entanglement, even if very useful, does not rely on molecular basis, and the question What i an entanglement in a melt is still relevant. 

Hess derived a similar expression from his microscopic model by explicitly considering the effective entanglement as a dynamic effect. Hess included the important many chain cooperative effects of constraint release and tube renewal, which are necessary in order to get quantitative predictions for the stress relaxation functions. Ultimately this does not affect the N dependence of the relaxation time. He found that after an initial fast Rouselike decay up to time r, Tp Hess = / irp Rep- Both models describe essentially the same physical picture. For the generalized Rouse model, Kavassalis and Noolandi found that Tp rm N /p. MD simulation results of Kremer and Grest could not distinguish between the standard reptation and Hess models but could rule out the generalized Rouse model. 

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