Entangled system reptation branch

Note that the first and the second terms in (6.49) at w —> oo have the orders of magnitudes nTib 2 and nTy-1, respectively. The ratio of the quantities is very small for systems of long macromolecules, so that the contribution of the first, conformation branch to the linear viscoelasticity is negligibly small at X x. Note also that, for strongly entangled systems, at x X or Af M, as it was shown in Section 4.2.3, conformational relaxation cannot be occurred via the diffusive mechanism (considered here), but via the reptation mechanism, so that the first term in equation (6.49) ought to be replaced by other term, for example, in the form... 

This theoretical conclusion has not been confirmed by direct reptation experiments, but it has some implications. Mechanical measurements on strongly entangled, high molecular weight chains may be completely dominated by the presence of a few branch points. If exponential laws such as eq. (VIII.23) are involved, we need only a small fraction of branch points, and such fractions cannot be detected by standard physicochemical methods. We conclude that mechanical measurements in long chain systems can be extremely sensitive to certain chemical defects. Unfortunately, we do not have reptation data on controlled branched polymers. We do have data on mechanical properties of branched melts,but the melt problem is much more complex than the reptation problem, as shown in next section. 

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