The tube model of polymer melt dynamics is extended to examine multiply branched molecules. The case of the regular tree exhibits a hierarchy of relaxation times, each associated with a different tube diameter. A log-quadratic relaxation curve is predicted, and compared to relaxation of low-density polyethylene. At the longest times the polymer behaves as if it were not entangled. The geometric mean of the disentanglement timescale and the monomeric timescale is of the order of the relaxation times of the free ends.
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Tom C. B. McLeish (1988) studied this question.
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