Tube model in uncrosslinked systems

The idea of the tube is intuitively appealing, and one can imagine that the same picture will be useful for uncrosslinked system such as polymer melts. However, one has to face a new problem that, in melts, the tube itself changes with time because all conformations in a melt are accessible. A key concept to solve this problem was introduced by de Gennes who discussed the Brownian motion of an unattached chain 

Our current understanding of the dynamics of the highly entangled state is based on the concept of reptation. This picture is rigorously correct for the system that has been presented, i.e., a single chain in a 

---