A preaveraged topological parameter, $\tilde{N}$, is introduced to provide a criterion for the presence of entanglements in polymer melts. The theory predicts a geometrical transition from the entangled to the unentangled state in agreement with experimental data. A generalized Rouse theory is used to describe polymer dynamics in both states.

• Received 3 June 1987

DOI:https://doi.org/10.1103/PhysRevLett.59.2674