Direct Observation of the Transition from Free to Constrained Single-Segment Motion in Entangled Polymer Melts

We report a direct determination of the time dependent mean-squared segment displacement of a polymer chain in the melt covering the transition from free to constraint Rouse relaxation along the virtual tube of the reptation model. This has been achieved by a neutron spin-echo (NSE) measurement of the segmental self-correlation function as conveyed by the spin-incoherent scattering from two fully protonated polymer melts, polyethylene and polyethylene propylene. Within the scenario of de Gennes reptation model a transition of the time dependence of segmental mean-squared displacements from $\propto t^{1/2}$ to $\propto t^{1/4}$ is expected and clearly corroborated by the incoherent NSE results.