Chain Dynamics near the Unentangled-Entangled Transition of Polymer Melts

It is well-known that the transition between unentangled to entangled dynamics occurs at a critical molecular weight (Mc), typically assumed to be twice the entanglement molecular weight (Me). Recently, we have reiterated a previous finding that the ratio between Mc and Me doesn't assume a universal value of 2 for all polymer melts but in fact shows a dependence on the packing length (p). Not withstanding, the physical picture behind the independent existence of Me and Mc remains unclear.Here, we reinvestigate the problem by probing the microscopic dynamics of polybutadiene melts near the transition by neutron spin echo spectroscopy. We analyze the dynamic structure factor within the framework of the Rouse model with modified mode spectrum. We find that suppression of long-wavelength modes in the spectra already occurs for melts with molecular weight above Me, even if they are still below Mc. We rationalize these results based on earlier ideas on entanglement formation. We also apply this framework in confronting our viscosity data for various polymers