Cooperative dynamics in polymer melts from the unentangled to the entangled regime

Abstract

The dynamics of polymer liquids present a rich variety of phenomena with characteristic scaling exponents that change across the transition from unentangled to entangled dynamics as the degree of polymerization of the polymer increases beyond a specific value. Entanglements are the result of topological interactions that have their origin in hard-core repulsive interactions between chains, which prevent the chains from crossing themselves and other chains. Entanglements are present in liquids of polymers with any degree of polymerization, but they only affect the dynamics of long chains. Conventional theoretical approaches to describing entangled and unentangled dynamics (i.e. the Rouse theory and the reptation model) are formally incompatible and do not encompass the dynamics across the transition. In this paper, we extend our approach for the cooperative dynamics of a group of polymers across the transition from unentangled to entangled dynamics. We test the robustness of the approach by comparing theoretical predictions against simulation trajectories of unentangled and entangled polyethylene melts. We find a good agreement between theory and simulations in both regimes.