Local Chain Segregation and Entanglements in a Confined Polymer Melt

The reptation mechanism, introduced by de Gennes and Edwards, where a polymer diffuses along a fluffy tube, defined by the constraints imposed by its surroundings, convincingly describes the relaxation of long polymers in concentrated solutions and melts. We propose that the scale for the tube diameter is set by local chain segregation, which we study analytically. We show that the concept of local segregation is especially operational for confined geometries, where segregation extends over mesoscopic domains, drastically reducing binary contacts, and provide an estimate of the entanglement length. Our predictions are quantitatively supported by extensive molecular dynamics simulations on systems consisting of long, entangled chains.