Microscopic theory of entangled polymer melt dynamics: Flexible chains as primitive-path random walks and supercoarse grained needles

We qualitatively extend a microscopic dynamical theory for the transverse confinement of infinitely thin rigid rods to study topologically entangled melts of flexible polymer chains. Our main result treats coils as ideal random walks of self-consistently determined primitive-path (PP) steps and exactly includes chain uncrossability at the binary collision level. A strongly anharmonic confinement potential ("tube") for a primitive path is derived and favorably compared with simulation results. The relationship of the PP-level theory to two simpler models, the melt as a disconnected fluid of primitive-path steps and a "supercoarse graining" that replaces the entire chain by a needle corresponding to its end-to-end vector, is examined. Remarkable connections between the different levels of coarse graining are established.