A theory for heterogeneous states of polymer melts produced by single chain crystal melting

We consider the polymer physics of a possible molecular mechanism for disentangled melt states observed recently. We find that the route from molten, but only marginally-overlapping single crystals to the equilibrium state must pass over a free-energy barrier that becomes large at high molecular weights. The penalty arises from elastic distortions of the entanglement network as the chains diffuse. A critical molecular weight arises naturally from the competition of elastic distortion and the free-energy of confinement. We calculate the barrier and critical molecular weight at both a simple single-chain level, and at a "one-loop" level of co-operative motion, finding that many-chain effects alter the physics quantitatively, but not qualitatively. Several new experiments are suggested.