Memory effects in entangled polymer melts

A chain reptating through a high molecular weight polymer melt leaves a trace in the form of elastic distortions of an entanglement network. Neighboring chains can partially relax these elastic distortions by following this trace with some accuracy. Thus the memory of chain configuration is reproduced by other chains when the first one leaves the tube after time ${\mathrm{\tau }}_{\mathrm{dif}}$. The number of diffusion steps of duration ${\mathrm{\tau }}_{\mathrm{dif}}$ required to completely lose the memory of chain configuration grows with the molecular weight M of the chain as ${\mathrm{\tau }}_{\mathrm{relax}}$/${\mathrm{\tau }}_{\mathrm{dif}}$∼${\mathit{M}}^{1/3}$ in agreement with experiments, where ${\mathrm{\tau }}_{\mathrm{relax}}$ is the relaxation time of the melt.