Discretized model of entangled-polymer dynamics

A discretized version of the reptation model is proposed. The tube is modeled by a one-dimensional lattice and the polymer is modeled by a cluster of walkers, called reptons, on this lattice. Each repton represents a part of the chain. Reptons are allowed to hop between neighboring sites, but the cluster always remains connected. This model is solved analytically and numerically. In the experimentally accessible range of molecular weights M it predicts the diffusion coefficient D∼${\mathrm{M}}^{\mathrm{-}2}$+O(${\mathrm{M}}^{\mathrm{-}3}$) and viscosity ${\mathrm{\eta }}_0$∼${\mathrm{M}}^{3.4\pm 0.1}$. .AE