Predictions of a recently proposed non-markovian model for polymer melts and concentrated solutions

Several predictions for a recently proposed mesoscopic model for polymer melts and concentrated solutions is presented. It is a single Kramers chain model in which elementary motions of the Orwoll-Stockmayer type are allowed. However, for this model, the bead jumps are no longer given by a Markovian probability, but rather are described by a fractal “waiting-time” distribution function, with a single adjustable parameter β, which describes the long-time behavior of the distribution: ∼ 1/t^1+β. We find that the model predicts D ∼ 1/N² and η₀ ∼ N^3.4 for β ≈︁ 1.4, where N is the degree of polymerization. The generalized model predicts that the relaxation spectrum has a plateau regime whose height is independent of N, but whose width is strongly N dependent, in agreement with experiment. The model also predicts that rings will diffuse somewhat more slowly than linear chains of the same molecular weight (about 80% as fast), with the same scaling dependence on N as linear chains, also in agreement with preliminary data.