A new model for polymer melts and concentrated solutions

Abstract

A new mesoscopic model is presented for polymer melts and concentrated solutions. 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 waiting time distribution function.’’ Such a distribution is supposed to occur when the chain is ‘‘frozen’’ in space until a ‘‘gap’’ in the solution or melt meets with the bead or chain segment. The time a bead must wait to jump is given by a distribution function with a single adjustable parameter β, which describes the long-time behavior of the distribution: ∼1/t1+β . We find that the model predicts non-Fickian diffusion in agreement with experimental data and Fickian diffusion for longer times which scales with chain length as 1/N2/α−1, where α is a function of β. For β=1.3, D∼1/N2.28. The autocorrelation of the end-to-end vector of the chain is a stretched-exponential form with a time constant which scales as the length of the chain to the 3.3 power for β=1.3.