A NEW MODEL FOR POLYMER MELTS AND CONCENTRATED-SOLUTIONS

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 beta, which describes the long-time behavior of the distribution: Approximately 1/t1+beta. 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/alpha-1, where alpha is a function of beta. For beta = 1.3, D approximately 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 beta = 1.3.