SCALING ANALYSIS OF MULTICHAIN COOPERATIVE MOTIONS IN THE LATERAL MOTION MODEL FOR POLYMER MELTS

A scaling analysis is presented for the evaluation of the time depende nce of the lateral chain motion in monodisperse polymer melts. This an alysis accounts for the correlations between the motions of neighborin g chains, as well as for the correlations between the motions of beads in the same chain. These correlations result in a slowing of the Brow nian chain dynamics. This analysis predicts that the bead mean squared displacement depends on time as g approximately t2/7 for times less t han the terminal time. The terminal time is found to scale as N3.5. Th e center of mass diffusion constant has a component, which arises from the relative motions of neighboring chains, that scales as N-2.5. The re is also a component, which accounts for the correlated motion of al l chains in a region of the melt, that scales as N-2.1. This latter co mponent should dominate for sufficiently long chains due to its milder scaling.