A QUANTITATIVE THEORY OF LINEAR-CHAIN POLYMER DYNAMICS IN THE MELT - GENERAL SCALING BEHAVIOR

A theory of melt polymer dynamics for linear chain systems is develope d. This theory generalizes recent work, which considers the lateral mo tion of the chains. A description is provided of the short time dynami cs and of the crossover from this early time regime to a highly entang led dynamics. In both of these regimes, an effective friction coeffici ent for the lateral motion is evaluated by considering the extent of c orrelation between the displacements of the beads. This correlation is required due to the chain connectivity and the noncrossability of the chain backbones. The crossover time between these two regimes is foun d to be independent of chain length. In the early time regime, the bea d mean squared displacement is found to have a time dependence between g similar to t(0.4) and g similar to t(0.5). In the highly entangled regime, g has a t(2/7) dependence. The reptative motion of the chains along their own backbones and the coupling between this motion and the lateral chain motion is also included. It is found that the inclusion of these features results in a shorter terminal time in the long chai n limit than would be the case otherwise. Long range correlated many c hain motions are also considered in this work. These motions are expec ted to dominate the chain diffusion in the long chain limit. This theo ry predicts a terminal time that scales as N-3.3 and a diffusion const ant that scales as N--2.1, where N is the number of monomer units per chain. (C) 1996 American Institute of Physics.