A quantitative theory of linear chain polymer dynamics in the melt. I. General scaling behavior

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Abstract
A theory of melt polymer dynamics for linear chain systems is developed. This theory generalizes recent work, which considers the lateral motion of the chains. A description is provided of the short time dynamics and of the crossover from this early time regime to a highly entangled dynamics. In both of these regimes, an effective friction coefficient for the lateral motion is evaluated by considering the extent of correlation 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 found to be independent of chain length. In the early time regime, the bead mean squared displacement is found to have a time dependence between g∼t 0.4 and g∼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 chain limit than would be the case otherwise. Long range correlated many chain motions are also considered in this work. These motions are expected to dominate the chain diffusion in the long chain limit. This theory predicts a terminal time that scales as N 3.3 and a diffusion constant that scales as N −2.1, where N is the number of monomer units per chain.