| Conceptual advances and rapidly unproved computer speed have fueled tremendous research in rheology of entangled polymer melts. At the molecular level, long polymer molecules in a melt are entangled with each other like spaghetti. The motion of these chain molecules at short and intermediate time scales is limited to a "tubelike" region surrounding the contour of the chain. Modern theories of polymer inelt rheology are therefore based on this so-called tube model. The most comprehensive version of this model, the hierarchical model, shows great promise for quantitatively predicting the linear rheology of commercial polymers. To improve the accuracy and versatility of this coarse-grained model, however, one needs to pill down all the parameters and assumptions using fine-grained simulations. In this work, we have performed extensive molecular dynamics (MD) simulations to evaluate a number of key quarntities for the tube model, such as tube diameter, the tube length distributions, and branch point motion. Evaluation of these quantities has assisted in improving the tube model to a more quantitative level.; There are three specific contributions to the research of entangled polymer melts model in this work. Firstly, we found that in MD simulations it is critical to choose a correct method of identifying the ''primitive path'', which is the centerline of the confining tube. Our proposed method, length minimization, yields a Gaussian distribution that agrees well with the long-recognized Doi-Kuzuu potential. Secondly, we have shown that the tube diameter is inherently a time-dependent quantity at least during the early stages of polymer relaxation. Thirdly, we have found inicroscopic evidence, for the first time, of hierarchical relaxation of branched polymers from MD simulations of three-arm asymmetric star polymers. In these simulations, the branch point remains anchored to a region of roughly a tube diameter before the short arm relaxes. After the relaxation of the short arm, the backbone of the star polymer diffuses as if it were a linear chain with a large frictional bead located at the branch point. The branch point motion---which manifests itself as a random hopping along a confining tube---is also directly visualized in the simulations. |
