Dynamics of Branched Polymers: A Combined Study by Molecular Dynamics Simulations and Tube Theory

We present large-scale computer simulations of entangled polymers with symmetric star-like and Cayley tree-like architectures. Unlike the usual observation for repational behaviour of linear chains, the simulated systems exhibit a strong dispersion, over several decades, of the relaxation times after the local reptative (‘Rouse in tube’) regime. Relaxation is dramatically slowed down by approaching the branch point from the outer segments. This is consistent with the expected retraction mechanism for strongly entangled branched polymers. In order to describe fluctuations around the branch point, we introduce a Rouse-like model adapted to star-like polymers and incorporate entanglements by means of localizing springs. Model predictions for localization of the branch point are compared with simulations with fixed arm ends, which suppress retraction and tube dilution. Strikingly, the simulations reveal a localization of the branch point weaker than expected. This suggests the presence of early constraint-release effects that are not captured by the standard mechanism of tube dilution. We quantify, as a function of time, the strength of such effects and the fraction of relaxed material directly from the simulations with free ends. This allows us to renormalize the tube diameter and entanglement time in our model as time-dependent quantities. With this renormalization, the model provides an excellent description of the early relaxation of the branch point.