The Role of the Functionality in the Branch Point Motion in Symmetric Star Polymers: A Combined Study by Simulations and Neutron Spin Echo Spectroscopy

We investigate the effect of the number of arms (functionality <i>f</i>) on the mobility of the branch point in symmetric star polymers. For this purpose we carry out large-scale molecular dynamics simulations of simple bead–spring stars and neutron spin echo (NSE) spectroscopy experiments on center labeled polyethylene stars. This labeling scheme unique to neutron scattering allows us to directly observe the branch point motion on the molecular scale by measuring the dynamic structure factor. We investigate the cases of different functionalities <i>f</i> = 3, 4, and 5 for different arm lengths. The analysis of the branch point fluctuations reveals a stronger localization with increasing functionality, following 2/<i>f</i> scaling. The dynamic structure factors of the branch point are analyzed in terms of a modified version, incorporating dynamic tube dilution (DTD), of the Vilgis–Boué model for cross-linked networks [J. Polym. Sci., Part B 1988, 26, 2291−2302]. In DTD the tube parameters are renormalized with the tube survival probability φ­(<i>t</i>). As directly measured by the simulations, φ­(<i>t</i>) is independent of <i>f</i>, and therefore the theory predicts no <i>f</i> dependence of the relaxation of the branch point. The theory provides a good description of the NSE data and simulations for intermediate times. However, the simulations, which have access to much longer time scales, reveal the breakdown of the DTD prediction since increasing the functionality actually leads to a slower relaxation of the branch point