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

摘要

We investigate the effect of the number of arms (functionality f ) on themobility of the branch point in symmetric star polymers. For this purpose wecarry out large-scale molecular dynamics simulations of simple bead-springstars and neutron spin echo (NSE) spectroscopy experiments on center labeledpolyethylene stars. This labeling scheme unique to neutron scattering allows usto directly observe the branch point motion on the molecular scale by measuringthe dynamic structure factor. We investigate the cases of differentfunctionalities f = 3, 4 and 5 for different arm lengths. The analysis of thebranch point fluctuations reveals a stronger localization with increasingfunctionality, following 2/f-scaling. The dynamic structure factors of thebranch point are analyzed in terms of a modified version, incorporating dynamictube dilution (DTD), of the Vilgis-Boue model for cross-linked networks [J.Polym. Sci. B 1988, 26, 2291-2302]. In DTD the tube parameters are renormalizedwith the tube survival probability \phi(t). As directly measured by thesimulations, \phi(t) is independent of f and therefore the theory predicts nof-dependence of the relaxation of the branch point. The theory provides a gooddescription of the NSE data and simulations for intermediate times. However,the simulations, which have access to much longer time scales, reveal thebreakdown of the DTD prediction since increasing the functionality actuallyleads to a slower relaxation of the branch point.