Monomer Fluctuations and the Distribution of Residual Bond Orientations in Polymer Networks

Abstract

In the present work, four series of simulations are analyzed: entangled model networks of a) mono-disperse or b) poly-disperse weight distribution between the crosslinks, c) non-entangled phantom model networks and d) non-entangled model networks with excluded volume interactions. Previous work on the average residual bond orientations (RBO) of model networks [1] is extended to describe the distribution of RBOs for the entangled networks of the present study. The phantom model can be used to describe the monomer fluctuations, average RBOs, and the distribution of RBOs in networks without entanglements and without excluded volume. Monomer fluctuations in networks with excluded volume but without entanglements can be described if the phantom model is corrected by the effect of the incompletely screened excluded volume. It is shown that parameters of the tube model can be determined from monomer fluctuations in polymer networks and from the RBO. A scaling of the RBO $\propto N^{-1/2}$ is observed in both mono-disperse and poly-disperse entangled networks, while for all networks without entanglements an RBO $\propto N^{-1}$ is found. The distribution of the RBO of entangled samples can be described by assuming a normal distribution of tube lengths that is broadened by local fluctuations in tube curvature. Both observables, monomer fluctuations and RBO, are in agreement with slip link or slip tube models [2] for networks and disagree with network models that do not allow a sliding motion of the monomers along a confining tube.