  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.
