  Melts of 3-dimensional dendritic beads-springs, namely soft-clusters, are
studied by molecular dynamics simulations to elucidate the dynamics of
3-dimensional shaped polymers. Constituted by more than the critical number
around 200 beads, soft-clusters cannot diffuse or relax far above their glass
transition temperature, even though beads can relax within the soft-cluster.
Each soft-cluster can only rotate in the cage formed by neighboring
soft-clusters. We claim they are in a glass-like state: "cooperative glass"
because of the "cooperation" from beads connected in 3-dimension. The
cooperative glass would only transform to the liquid state at exceptionally
high temperature, e.g. 10 times the glass transition temperature. Agreeing with
experiments, 3-dimensional hierarchies lead to unique dynamics, especially
their divergent relaxation times with the number of beads. These features are
in sharp contrast with 1-dimensional chain-like polymers. Soft-clusters may
also resemble cooperative rearranging regions where cooperativeness is
contributed by low temperature, thus offer further insights into the glass
problem.
