  We investigate the efficiency of gelation and network formation in telechelic
star polymer melt, where the tips of polymer arms are dipoles while rest of the
monomers are uncharged. Our work is motivated by the experimental observations
[A.Kulkarni et.al, Macromolecules, {\bf 48}, 6580 (2015)], in which rheological
studies of telechelic star polymers of poly-(L-actide), a bio-degradable
polymer, showed a drastic increase in elastic properties (up to $2000$ times)
compared to corresponding star polymers without the telechelic arm ends. In
contrast to previous studies, we avoid using effective attractive Lennard Jones
potentials or dipolar potentials to model telechelic interactions. Instead we
use explicit Coulomb positive and negative charges at the tip of polymer-arms
of our bead-spring model of star polymers. By our simulations we show that the
dipoles at the tip of star arms aggregate together to form clusters of dipoles.
Each cluster has contribution from several stars, and in turn each star
contributes to several clusters. Thus the entire polymer melt forms a connected
network. Network forming tendencies decrease with decrease of the value of the
effective charge constituting the dipole: this can be experimentally realized
by choosing a different ionomer for the star tip. We systematically varied the
value of dipole charges, the fraction of star-arms with dipoles at the tip and
the length of the arms. The choice of explicit charges in our calculations
enables us to make better quantitative predictions about the onset of gelation,
moreover we get qualitatively distinct results about structural organization of
dipoles within a dipole-cluster.
