  Unlike hard materials such as metals and ceramics, rubbery materials can
endure large deformations due to the large conformational degree of freedom of
the crosslinked three-dimensional polymer network. However, the effect of the
branching factor of the network on the ultimate mechanical properties of
rubbery materials has not yet been clarified. This study shows that
tri-branching, which entails the lowest branching factor, results in a large
elastic deformation near the theoretical upper bound. This ideal elastic limit
is realized by reversible strain-induced crystallization, providing on-demand
reinforcement. The findings indicate that the polymer chain is highly
orientated along the stretching axis, whereat enhanced reversible
strain-induced crystallization is observed in the tri-branched and not in the
tetra-branched network. A mathematical theory of structural rigidity is used to
explain the difference in the chain orientation. Although tetra-branched
polymers have been preferred since the development of vulcanization, these
findings highlighting the merits of tri-branching will prompt a paradigm shift
in the development of rubbery materials.
