  We introduce a novel coarse-grained bead-spring model for flexible polymers
to systematically examine the effects of an adjusted bonded potential on the
formation and stability of structural macrostates in a thermal environment. The
density of states obtained in advanced replica-exchange Monte Carlo simulations
is analyzed by employing the recently developed generalized microcanonical
inflection-point analysis method, which enables the identification of diverse
structural phases and the construction of a suitably parameterized hyperphase
diagram. It reveals that icosahedral phases dominate for polymers with
asymmetric and narrow bond potentials, whereas polymers with symmetric and more
elastic bonds tend to form amorphous structures with non-icosahedral cores. We
also observe a hierarchy in the freezing transition behavior associated with
the formation of the surface layer after nucleation.
