  We propose a two-body spherically symmetric (isotropic) potential such that
particles interacting by the potential self assemble into linear semiflexible
polymeric chains without branching. By suitable control of the potential
parameters we can control the persistence length of the polymer, and can even
introduce a controlled number of branches. Thus we show how to achieve
effective directional interactions starting from spherically symmetric
potentials. The self assembled polymers have a exponential distribution of
chain lengths akin to what is observed for worm-like micellar systems. On
increasing particle density the polymeric chains self-organize to an ordered
line-hexagonal phase where every chain is surrounded by six parallel chains,
the transition is first order. On further increase in monomer density, the
order is destroyed and we get a branched gel like phase. This potential can be
used to model semi-flexible equilibrium polymers with tunable semiflexibility
and excluded volume. The use of the potential is computationally cheap and
hence, can be used to simulate and probe complex micellar dynamics with long
chains. The potential also gives a plausible method of tuning colloidal
interactions in experiments such that one can obtain self-assembling polymeric
chains made up of colloids and probe polymer dynamics using an optical
microscope.
