  In the present work, with the intent of exploring the out-of-equilibrium
polymerization of active patchy particles in linear chains, we study a
suspension of active bivalent Brownian particles (ABBPs). At all studied
temperatures and densities, ABBPs self-assemble in aggregating chains, as
opposed to the uniformly space-distributed chains observed in the corresponding
passive systems. The main effect of activity, other than inducing chain
aggregation, is to reduce the chain length and favor alignment of the
propulsion vectors in the bonding process. At low activities, attraction
dominates over activity in the bonding process, leading self-assembly to occur
randomly regardless of the particle orientations.Interestingly, we find that at
the lowest temperature, as density increases, chains aggregate forming a novel
state: MISP, i.e., Motility-Induced Spirals, where spirals are characterised by
a finite angular velocity. On the contrary, at the highest temperature, density
and activity, chains aggregate forming a different novel state (a spinning
crystalline cluster) characterized by a compact and hexagonal ordered
structure, both translating and rotating. The rotation arises from an effective
torque generated by the presence of competing domains where particles
self-propel in the same direction.
