  The self-assembly of functionalized (patchy) particles with directional
interactions into target structures is still a challenge, despite the
significant experimental advances on their synthesis. The self-assembly
pathways are typically characterized by high energy barriers that hinder the
access to stable (equilibrium) structures. A possible strategy to tackle this
challenge is to perform annealing cycles. By periodically switching on and off
the inter-particle bonds, one expects to smooth-out the kinetic pathways and
favor the assembly of targeted structures. Preliminary results have shown that
the efficiency of annealing cycles depends strongly on their frequency. Here,
we study numerically how this frequency-dependence scales with the strength of
the directional interactions (size of the patch $\sigma$). We use analytical
arguments to show that the scaling results from the statistics of a random walk
in configurational space.
