  We present a novel simulation technique derived from Brownian cluster
dynamics used so far to study the isotropic colloidal aggregation. It now
implements the classical Kern-Frenkel potential to describe patchy interactions
between particles. This technique gives access to static properties, dynamics
and kinetics of the system, even far from the equilibrium. Particle thermal
motions are modeled using billions of independent small random translations and
rotations, constrained by the excluded volume and the connectivity. This
algorithm, applied to a single polymer chain leads to correct static and
dynamic properties, in the framework where hydrodynamic interactions are
ignored. By varying patch angles, various chain flexibilities can be obtained.
We have used this new algorithm to model step-growth polymerization under
various solvent qualities. The polymerization reaction is modeled by an
irreversible aggregation between patches while an isotropic finite square-well
potential is superimposed to mimic the solvent quality. In bad solvent
conditions, a competition between a phase separation (due to the isotropic
interaction) and polymerization (due to patches) occurs. Surprisingly, an
arrested network with a very peculiar structure appears. It is made of strands
and nodes. Strands gather few stretched chains that dip into entangled globular
nodes. These nodes act as reticulation points between the strands. The system
is kinetically driven and we observe a trapped arrested structure. That
demonstrates one of the strengths of this new simulation technique. It can give
valuable insights about mechanisms that could be involved in the formation of
stranded gels.
