We present a phenomenological description of relevant aspects of the g
rain surface chemistry on pre-existing carbonaceous seed particles. Th
e production of radical surface sites is calculated by means of modifi
ed analogous gas-phase thermodynamic and reaction kinetic data. Our re
sults suggest that surface growth processes mainly take place at sp(3)
bonded carbon atoms rather than at the edges of graphitic plates or p
olycyclic aromatic hydrocarbons and that the resulting grain material
will be amorphous diamond-like carbon. Furthermore, we argue that the
sticking efficiency of the key growth species C2H2 al radical sites is
high even for considerable grain drift velocities. The dust growth ra
te will generally be proportional to the radical surface coverage.