Catalystlike role of impurities in speeding layer-by-layer growth

Molecular self-assembly is usually done at low supersaturation, leading to low rates of growth, in order to allow time for binding mistakes to anneal. However, such conditions can lead to prohibitively long assembly times where growth proceeds by the slow nucleation of successive layers. Here we use a lattice model of molecular self-assembly to show that growth in this regime can be sped up by impurities, which lower the free-energy cost of layer nucleation. Under certain conditions impurities behave almost as a catalyst in that they are present at high concentration at the surface of the assembling structure, but at low concentration in the bulk of the assembled structure. Extrapolation of our numerics using simple analytic arguments suggests that this mechanism can reduce growth times by orders of magnitude in parameter regimes applicable to molecular systems.