Single-file diffusion and kinetics of template assisted assembly of colloids

We report computer simulation studies of the kinetics of ordering of a two dimensional system of particles on a template with a one dimensional periodic pattern. In equilibrium one obtains a re-entrant liquid-solid-liquid phase transition as the strength of the substrate potential is varied. We show that domains of crystalline order grow as $\sim t^{1\mathrm{/}z}$, with $z\sim 4$ with a possible cross-over to $z\sim 2$ at late times. We argue that the $t^{1\mathrm{/}4}$ law originates from {\em single-file} motion and annihilation of defect pairs of opposite topological charge along channels created by the template.