Kinetics of docking in postnucleation stages of self-assembly

Reaction efficiency of diffusion-controlled processes on finite, planar arrays. II. Crystal surfaces

We consider 36 planar nets identified by O'Keeffe and Hyde and calculate for each, using the theory of finite Markovian processes, the overall mean walk length n (first passage time) of a reactant diffusing randomly on a finite platelet before being trapped at a reaction center; the results are analyzed in terms of the total number N of lattice sites, the number N(b) of boundary sites, the average valence nu, and the bond orientation function Psi. We establish that crystalline platelets that are members of the same compatible class are characterized by very comparable catalytic efficiencies. The results obtained are also linked to an analysis of the kinetics of docking in postnucleation stages of protein self-assembly and to a recent conjecture on the symmetries of planar nets and the hard disk freezing transition.