FIG. 3: Maximal growth velocity as a function of supersaturation, log ( x/x $^{∗}$), for the parameters given in the text. The broken lines extrapolate the values into asymptotic regions. (SOS) model[35]. The system consists of a set of growth sites arranged as a one-dimensional lattice. There are N sites, each characterized by a height h$_{i}$ where i = 0 , ..., N − 1. Periodic boundaries are used so that formally, one has h$_{N}$ = h$_{0}$ . The idea is that molecules randomly land on the surface at some specified rate ν$_{hit}$ representing the diffusion of molecules onto the surface. Once on the surface, a molecule attempts to leave the surface at a rate ν$_{evap}$ . Physically, ν$_{hit}$ will be determined by the concentration of the molecules in solution and the rate at which they move while ν$_{evap}$ is a measure of how fast a molecule makes an attempt to leave the surface. Nucleation is anomalous in one dimension due to the fact that the “surface area” of a cluster does not depend on its size. We therefore introduce a rule designed to capture the most important feature of surface nucleation which is the existence of a critical cluster size. Specifically, molecules are not allowed to leave the surface if they are part of a cluster that is of a specified critical size or larger. The critical size n$_{c}$ is a parameter. Molecule j is ”part of a cluster” of size n if there are n contiguous sites, including site j , with heights the same as or greater than h$_{j}$ . Thus, small clusters can form spontaneously and dissociate but a cluster at or above the critical size is stable. A time step dt = 1 / ( ν$_{hit}$ + ν$_{evap}$ ) is defined and the dynamics of the kinetic Monte Carlo algorithm are as follows: 9