Pattern formation of anisotropic molecules on surfaces under non-equilibrium conditions as described by a minimum model.

The self-organization of lipophilic chain molecules on surfaces in vacuum deposition experiments has been recently studied by Monte Carlo simulations of a coarse grained microscopic model system. Surprisingly, the final potential energy depends in a non-monotonous way on the chosen flux and the surface temperature. Here we introduce a schematic model which contains the relevant physical ingredients of the microscopic model and which elucidates the origin of this anomalous non-equilibrium effect. Intra-cluster effects, reflecting the chain arrangement within one cluster, and inter-cluster effects, based on the distribution of chains among the different formed clusters, are taken into account. This schematic model is solved numerically as well as via analytical means. From the analytical solutions, it is possible to understand quantitatively for which interaction parameters the observed anomalies can indeed be observed. The generality of the observed phenomena is stressed. It is related to the concept of kinetic trapping, which often occurs during self-assembly.