Nanoscale Domain Stability in Organic Monolayers on Metals

Certain organic molecules, such as alkanethiols, can adsorb on metals to form monolayers. Sometimes domains appear in the monolayers. For example, an incomplete monolayer may form islands, and a mixed-composition monolayer may separate into distinct phases. During annealing, the molecules diffuse on the metal surface. The domain boundary energy drives the domains to coarsen. The contact potential between the dissimilar domains drives the domains to refine. On the basis of existing experimental information, we suggest that the competition between coarsening and refining should stabilize certain domain patterns. We formulate a free energy functional to include the effects of mixed species, domain boundary, and contact potential. An approximate energy minimization estimates the equilibrium domain size. We derive a diffusion equation consistent with the free energy functional. The numerical solution of the diffusion equation follows the evolution of the monolayers from a random initial concentration field to patterns of dots and stripes. We also discuss the practical implications of the theory and, in particular, the possibility of guided self-assembly.