Symmetry breaking in self-assembled monolayers on solid surfaces. II. Anisotropic substrate elasticity

On a solid surface a monolayer mixture may separate into two phases. The phases can self-assemble into a variety of patterns, with the feature size on the scale of 1-100 nm. This paper studies how the elastic anisotropy of the substrate affects the patterns. The substrate is taken to be of cubic crystal symmetry, although the method developed can be readily extended to treat substrates of any other crystalline symmetry. The surface stress differs from one phase to the other, and the difference refines the phases to reduce the elastic energy. The phase boundary energy tends to coarsen the phases. The two competing effects set the phase sizes and the phase patterns. The anisotropy of the substrate elasticity breaks the symmetry of the system. We formulate a phase field model on the basis of this physical picture. The numerical simulation shows that stripes tend to orient along the two compliant directions of the substrate, forming a tweedlike pattern. A square lattice of dots can also be obtained when the anisotropy is weak and the average concentration sufficiently deviates from half filling. We interpret these findings in terms of free energy minimization.