The orientation of the self-assembled monolayer stripes on a crystalline substrate

Two-phase monolayers adsorbed on crystalline substrates can form many patterns. After reviewing the experimentally observed patterns on various substrates, we extend a thermodynamic theory to account for the anisotropy in surface stress, substrate stiffness, and phase boundary energy. We solve the elastic field in the anisotropic substrate by using the Stroh formalism. We then focus on the pattern of periodic stripes, and determine the orientation of the stripes that minimizes the free energy. As an example, we examine in detail the (1 1 0) surface of a cubic crystal. Depending on the parameters that characterize anisotropy, the stripes can orient along either [1̄ 1 0], or [0 0 1], or certain directions off the two crystalline axes. The transition between these orientations can be of either first or second order. The predications point to additional experiments that are needed to further the understanding.