Diblock copolymer thin film melts on striped, heterogeneous surfaces: Parallel, perpendicular and mixed lamellar morphologies

We consider the problem of a diblock copolymer melt thin film on a striped surface. Because of the different surface energies, the different stripes have different preferences for each of the blocks, while the upper free surface may also prefer one of the blocks. As a result of a combination of factors such as the surface tensions and chain stretching, a number of morphologies may appear. We allow for perpendicular, parallel, and mixed type lamellae and study the resulting phase diagrams. These diagrams should provide a crude guide for experimental studies on such systems. Our main conclusions are a-fold. First the phase diagram is intricate and complicated. Second, to produce a single crystal oriented along the stripes, it is best to use thin films and a diblock lamellar size equal to or larger than the stripe width.