Coupling between mean curvature and textures in block copolymer thin films deposited on curved substrates

We study the dynamics of coarsening in a cylinder-forming polystyrene-block-poly(ethylene-alt-propylene) block copolymer thin film deposited on a topographically patterned substrate. Thermal annealing leads to highly ordered arrays of polystyrene cylinders embedded in the poly(ethylene-alt-propylene) matrix, lying in-plane and oriented perpendicular to the trenches of the substrate. We show that this configuration corresponds to an equilibrium state. The coupling between the block copolymer morphology and the mean curvature of the substrate is dictated by the out-of-plane deformations of the block copolymer structure. Thus, with appropriate control over the substrate features, it should be possible to obtain novel structures with controlled orientation.