Hierarchical nanostructures of diblock copolymer thin films directed by a saw-toothed substrate

An extensive and systematic calculation was performed to explore hierarchical cylindrical structures and the order-to-order transitions of AB diblock copolymers (f(A) = 0.3) on a saw-toothed substrate using self-consistent mean-field theory. We obtained fifteen relatively simple morphologies, including the existing morphologies observed experimentally and from simulations, and five more complicated structures, by varying the lateral periodicity of the substrate, the film thickness of diblock copolymers, the interaction between the A-block and the substrate and the tilt angles (or the shape) of the substrate. These structures show that the orientation and number of layers of cylinders can be tailored. Even lamellae and spherical microdomains were observed. Most interestingly, hierarchical structures are also observed, such as the morphology of C(ab)(//) within the upper cylinder perpendicular to the bottom cylinder, SC(b)(//) morphology that the upper is a cylinder but the bottom is a sphere. In addition, we discussed these complex hierarchical structures in detail and have analyzed the order-to-order transitions between the cylindrical morphologies with distinct orientations and layers.