Self-Assembly of AB Diblock Copolymers under Confinement into Topographically Patterned Surfaces

Motivated by recent experiments of copolymer patterning by nanoimprinting, we investigate microphase separation and morphology for symmetric AB diblock copolymers with lamellar structure in bulk, confined between a flat bottom surface and a square-wave top surface by using the self-consistent field theory (SCFT). The efficient and high-order accurate pseudospectral method is adopted to numerically solve the SCFT equations in irregularly shaped domains with the help of the "masking" technique by embedding the confined domains of arbitrary shape within a larger rectangular computational cell. Our simulations reveal that the inverted T-style and trapezoid structures occurring in the relatively strong and weak surface fields, respectively, are following our topographically patterned surface. For neutral walls, when the thickness of the lower section is commensurate with the lamellae period of bulk block copolymers, the topographically patterned surface in this work leads to parallel lamellae, and completely parallel lamellae are favored when both the width and height of the upper section are equal to the lamellae bulk period. Furthermore, the prevalent structures are the parallel lamellae in the upper section combined with the perpendicular lamellae in the lower section. When the walls repel one of the block species, parallel lamellae occur in a wide range of film thicknesses compared to the case of neutral walls. To our knowledge, some new structures, however, such as square and partial square structures and reversed-T and trapezoid structures, have not been reported before under parallel surface confinement. In general, the required structures can be obtained by choosing the proper degree of spatial confinement, characterized by variations of the ratio of film thicknesses to bulk repeat period, and the block-substrate interactions. Moreover, we show that the confinement width of the lower section (or the period of the square wave) plays a critical role in microstructure formation. These findings provide a guide to designing novel microstructures involving symmetric diblock copolymers via topographically patterned surfaces and surface fields, relevant to nanoimprinting.