Diblock copolymer ordering induced by patterned surfaces above the order-disorder transition

We investigate the morphology of diblock copolymers in the vicinity of flat, chemically patterned surfaces. We use a Ginzburg-Landau free energy to describe the spatial variations of the order parameter in terms of a general two-dimensional surface pattern above the order-disorder transition. The propagation of several surface patterns into the bulk is investigated. The oscillation period and decay length of the surface Fourier modes are calculated in terms of system parameters. We show that two parallel surfaces having simple one-dimensional patterns can induce a complex three-dimensional copolymer structure between them. Lateral order is observed parallel to a patterned surface as a result of order perpendicular to the surface. Surfaces which have a finite chemical pattern size (e.g., a stripe of finite width) induce lamellar ordering extending into the bulk. Close to the surface pattern the lamellae are strongly perturbed as they try to adjust to the surface pattern.