Diblock copolymer ordering induced by patterned surfaces

We use a Ginzburg-Landau free energy functional to investigate diblock copolymer morphologies when the copolymer melt interacts with one surface or is confined between two chemically patterned surfaces. For temperatures above the order-disorder transition a complete linear response description of the copolymer melt is given, in terms of an arbitrary two-dimensional surface pattern. The appearance of order in the direction parallel to the surface is found as a result of the order in the perpendicular direction. Below the order-disorder point and in a thin-film geometry, our procedure enables the analytic calculation of distorted perpendicular and tilted lamellar phases in the presence of uniform or modulated surface fields.