  We present numerical calculations of lamellar phases of block copolymers at
patterned surfaces. We model symmetric di-block copolymer films forming
lamellar phases and the effect of geometrical and chemical surface patterning
on the alignment and orientation of lamellar phases. The calculations are done
within self-consistent field theory (SCFT), where the semi-implicit relaxation
scheme is used to solve the diffusion equation. Two specific set-ups, motivated
by recent experiments, are investigated. In the first, the film is placed on
top of a surface imprinted with long chemical stripes. The stripes interact
more favorably with one of the two blocks and induce a perpendicular
orientation in a large range of system parameters. However, the system is found
to be sensitive to its initial conditions, and sometimes gets trapped into a
metastable mixed state composed of domains in parallel and perpendicular
orientations. In a second set-up, we study the film structure and orientation
when it is pressed against a hard grooved mold. The mold surface prefers one of
the two components and this set-up is found to be superior for inducing a
perfect perpendicular lamellar orientation for a wide range of system
parameters.
