  A phenomenological mean-field theory is used to investigate the properties of
solvent-diluted di-block copolymers (BCP), in which the two BCP components (A
and B) form a variety of phases that are diluted by a solvent (S). Using this
approach, we model mixtures of di-block copolymers and a solvent and obtained
the corresponding critical behavior. In the low solvent limit, we find how the
critical point depends on the solvent density. Due to the non-linear nature of
the coupling between the A/B and BCP/solvent concentrations, the A/B modulation
induces modulations in the polymer-solvent relative concentration with a double
wavenumber. The free boundary separating the polymer-rich phase from the
solvent-rich one is studied in two situations. First, we show how the presence
of a chemically patterned substrate leads to deformations of the BCP
film/solvent interface, creation of terraces in lamellar BCP film and even
formation of multi-domain droplets as induced by the patterned substrate. Our
results are in agreement with previous self-consistent field theory
calculations. Second, we compare the surface tension between parallel lamellae
coexisting with a solvent phase with that of a perpendicular one, and show that
the surface tension has a non-monotonic dependence on temperature. The
anisotropic surface tension can lead to deformation of spherical BCP droplets
into lens-shaped ones, together with re-orientation of the lamellae inside the
droplet during the polymer/solvent phase separation process in agreement with
experiment.
