Surface-Induced Lamellar Ordering in a Hexagonal Phase of Diblock Copolymers

We study theoretically the hexagonal phase of diblock copolymer melts and determine the conditions under which a region of lamellar ordering is induced near a flat surface. In the weak segregation limit we employ a Landau-Ginzburg mean-field theory to describe the interfacial structure of the ordered hexagonal phase. The surface field, proportional to the differential affinity of blocks A and B to the surface, couples to the wave component perpendicular to the interface and increases the lamellar character of the ordered structure close to the surface. The extent of the region where this lamellar character predominates diverges logarithmically when the bulk hexagonal-lamellar transition is approached. In the strong segregation limit we find that the lamellar region exists provided that the surface field is larger than some critical value, readily obtainable in experiments. We find that the extent of the region of lamellar ordering also increases logarithmically with decreasing free energy difference between the hexagonal and lamellar phases.