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In this paper we consider thin films of AB block copolymer melts confinedbetween two parallel plates. The plates are identical and may have a preferencefor one of the monomer types over the other. The system is characterized byfour parameters: the Flory-Huggins chi-parameter, the fraction f of A-monomersin the block copolymer molecules, the film thickness d, and a parameter hquantifying the preference of the plates for the monomers of type A. In certainregions of parameter space, the film will be microphase separated. Variousstructures have been observed experimentally, each of them characterized by acertain symmetry, orientation, and periodicity. We study the systemtheoretically using the weak segregation approximation to mean field theory. Werestrict our analysis to the region of the parameter space where the filmthickness d is close to a small multiple of the natural periodicity. We willpresent our results in the form of phase diagrams in which the absolute valueof the deviation of the film thickness from a multiple of the bulk periodicityis placed along the horizontal axis, and the chi-parameter is placed along thevertical axis; both axes are rescaled with a factor which depends on theA-monomer fraction f. We present a series of such phase diagrams for increasingvalues of the surface affinity for the A-monomers. We find that if the filmthickness is almost commensurate with the bulk periodicity, parallelorientations of the structures are favoured over perpendicular orientations. Wealso predict that on increasing the surface affinity, the region of stabilityof the bcc phase shrinks.Comment: 35 pages, 20 figure

Microphase Separation in Thin Block Copolymer Films: A Weak Segregation Mean-Field Approach