Diblock copolymer thin films on heterogeneous striped surfaces: Commensurate, incommensurate and inverted lamellae

We study a symmetric melt AB diblock copolymer thin film which is placed on a periodically striped CD surface. Because of different surface energies each stripe has a different preference for each of the blocks. There is thus a competition between the preferred bulk lamellar spacing, L-b, and the width of the stripes, lambda. This system is similar to the Frenkel-Kontorowa model of solid state physics. We consider the case L-b greater than or equal to lambda, and assume perpendicular alignment. The periodic striped surface will induce lamellae with unequal spacings. We also show that the striped potential can induce inverted bilayers, i.e., an AB,AB pattern rather than the more usual AB, BA.