Coupling between mean curvature and texture in thin block copolymer film

Using a phase field approach we study the orientational coupling between the pattern developed by a lamellae forming block copolymer thin film and a topographically patterned substrate. Utilizing the Brazovskii free energy functional for a conserved order parameter, we perform a Taylor series expansion on the film thickness to obtain an effective geometric potential that correlates the smectic texture orientation to the curvature of the underlying surface. The results of this expansion are in good agreement with numerical results obtained through a Cahn-Hilliard model and experimental data on curved monolayers of asymmetric diblock copolymers.