Thin film diblock copolymers in electric field: Transition from perpendicular to parallel lamellae

We examine the alignment of thin film diblock copolymers subject to a perpendicular electric field. Two regimes are considered separately: weak segregation and strong segregation. For weakly segregated blocks and below a critical value of the field, Ec, surface interactions stabilize stacking of lamellae in a direction parallel to the surfaces. Above the critical field, a first-order phase transition occurs when lamellae in a direction perpendicular to the confining surfaces (and parallel to the field) become stable. The film morphology is then a superposition of parallel and perpendicular lamellae. In contrast to Helfrich-Hurault instability for smectic liquid crystals, the mode that gets critical first has the natural lamellar periodicity. In addition, undulations of adjacent intermaterial dividing surfaces are out-of-phase with each other. For diblock copolymers in the strong segregation regime, we find two critical fields E1 and E2 > E1. As the field is increased from zero above E1, the region in the middle of the film develops an orientation perpendicular to the walls, while the surface regions still have parallel lamellae. When the field is increased above E2, the perpendicular alignment spans the whole film. In another range of parameters, the transition from parallel to perpendicular orientation is direct.