Diblock copolymer melts in electric fields: the transition from parallel to perpendicular alignment using a capacitor analogy

We consider alignment of a symmetric diblock copolymer melt thin film or bulk phase by an electric field using a capacitor analogy. For the lamellar phase we show that alignment of the lamellae in the direction perpendicular to the bounding electrodes, compared to parallel alignment, occurs for thicker films. For thin films the critical electric field required for a transition from parallel to perpendicular alignment is proportional to H^{- 1/2} , where H is the film thickness. We also consider the possibility of a mixed lamellar morphology where, because the bounding electrodes prefer one block, parallel layers form adjacent to the electrodes, while in the interior region there is perpendicular alignment. We determine the conditions for such a morphology.