A surface interaction model for self-assembly of block copolymers under soft confinement

The surface interaction between substrates and block copolymers is one of the most important factors that control the alignment of self-assembled domains under thin film confinement. Most previous studies simply modeled substrates modified by grafting polymers as a hard wall with a specified surface energy, leading to an incomplete understanding of the role of grafted polymers. In this study, we propose a general model of surface interactions where the role of grafted polymers is decomposed into two independent contributions: the surface preference and the surface softness. Based on this model, we perform a numerical analysis of the stability competition between perpendicular and parallel lamellae of symmetric diblock copolymers on substrates modified by homopolymers using self-consistent field theory. The effects of the surface preference and the surface softness on the alignment of lamellar domains are carefully examined. A phase diagram of the alignment in the plane of the surface preference parameter and the surface softness parameter is constructed, which reveals a considerable parameter window for preparing stable perpendicular lamellae even on highly preferential substrates.