Self-consistent field simulations of self- and directed-assembly in a mixed polymer brush

While self-assembling block copolymer thin films have attracted attention as a promising high resolution lithographic tool, the self assembly of mixed polymer brushes for lithography is relatively unexplored. Here we study the directed self-assembly of a mixed polymer brush using self-consistent field theory (SCFT) simulations. Using the model equations and numerical methods introduced and verified in our previous study, the bulk phase behavior of a mixed melt brush is studied in depth through full three dimensional calculations. We assume that the mixed A/B polymer chains, which are of the same length, are exposed to a neutral top surface and are uniformly grafted at a high density. We identify phase-separated morphologies and calculate a phase diagram for the mixed brush under melt conditions as a function of the segregation force and composition. The observed lateral microphase separation is similar to that in block copolymer thin films, but the phase separation occurs at a smaller segregation force and the transition between cylindrical and spherical morphologies are quite different than the first-order phase transition in block copolymers. We demonstrate that lateral confinement can induce long-range, in-plane order in mixed brushes and suggest promising directed self-assembly methods for the application of self-assembled mixed polymer brushes in next-generation information storage and electronic devices.