Accelerated Method of Self-Consistent Field Theory for the Study of Gaussian Ring-Type Block Copolymers

Although self-consistent field theory (SCFT) has been become one of the most successful methods for the study of block copolymers, its application to ring copolymers has been hindered for years, especially for three-dimensional structures. Here, we have developed an accelerated pseudospectral algorithm to solve SCFT equations of ring copolymers by taking advantage of the symmetry of ordered structures. By combining various advanced techniques, speed-up of orders of magnitude has been achieved, making the construction of a complete phase diagram affordable. This accelerated algorithm has been applied to constructing the phase diagrams of AB ring and AB tadpole copolymers, consisting of the double gyroids, O-70, and even Frank-Kasper spherical phases. This algorithm is applicable for the studies of other ring copolymers that will add a piece of puzzle to the understanding of architectures on the self-assembly behavior of block copolymers.