Mechanisms of Multiple Reentrant Transitions between Frank-Kasper and Classical Spherical Phases in AB-Type Dendron-Like Copolymer

It has been commonly accepted that Frank-Kasper spherical phases are stabilized over the classical phases in AB-type block copolymers by expanding the spherical region toward a large volume fraction of the A-block (f). Qiang et al. drastically expand the spherical region to f > 0.5 and find multiple reentrant transitions between Frank-Kasper and classical phases, the mechanisms of which have not yet been fully understood. In this work, we probe into the mechanisms by quantitatively analyzing the geometrical deformation of domains as well as its relationship with the chain architecture. As f increases, domains undergo convex deformation, followed by concave deformation to release the nonuniformity of stretching of short B-blocks filling the matrix. When convex deformation solely occurs, Frank-Kasper phases are favorable due to their milder deformation. As concave deformation starts to appear, the classical phases become more stable because their more convex deformation at the vertices of the Voronoi cell can alleviate the concave deformation on the faces. Moreover, it is revealed that the geometrical deformation is closely related with the dendritic architecture.