MICROPHASE SEPARATION OF GRAFTED COPOLYMERS ON CURVED SUBSTRATES - LAYERING PREEMPTS RIPPLING

We study equilibrium phase separation of immiscible diblock copolymer chains, A-B and B-A, end-grafted to the interior surface of cylinders or spheres. We show that with the grafting surface curving moderately, the microphase separation pattern is qualitatively different from that for a flat surface. When h/R > rho(c) (h is the height of the polymer layer and R is the radius of the cylinder or sphere), the chains tend to <<layer>> with the free ends segregating radially. The local composition then forms a three-layer pattern: A-B-A or B-A-B. The values of rho(c). are found to be 0.32 and 0.13 for cylinder and sphere, respectively. Analogous layering occurs in homopolymer blends grafted on spherical surface when h/R > 0.44.