Wrinkles and splay conspire to give positive disclinations negative curvature

Recently, there has been renewed interest in the coupling between geometry and topological defects in crystalline and striped systems. Standard lore dictates that positive disclinations are associated with positive Gaussian curvature, whereas negative disclinations give rise to negative curvature. Here, we present a diblock copolymer system exhibiting a striped columnar phase that preferentially forms wrinkles perpendicular to the underlying stripes. In freestanding films this wrinkling behavior induces negative Gaussian curvature to form in the vicinity of positive disclinations.