Novel block copolymers (“BCPs”) having non-random distributions of comonomers within at least one of the blocks and methods of using those BCPs in directed self-assembly (“DSA”) processes are provided. The non-random (e.g., gradient-creating) distributions can be customized in order to concentrate the desired comonomer properties in predetermined areas of the BCP. These BCPs can achieve perpendicular orientation with simple annealing and offer superior long-range ordering and lower defectivity when compared to prior art BCPs. These BCPs can be incorporated into compositions that simultaneously offer the benefits of high-χ and rapid thermal-annealing kinetics while maintaining similar or improved guide process windows when compared to prior art BCPs.