Bulk fabrication of surface patterns with sub-20 nm feature sizes is immensely desirable for many existing and emerging technologies. Directed self-assembly (DSA) of block copolymers (BCPs) has been a recently demonstrated approach to achieve such feature resolution over large-scale areas with minimal defect populations. However, much work remains to understand and optimize DSA methods in order to move this field forward. This paper presents large-scale numerical simulations of zone annealing and chemo-epitaxy processing of BCP films to achieve long-range orientational order. The simulations utilize a Time-Dependent Ginzburg-Landau model and parallel processing to elucidate relationships between the magnitude and velocity of a moving thermal gradient and the resulting BCP domain orientations and defect densities. Additional simulations have been conducted to study to what degree orientational order can be further improved by combining zone annealing and chemo-epitaxy techniques. It is found that these two DSA methods do synergistically enhance long-range order with a particular relationship between thermal gradient velocity and chemical template spacing.The ability to accurately produce nanoscale surface patterns has become a driving factor for research in many fields. As the need for nanoscale manufacturing increases, new processing technologies must be developed in order to meet industry needs. A number of different patterning methods have shown progress in decreasing feature size beyond the capabilities of traditional lithography 1 . These methods include extreme ultraviolet lithography, nanoimprinting, maskless lithography, and directed self-assembly (DSA) of block copolymers (BCP) 2-7 . BCPs can form very monodisperse periodic domains with domain sizes that can be tailored as small as 5 nm. The domain sizes in a microphase separated BCP matrix correspond with the molecular lengths of each section of the copolymer chain 8 . Linear BCPs are commonly used for patterning research and applications, although other chain architectures are also being explored 9-11 . The phase-separated morphologies of linear BCPs are dependent on the interaction parameter χ, degree of polymerization N, and the ratio of the length of each block f. Stable and meta-stable morphologies include ordered spheres, cylinders, lamellae, and gyroid structures [12][13][14][15][16] . The variety, regularity, and small size of these structures make BCPs highly attractive for many nano-manufacturing applications.The microphase separation of BCP thin films has been broadly studied and shown to be useful for surface patterning and membrane applications 17 . These formations, while periodic, are prone to defects such as dislocations and grain boundaries that detract from their utility in some applications. A variety of strategies have been developed to extend defect-free uniformity during self-assembly including solvent annealing 18 , shear alignment 19 , epitaxy [20][21][22][23] , zone casting 24 , and field alignment [25][26][27][28][29] . Studies...