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A topographically patterned substrate can be used to template a large, single crystalline grain of block copolymer spherical domains. Both the geometry of the substrate and the annealing temperature can be used to control the degree of order as well as the crystallographic orientation of the grain. The presence of a hard edge imparts translational order onto the hexatic, which has quasi-long-range orientational order and short-range translational order, and onto the liquid which has short-ranged translational and orientational order. This ordering influence is seen to fade as the distance from the edge increases. As a result, the regions near the edge appear to melt from crystalline order to hexatic by dislocation pair unbinding and then to a liquid through a disclination unbinding transition at higher temperatures than regions far from the edges. Crystalline grains templated by a hard step wall also have superior translational order as compared to those templated by a vacuum edge. The adjacent step also plays a crucial role in determining the grain orientation of the crystalline array on top of a mesa.
Segalman et al. (2003) studied this question.