Disclosed are methods of forming polymer structures comprising: applying a solution of a block copolymer assembly comprising at least one block copolymer to a neutral substrate having a chemical pattern thereon, the chemical pattern comprising alternating pinning and neutral regions that are chemically distinct and have a first spatial frequency given by the number of paired sets of pinning and neutral regions along a given direction on the substrate; and forming domains of the block copolymer that form by lateral segregation of the blocks in accordance with the underlying chemical pattern, wherein at least one domain of the block copolymer assembly has an affinity for the pinning regions, wherein a structure extending across the chemical pattern is produced, the structure having a uniform second spatial frequency given by the number of repeating sets of domains along the given direction that is at least twice that of the first spatial frequency.