Ordering and Melting of Block Copolymer Spherical Domains in 2 and 3 Dimensions

Abstract

We observe that a 2-D single crystalline layer of spherical diblock copolymer domains templated by lateral substrate topology melts via a continuous defect generation process, similar to that predicted by Kosterlitz, Thouless, Halperin, Nelson, and Young. The layer of spheres is allowed to order (or disorder) by annealing for 72 h at a given temperature, T, that corresponds to a given χ N min, where χ is the temperature-dependent Flory−Huggins parameter and N min is the number of mers in the minority block. The structure of the layer is revealed by imaging the ion beam etched film using scanning force microscopy. If χ N min > 9, the film is polycrystalline and the system appears to be kinetically trapped. For 9 > χ N min > 7.4, we observe that the film is a single crystal with quasi-long-range order and few defects, as expected for the 2-D crystal. As T is increased further (χ N min is decreased), we observe that defects are generated, predominantly dislocation pairs and other dislocation clusters with no long-range strain field. Increasing numbers of free dislocations are observed as χ N min is decreased further. This dislocation unbinding produces a hexatic phase which has quasi-long-range orientational order but only short-range translational order. At still higher T (χ N min = 7.2), the dislocations unbind into +60° and −60° free disclinations to form an isotropic 2-D liquid of block copolymer micelles. This hexatic to liquid transition occurs at a χ N min below that corresponding to the bulk lattice disordering−ordering transition as measured by small-angle X-ray scattering.