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

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 χN 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 χN min > 9, the film is polycrystalline and the system appears to be kinetically trapped. For 9 > χN 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 (χN 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 χN 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 (χN 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 χN min below that corresponding to the bulk lattice disordering−ordering transition as measured by small-angle X-ray scattering.