Defect dynamics and domain growth in 2D curved crystals

NICOLÁS A. GARCÍA; RICHARD A. REGISTER; LEOPOLDO R. GÓMEZ; DANIEL A. VEGA

Villa Carlos Paz

Workshop; Latin American Workshop on Nonlinear Phenomena; 2013

FAMAF

Curved crystalline structures are ubiquitous in nature. For example, they can be found in viral capsids, insect eyes, pollen grains, and radiolaria. During the last decade these crystals have attracted the interest of different communities because of the richness associated with the coupling between geometry, structure, and functionality. Recently, curved crystals have been obtained in a controlled fashion by the use of colloidal matter [W. T. M. Irvine et al., Nature, 2010; W. T. M. Irvine et al., Nat. Mater., 2012]. Other self-assembled systems with great potential to develop such structures are block copolymers and liquid crystals [N. Xie et al., Soft Matter, 2013]. In curved crystals, defects can be a feature of the fundamental (equilibrium) state. Depending on the substrate´s topology and curvature, defects can be required to reduce lattice distortions and to satisfy topological constraints. Thus, from a condensed matter perspective, the presence of curvature in ordered phases appears as an opportunity for accurate control of the density and location of topological defects [D. R. Nelson et al., Nano Lett., 2002]. Although theoretical and experimental work has led to a substantial advance in the knowledge of equilibrium structures and features, the out-of-equilibrium dynamics leading to the formation of curved crystals, highly relevant for technological applications like defect functionalization engineering or soft lithography, remain almost unexplored. In this work we study the processes leading to the formation of two-dimensional (2D) curved crystal structures. This crystallization process is found to strongly deviate from its counterpart in flat systems. The quenching of a liquid into a crystal phase leads to the formation of a curved polycrystalline structure, characterized by different domains of the crystal phase and the location of defect configurations with a net topological charge on regions of high curvature. In general, the formation of the crystal order starts in regions of low curvature, where the geometrically-induced frustration to form the lattice is reduced. Mechanisms of curvature-driven grain growth and defect annihilation lead to increasing crystalline order. Linear arrays of defects diffuse to regions of high curvature, where they are absorbed by free disclinations. At long times, grain boundaries may become pinned due to the local traps generated by high curvature regions, inducing the formation of stable but not fully equilibrated domain structures.