efect dynamics and domain growth in 2D curved crystals

GARCIA NA; REGISTER RA; DA VEGA; GOMEZ LR

Córdoba

Workshop; XIII LATIN AMERICAN WORKSHOP ON NONLINEAR PHENOMENA; 2013

LAWNP

Curved crystalline structures are ubiquitous in nature. For example, they can be found inviral capsids, insect eyes, pollen grains, and radiolaria. During the last decade these crystalshave attracted the interest of dierent communities because of the richness associated with thecoupling between geometry, structure, and functionality. Recently, curved crystals have beenobtained 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 greatpotential to develop such structures are block copolymers and liquid crystals [N. Xie et al., SoftMatter, 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 reducelattice distortions and to satisfy topological constraints. Thus, from a condensed matter perspective,the presence of curvature in ordered phases appears as an opportunity for accuratecontrol 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 knowledgeof equilibrium structures and features, the out-of-equilibrium dynamics leading to theformation of curved crystals, highly relevant for technological applications like defect functionalizationengineering or soft lithography, remain almost unexplored.In this work we study the processes leading to the formation of two-dimensional (2D) curvedcrystal structures. This crystallization process is found to strongly deviate from its counterpartin at systems. The quenching of a liquid into a crystal phase leads to the formation of acurved polycrystalline structure, characterized by dierent domains of the crystal phase andthe location of defect congurations 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 thegeometrically-induced frustration to form the lattice is reduced. Mechanisms of curvaturedrivengrain growth and defect annihilation lead to increasing crystalline order. Linear arraysof defects diuse 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 highcurvature regions, inducing the formation of stable but not fully equilibrated domain structures.