Geometric Theory of Columnar Phases on Curved Substrates

Abstract

We study thin self-assembled columns constrained to lie on a curved, rigid substrate. The curvature presents no local obstruction to equally spaced columns in contrast to curved crystals for which the crystalline bonds are frustrated. Instead, the vanishing compressional strain of the columns implies that their normals lie on geodesics which converge (diverge) in regions of positive (negative) Gaussian curvature, in analogy to the focussing of light rays by a lens. We show that the out of plane bending of the cylinders acts as an effective ordering field.

4 pages, RevTeX, 2 included figures

References in corpus (5)

• Grain Boundary Scars and Spherical Crystallography
• Crystallography on Curved Surfaces
• Anomalous coupling between topological defects and curvature
• Helical Ribbons as Isometric Textures
• BPS Configurations in Smectics

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