Geometric Theory of Columnar Phases on Curved Substrates

Details Geometric Theory of Columnar Phases on Curved Substrates Geometric Theory of Columnar Phases on Curved Substrates

2007-03-08

arxiv.org/abs/cond-mat/0703206v1

Phys. Rev. Lett. 99 (2007) 017801

Physics

Condensed Matter

Soft Condensed Matter

4 pages, RevTeX, 2 included figures

Scientific paper

10.1103/PhysRevLett.99.017801

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.

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