Geometric theory of columnar phases on curved substrates

Christian D. Santangelo, Vincenzo Vitelli, Randall D. Kamien, David R. Nelson

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


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 with 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 focusing of light rays by a lens. We show that the out of plane bending of the cylinders acts as an effective ordering field.

Original languageEnglish (US)
Article number017801
JournalPhysical Review Letters
Issue number1
StatePublished - Jul 6 2007
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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