Skip to main content
Unpublished Paper
Geometric Theory of Columnar Phases on Curved Substrates
Physical Review Letters (2007)
  • Christian Santangelo
  • Vincenzo Vitelli
  • Randall D. Kamien
  • David R. Nelson

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.

Publication Date
Prepublished version downloaded from ArXiv. Published version is located at
Citation Information
Christian Santangelo, Vincenzo Vitelli, Randall D. Kamien and David R. Nelson. "Geometric Theory of Columnar Phases on Curved Substrates" Physical Review Letters (2007)
Available at: