TY - JOUR
T1 - Geometric theory of columnar phases on curved substrates
AU - Santangelo, Christian D.
AU - Vitelli, Vincenzo
AU - Kamien, Randall D.
AU - Nelson, David R.
PY - 2007/7/6
Y1 - 2007/7/6
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.99.017801
DO - 10.1103/PhysRevLett.99.017801
M3 - Article
C2 - 17678190
AN - SCOPUS:34547239319
SN - 0031-9007
VL - 99
JO - Physical Review Letters
JF - Physical Review Letters
IS - 1
M1 - 017801
ER -