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Geometric theory of columnar phases on curved substrates. (English) Zbl 1228.82086
Summary: 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.

82D25 Statistical mechanical studies of crystals
Full Text: DOI
[1] DOI: 10.1007/BF00117160 · doi:10.1007/BF00117160
[2] DOI: 10.1103/PhysRevLett.35.1399 · doi:10.1103/PhysRevLett.35.1399
[3] DOI: 10.1103/PhysRevLett.17.1133 · doi:10.1103/PhysRevLett.17.1133
[4] DOI: 10.1007/BF01646487 · Zbl 1125.81321 · doi:10.1007/BF01646487
[5] L. D. Landau, Phys. Z. Sowjetunion 11 pp 545– (1937) ISSN: http://id.crossref.org/issn/0369-9811
[6] R. E. Peierls, Helv. Phys. Acta Suppl. 7 pp 81– (1934)
[7] DOI: 10.1126/science.1133162 · doi:10.1126/science.1133162
[8] DOI: 10.1126/science.1081160 · doi:10.1126/science.1081160
[9] DOI: 10.1098/rspa.2004.1371 · Zbl 1145.74380 · doi:10.1098/rspa.2004.1371
[10] DOI: 10.1103/PhysRevLett.91.045506 · doi:10.1103/PhysRevLett.91.045506
[11] DOI: 10.1098/rspa.2005.1534 · Zbl 1186.82091 · doi:10.1098/rspa.2005.1534
[12] DOI: 10.1103/PhysRevLett.93.215301 · doi:10.1103/PhysRevLett.93.215301
[13] DOI: 10.1103/PhysRevB.62.8738 · doi:10.1103/PhysRevB.62.8738
[14] DOI: 10.1073/pnas.0602755103 · Zbl 1160.82355 · doi:10.1073/pnas.0602755103
[15] F. S. Bates, Phys. Today 52 pp 32– (1999) ISSN: http://id.crossref.org/issn/0031-9228 · doi:10.1063/1.882522
[16] DOI: 10.1126/science.290.5496.1558 · doi:10.1126/science.290.5496.1558
[17] DOI: 10.1126/science.276.5317.1401 · doi:10.1126/science.276.5317.1401
[18] DOI: 10.1126/science.1100090 · doi:10.1126/science.1100090
[19] F. David, J. Phys. (France) 48 pp 2059– (1987) ISSN: http://id.crossref.org/issn/0302-0738 · doi:10.1051/jphys:0198700480120205900
[20] DOI: 10.1007/s101890170134 · doi:10.1007/s101890170134
[21] DOI: 10.1140/epje/e2005-00005-2 · doi:10.1140/epje/e2005-00005-2
[22] M. P. Do Carmo, in: Differential Geometry of Curves and Surfaces (1976) · Zbl 0326.53001
[23] P. Schneider, in: Gravitational Lensing: Strong, Weak and Micro (2006)
[24] DOI: 10.1021/ma050479l · doi:10.1021/ma050479l
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