Thick smectic shells |
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| Affiliation: | 1. Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany;2. CNRS, UMR 7190, Institut Jean Le Rond d׳Alembert, F-75005 Paris, France;3. UPMC Univ Paris 06, UMR 7190, Institut Jean Le Rond d׳Alembert, F-75005 Paris, France;1. School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK;2. Dipartimento di Ingegneria dell’Innovazione, Università del Salento. Via per Monteroni Edificio “Corpo O”, 73100, Lecce, Italy;3. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20132 Milano, Italy;1. Laboratoire de Physique des Solides, Université Paris-Sud, UMR CNRS 8502, Bâtiment 510, 91405 Orsay Cedex, France;2. Saint-Gobain Recherche, Saint-Gobain Recherche, 39 quai Lucien Lefranc, 93303 Aubervilliers Cedex, France;1. Servicio de Dermatología, Instituto de Biomedicina de Málaga (IBIMA), Hospital Universitario Virgen de la Victoria/Universidad de Málaga, Málaga, Spain;2. Servicio de Anatomía Patológica, Instituto de Biomedicina de Málaga (IBIMA), Hospital Universitario Virgen de la Victoria/Universidad de Málaga, Málaga, Spain;3. Departamento de Anatomía Patológica, Instituto Valenciano de Oncología, Valencia, Spain;4. Servicio de Dermatología, Instituto Valenciano de Oncología, Valencia, Spain;1. Mechanical Engineering Department, Petroleum University of Technology, P.O. Box: 61991-71183, Ahwaz, Iran;2. Mechanical Engineering Department, Yasouj University, P.O. Box: 75914-353, Yasouj, Iran |
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| Abstract: | The known ground state of ultrathin smectic films confined to the surface of a sphere is described by four +1/2 defects assembled on a great circle and a director which follows geodesic lines. Using a simple perturbative approach we show that for thick smectic films on a sphere with planar anchoring this solution breaks down, distorting the smectic layers. The instability happens when the bend elastic constant exceeds the anchoring strength times the radius of the inner sphere. Above this threshold, the formation of a periodic chevron-like structure, observed experimentally as well, relieves geometric frustration. We quantify the effect of thickness and curvature of smectic shells and provide insight into the wavelength of the observed texture. |
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| Keywords: | Geometric frustration Smectic liquid crystals Periodic structure |
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