Abstract
Both smectic A and columnar liquid crystals possess quantized symmetry translations (one such translation in SmAs, two in columnar phases). This is the reason why dislocations, the defects that break translational symmetries, are found in these phases. Defects involving other kinds of symmetry breaking might exist, such as disclinations or topological singular points, which break rotations.
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Further Reading
G. Darboux, Théorie Générale des Surfaces, Chelsea Publishing, New York, 1954.
J. D. Ferry, Viscoelastic Properties of Polymers, 3rd edition, John Wiley & Sons, New York, 1980.
G. Friedel, Annales de Physique (Paris) 18,273 (1922).
D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination, Chelsea Publishing, New York, 1952.
M. Kléman, Points, Lines and Walls, John Wiley & Sons, Chichester, 1983.
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(2003). Curvature Defects in Smectics and Columnar Phases. In: Kleman, M., Lavrentovich, O.D. (eds) Soft Matter Physics: An Introduction. Partially Ordered Systems. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21759-8_10
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DOI: https://doi.org/10.1007/978-0-387-21759-8_10
Publisher Name: Springer, New York, NY
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