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Soft Matter and Biological Physics


Eur. Phys. J. E 8, 67-78 (2002)
DOI: 10.1140/epje/i2002-10009-1

Defects in a TGBA phase: A theoretical approach

M. Kleman1, Yu.A. Nastishin1, 2 and J. Malthête3

1  Laboratoire de Minéralogie-Cristallographie de Paris (UMR7590), T16 case 115, 4 place Jussieu, F-75252 Paris cédex 05, France
2  Institute for Physical Optics, 23 Dragomanov str., Lviv 79005 Ukraine
3  Institut Curie, Section de recherche, CNRS UMR 168, 11 rue Pierre et Marie Curie, Paris cédex, 05 France

maurice.kleman@mines.org

(Received 20 February 2002)

Abstract
Following our experimental observations of disclination lines in freely suspended droplets and free-standing films (Yu.A. Nastishin et al., Eur. Phys. J. E 5 353 (2001)), topological defects of the twist grain boundary (TGBA) phase are considered according to two aspects: topological and energetical. There are two classes of line defects, disclinations (as in the cholesteric (N*) phase and the liquid vortices phase (NL*), relating to the directors tripod symmetries) and dispirations (relating to the translation-rotation symmetries); there are no topological point defects. Differences between N*, NL* and TGBA disclinations are physical, not topological. The absence of focal conic domains in the TGBA phase is an immediate consequence of the materialization of the helical axis (along the ${\chi}$-director); the same feature, coupled to the trend to parallelism of the smectic layers, accounts for the predominance of $\lambda$-lines. Finally, the presence of defects akin to developable domains is explained in the frame of the least curvature model, that requires the introduction of a third type of defects: the densities of edge dislocations of the smectic layers.

PACS
61.30.Jf - Defects in liquid crystals.
64.70.Md - Transitions in liquid crystals.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002