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. Malthête31 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
-director); the same feature, coupled to the trend to
parallelism of the smectic layers, accounts for the predominance
of
-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.
61.30.Jf - Defects in liquid crystals.
64.70.Md - Transitions in liquid crystals.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002
