Numéro |
J. Phys. II France
Volume 5, Numéro 10, October 1995
|
|
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Page(s) | 1525 - 1532 | |
DOI | https://doi.org/10.1051/jp2:1995197 |
J. Phys. II France 5 (1995) 1525-1532
Influence of the Electric Field on Edge Dislocations in Smectics
Robert Holyst1, 2 and Patrick Oswald21 Institute of Physical Chemistry of the Polish Academy of Sciences and College of Sciences, Dept III, Kasprzaka 44/52, 01224 Warsaw, Poland
2 Ecole Normale Superieure de Lyon, Laboratoire de Physique, 46 Allée d'Italie, 69364 Lyon Cedex 07, France
(Received 11 May 1995, received in final form 29 June 1995, accepted 6 July 1995)
Abstract
The electric field applied perpendicularly to smectic layers breaks the rotational symmetry of the system. Consequently, the
elastic energy associated with distortions induced by an edge dislocation diverges logarithmically with the size of the system.
In freely suspended smectic films the dislocations in the absence of the electric field are located exactly in the middle
of the film. The electric field,
E, above a certain critical value,
, can shift them towards the surface. This critical field (in Gauss cgs units) is given by the following approximate formula
. Here,
B and
K are smectic elastic constants,
is the surface tension,
N is the number of smectic layers and
is the dielectric anisotropy. The constant
and
. Additionally, we assumed that
, where
d is the smectic period. This formula is valid for
and
N>12. For smaller values of the surface tension and large
N the linear relation between
and
breaks down, since eventually for
and
,
approaches 0. The equilibrium location of a dislocation in the smectic film,
, equals
NdG(x), where
and
G(x) is a function independent of the film thickness (for
N>12) and of the value of the surface tension.
© Les Editions de Physique 1995