J. Phys. II France
Volume 4, Numéro 2, February 1994
Page(s) 377 - 404
DOI: 10.1051/jp2:1994135
J. Phys. II France 4 (1994) 377-404

Nucleation of focal conic domains in smectic A liquid crystals

O. D. Lavrentovich1, M. Kléman2, 3 and V. M. Pergamenshchik4

1  Liquid Crystal Institute and Department of Physics, Kent State University, Kent, 44242 Ohio, U.S.A.
2  Laboratoire de Physique des Solides, Université de Paris-Sud, 91405 Orsay Cedex, France
3  Laboratoire de Minéralogie-Cristallographie, Universités Pierre et Marie Curie et Paris VII, 4 Place Jussieu, 75252 Paris Cedex 05, France
4  Faculty of Mathematical Sciences, University of Southampton, Southampton, SO9 5NH, U.K.

(Received 25 May 1993, received in final form 19 October 1993, accepted 22 October 1993)

The first-order structural transitions caused by an external magnetic field or by a surface anchoring are considered for a smectic A liquid crystal in the restricted geometry of a flat cell. The transition occurs by nucleation of focal conic domains. The free energy of the system is calculated as a function of the order parameter $\rho =$ domain radius/cell thickness for finite value of the splay ( K) and a saddle-splay ( $\bar{K}$) elastic constants and the anchoring coefficient. For small $\rho$ the behavior of the system is defined by the balance of the stabilising elastic term and destabilising field (or anchoring) term. Homogeneous nucleation from ideal uniform state is hindered by high energetic barrier unless $\bar{K}$ is positive and comparable (or larger) than K. A few possible scenarios of heterogeneous nucleation have been considered, among them the nucleation at local layer undulations and the nucleation at field-induced dislocations. The most effective and general scenario is the nucleation at distortions (dislocations) caused by bulk or surface irregularities. The expansion of the domain ( $\rho\gg 1$) is governed by the balance between the field and surface anchoring and does not depend directly on the elastic constants. The saturation field that provides the domain expansion can be smaller than the threshold field for other known mechanisms of the SmA instabilities.

© Les Editions de Physique 1994