2021 Impact factor 1.624
Soft Matter and Biological Physics
Eur. Phys. J. E 2, 47-57

Grain boundaries and the law of corresponding cones in smectics

M. Kléman1 - O.D. Lavrentovich2

1 Laboratoire de Minéralogie-Cristallographie (UMR 7590), Universités de Paris-VI & de Paris-VII, Case 115; 4 place Jussieu 75252 Paris cédex 05, France
2 Chemical Physics Interdisciplinary Program and Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA

Received 21 June 1999 and Received in final form 10 September 1999

Focal Conic Domains (FCDs) in smectic phases often assemble according to a particular rule, experimentally discovered by G. Friedel, the law of corresponding cones (l.c.c.). This paper reports various results relating to this type of association. First we show that a l.c.c. contact between 2 focal conic domains has a vanishing energy, yielding metastable local equilibrium. Then we use some projective properties of conic sections to extend the celebrated Apollonian tiling, which describes a tilt grain boundary (TiGB) of vanishing disorientation $\omega=0$ made of toric focal conic domains, to any $\omega\not=0$ TiGB. Finally we present a realistic model of the energy of the $\omega\not=0$ TiGB, which we compare to the energy of a TiGB split into dislocations, and to the energy of a curvature wall. This model explains why FCD tilings show macroscopic zones not filled with FCDs.

61.30.Jf Defects in liquid crystals - 61.72.Lk Linear defects: dislocation disclinations - 61.72.Mm Grain and twin boundaries

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