CRYSTALS OF DEFECTS IN CHIRAL THERMOTROPIC MESOGENS: PERIODIC ARRAYS OF TWIST GRAIN BOUNDARIES. A.-M. Levelut, Laboratoire de Physique des Solides, Université Paris-Sud, F91405 Orsay Cédex, France

Crystals of defects form a distinct class of mesophases in which a periodic array of defects such as disclinations or dislocations coexist with the fluid organization at a molecular scale. These periodic networks are an intermediate step in a process where intrinsic bending or twisting forces tend to destroy the nematic or smectic organization [1].

Recently crystals of defects with a tetragonal lattice have been put in evidence in some chiral mesogenic molecules [2]. The tetragonal phase is obtained directly by cooling the isotropic liquid state. At lower temperature the only possible mesophase- mesophase transformation is toward a smectic (lamellar) mesophase with antiferroelectric properties. Finally the temperature range of existence of the tetragonal mesophase in a binary mixture decreases as the optical activity decreases so that this phase was never detected in racemic mixtures or in achiral compounds. X ray diffraction studies have been performed on single crystals of the tetragonal mesophase of several compounds. First of all the liquid ordering at a molecular scale is asserted by a wide angle isotropic diffuse ring. At small angle a set of sharp Bragg spots corresponds to a tetragonal tridimensional lattice. The unit cell contains about 500 molecules which confirms the "crystal of defects" nature of the mesophase. The lattice constants compare to the layer periodicity of the smectic antiferroelectric phase. In fact three different space groups have been identified : I4, I 4₁, P 4₁.

A description of the tetragonal phases as crystalline arrays of twist grain boundaries [3] (which can form a triply periodic minimal surface) inside an antiferroelectric structure is proposed. The twist grain boundaries perpendicular to the smectic planes divide the smectic structure in narrow sheets, the smectic planes are twisted by an angle of [[pi]]/2 on each side of a boundary and the successive sheets correspond one each other by a 4₁ or a 4₂ helical axis.

[1] International Workshop on Geometry and Interfaces, Colloque de Physique, Ndeg. 7, 23, (1990 )

[2] B. Bennemann, G; Heppke, A.-M. Levelut and D. Lötzsch, Molecular Crystals Liquid Crystals, 260, 351 (1995)

[3]T. C. Lubensky, S.R. Renn , T. Tokishiro in Quasicrystals, the state of the Art ed. by P DiVincenzo and P. Steinhardt World Scientific Ed. (1991)