Bouligand plane

In one of his early classic papers from 1969, Bouligand [115] showed that if a cut is made in a cholesteric structure at an oblique angle to the helix axis, an arc pattern of the kind in Fig. 34b will be observed as the projection of the director field onto the cut plane, as illustrated in Fig. 36. We will call this oblique plane the Bouligand plane or the Bouligand cut. Evidently, if we turn the director around an axis perpendicular to the helix axis until it is aligned along the Bouligand plane, we will have exactly... 

Bom approximations, nematics 171 Bose-Einstein condensation, ferroelectrics 517 Bouligand pattern 1004 Bouligand plane 560 boundary conditions, director fields 73 Bragg angle, cubic phases 895 Bragg peaks, nonchiral smectics 444 Bragg reflection... 

The symmetry elements in the hexagonal structure composed of liquid-like columns are shown in fig. 6.4.1. The director n is parallel to the column axis a (or equivalently a or a") is the lattice vector of the two-dimensional hexagonal lattice L, and 6 are two-fold axes of symmetry 3 is a three-fold axis and g a six-fold axis. Any point on or , is a centre of symmetry. Any planes normal to n and the planes ( 7 ) and (Lg, 0 are planes of symmetry. Defects in such a structure have been investigated in detail by Bouligand and by Kleman and Oswald. ... 

Fig. 6.4.6. Developable domains in the columnar phase, (a) The developable surface is degenerated into a straight line d common to the planes P. The columnar axes C form coaxial circles about 5. b) The developable surface Z) is a cylinder. The columns (or the layers in the case of smectic A) are a set of parallel and equispaced involutes of a circle, (c) A Reimann surface generated by half-tangents to a helix. The columns are normal to the half-tangents. (Bouligand. )...

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