Bouligand pattern

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... 

Fig. 1.8 The twisted nematic N (cholesteric) structure, formed by chiral modifications of nematic compounds tmd by non-chiral nematagens doped with chiral solutes. Where the pitch of this helicoidal stiucture is comparable with the wavelength of light, the phase gives iridescent reflections. Larger pitch structures, where the repeat distance can be resolved in the optical microscope, appear as fingerprint textures with bands separated by half a pitch. Helicoidal structures of this type are common in biological material, most obviously in the carapaces of iridescent beetles. Their electron microscope pictures show a characteristic pattern of nested arcs, known as Bouligand patterns [4]...

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... 

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