Grandjean-Cano wedge

A cholesteric liquid crystal with pitch of about 0.3 im in wedge geometry showing Grandjean steps (Grandjean-Cano wedge cell). 

Similar studies have been carried out by Cano and Chatelain< on mixtures of nematic and cholesteric liquid crystals. The birefringence of the nematic being very large, dn of the mixture could be assumed without sensible error to be equal to that of the nematic itself. The pitch P of the mixture was measured directly from the Grandjean-Cano steps formed in a wedge (fig. 4.2.9). The values of dn and P when inserted in (4.1.13) gave a rotatory power in quantitative accord with observations. 

Fig. 4.2.9. Grandjean-Cano pattern of edge dislocations in a cholesteric wedge formed between a cylindrical lens and a flat plate (a) without a magnetic field and (b) with a magnetic field normal to the spiral axis and the dislocation line. The double dislocations - the darker lines-become zig-zag in the presence of the magnetic field while the single dislocations remain stable. (The Orsay Liquid...

Berreman and Heffner [59] considered the cholesteric Grandjean texture with tilted director orientation on the boundaries, Fig. 6.16. In the absence of the tilt, the free energy g is minimum at the following thicknesses d of the Cano wedge ... 

Figure 9. Typical Cano-wedge textures for a chiral nematic. The Grandjean-Cano disclination lines occur at the blue-yellow interface. The slightly curved distortion shows how sensitive the technique is to undulations in the glass of the wedge cell used here.

A special case was considered in [21]. The dielectric instability was investigated in the hybrid [4] or so-called corkscrew texture. A wedge-form cell was prepared with the planar and homeotropic orientation of a cholesteric mixture at opposite boundaries. It was shown that the Cano-Grandjean disclinations are not observed in this case and the electrooptical response... 

To obtain the pitch value we can use the Cano-Grandjean texture in a wedge-shaped cell having the helical axis perpendicular to the substrates. In this case, Rq is equal to double the distance between two neighboring disclinations [23, 44]. Rq could also be defined by measuring the positions of the optical Bragg reflection maxima, if the refractive indices are known... 

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