Liquid crystal, wedge

Figure 8. Wedge disclinations, with rotational strength -it, in a cubic crystal and in a liquid crystal. Note that the molecular scale of the liquid crystal is much larger than the atomic scale of the cubic crystal.

The Cano wedge can be used to measure the cholesteric pitch. Two substrates are wedged by a small angle 2y. The cholesteric liquid crystal between the substrates is homogeneously aligned. Under polarized microscopy, the equally spaced disclinations appear at the middle of the wedge. The separation of the lines 2d is associated with the pitch P... 

Numerical Analysis of Layered Liquid Crystals in a Thin Wedge... 

Theoretical work on dislocations in smectic liquid crystals was first done by de Gennes Q) followed by Pershan (2). For an incompressible smectic A liquid crystal in the hnear hydrodynamic approximation, the elastic strain can be described in terms of a single variable w(x,y,z) Aat specifies local displacements of the smectic layers. The stress-strain field was derived for an isolated dislocation in an unbounded liquid crystal media and extended their results to bounded media using the concept of an "image dislocation." The solution is valid for a thick wedge (relative to a characteristic length of the dislocation) of small angle. However, the... 

We only consider here conditions in which the liquid crystal does not flow and the wedge surfaces are stationary. In this case the permeation process does not occur and the elastic splay and compression forces are in balance. Obviously, the publication process involves relative motion of the surfaces and a considerably more complex formulation. A study combining the flow considerations of Ref.(7) and the present work focussing only on dislocations is in progress. 

Figure 1. Schematic of thin wedge homeotropically filled with smectic liquid crystals.

Figures 3a and 3b show the layer displacement and corresponding layer locations assuming that there are no dislocations. The layer displacement looks like a twisted trapezoid and the layers accommodate the wedge angle by reducing their thickness, just like an elastic solid. This behavior is quite unrealistic for a smectic liquid crystal when the compression is greater than the order of one layer thickness.

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. 

Structural forces due to long-range positional order are quite easily observed in the smectic A liquid crystals. SFA measurements have been performed on lamellar lyotropic smectics [42,43] and in thermotropic smectics [44-46]. These works extend to a nanometer scale the early studies on elasticity, viscoelastic response and layers instability of smectic A, observed in macroscopic wedge-shaped piezoelectric cells [47,48]. 

J.H. Wild, K. Bartle, M. O Neill, S.M. Kelly and R.P. Tuffin, Synthesis and mesomorphic behaviour of wedge-shaped nematic liquid crystals with flexoelectric properties, Liq. Cryst. 33(6), 635-644, (2006). 

Figure 11 shows the dependence of the critical unwinding voltage Vf on the cell thickness-to-pitch ratio for a cholesteric layer with perpendicular boundary orientation. For these measurements two reusable cells, having thicknesses of 7.8 and 10.9 ym, were filled with various mixtures of the nematic liquid crystal RO-TN-103 and the chiral substance CB 15.We used the Cano wedge technique to determine the pitch of the mixtures and found the simple inverse relationship... 

Figure 2.10. The texture of a cholesteric liquid crystal in the Cano wedge the number of half-pitches located in the gap varies as a function of the thickness h x).

Figure 2.15. Variation of the cholesteric pitch versus the magnetic field measured by the method of the Cano wedge by Durand et al. [5]. The liquid crystal used in this experiment was the mixture of PA A with cholesteryl chloride at concentration 0.02%. The continuous line corresponds to the theoretical prediction by de Gennes.

In between the two domes, there is some kind of liquid-region wedge. At the bottom of this region, a third type of liquid crystal, the so-called cubic, is often found at the overlap between the lamellar and hexagonal liquid-crystal regions. Whereas lamellar and... 

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