Distortions chiral nematics

Fig. 7.3. The deviation of the optic axis in a cholesteric (hard-twisted chiral nematic, p <, where p is the cholesteric pitch and A is the wavelength of light) when an electric field E is applied perpendicular to the helical axis. The cholesteric geometry allows a fiexoelectric polarization to be induced in the direction of E. The plane containing the director, which is perpendicular to the page in the middle figure and is shown in the lower figure, illustrates the splay-bend distortion and the corresponding polarization that arises. (After Rudquist, inspired by Meyer and Patel.

Vanin et al. studied order proflles of the perdeuterated laurate chain in chiral and achiral phases by means of deuterium NMR. The quadrupole splittings measured for the sequence of CD2 moieties are all quite similar for the nematic and chiral nematic phase the conclusion was that chiral distortions of the micellar shape must be very small. Their proposal for the mechanism behind the phase chirality is analogous to the one for polypeptides an asymmetric point charge distribution which in this case was speculated to be created by the chiral dopant on the micellar surface [19]. Radley and Tracey prepared samples from a racemic detergent and observed high fluidity, whereas those consisting of some enantiomeric excess showed a significantly increased viscosity [30]. But this is no proof for the association of micelles to necklaces. 

Torsional distortions can now be written in terms of derivatives of a and c, and it is found [10] that nine torsional elastic constants are required for the smectic C phase. Mention should be made of the biaxial smectic C phase, which has a twist axis along the normal to the smectic layers. This helix is associated with a twist in the c-di-rector, and so elastic strain energy associated with this can be described by terms similar to those evaluated for the chiral nematic phase. 

External field distortions in SmC and chiral SmC phases have been investigated [38], but the large number of elastic terms in the free-energy, and the coupling between the permanent polarization and electric fields for chiral phases considerably complicates the description. In the chiral smectic C phase a simple helix unwinding Fr6ede-ricksz transition can be detected for the c director. This is similar to the chiral nematic-nematic transition described by Eq. (83), and the result is identical for the SmC phase. Indeed it appears that at least in interactions with magnetic fields in the plane of the layers, SmC and SmC phases behave as two dimensional nematics [39]. 

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.

As discussed in Sec. 2.2.2.1, the foundations of the continuum model were laid by Oseen [61] and Zocher [107] some seventy years ago, and this model was reexamined by Frank [65], who introduced the concept of curvature elasticity to describe the equilibrium free energy. This theory is used, to this day, to determine splay, twist, and bend distortions in nematic materials. The dynamic models or how the director field behaves in changing from one equilibrium state to another have taken much longer to evolve. This is primarily due to the interdependency of the director it (r, t) and v (r, /) fields, which in the case of chiral nematics is made much more complex due to the long-range, spiraling structural correlations. The most widely used dynamic theory for chiral... 

Figure 32. Schematic representation of the Helfrich or periodic distortions in a planar chiral nematic due to a magnetic field acting parallel to the helix axis (z). The lines denote equivalent director fields (in the x, y) plane (A K>0) and the periodicity is 2n k. ...

Thus the periodic distortion depends critically on the relationship between the chiral nematic pitch and the cell dimensions. Therefore these phenomena are only observed for cells in which the thickness is considerably greater than the helix pitch [135]. For low threshold fields, the diamagnetic anisotropy should be high with low bend and twist elastic constants. 

Figure 33. Schematic representation of the untwisting of a chiral nematic helix for a magnetic field H normal to the helix axis (z) with A f>0. A denotes regions where the helix becomes distorted and B denotes regions of 180° twist walls. For the helix has...

Figure 35. Representation of the director ( v, z) plane and the helix axis (x=h) for a chiral nematic undergoing flexoelectric distortion in negative ( <0) and positive ( >0) polarity electric fields ( ,). The z axis is out of the plane of the figure towards the observer.

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