Untwisting of the Cholesteric Helix

1 De Gennes-Meyer Model for Field Induced Cholesteric-Nematic Transition 

In the simplest case, this transition is observed in a cholesteric with positive dielectric or diamagnetic anisotropy in the electric or magnetic field applied perpendicular to the helical axis. Let a helix has a pitch Pq in the absence of a field and the thickness of a sample is much larger than Pq. Therefore, the boundary 

The threshold field can be calculated thermodynamically by comparison of the free energy of the helical and uniform structures in the presence of the field. In our geometry, the free energy density of a cholesteric in a magnetic field is 

Introducing the field coherence length = K22 /integrating over one period of the helix Pq along the z-axis we find the free energy 

The Euler equation (8.22) corresponding to the minimal free energy density (12.27) within a period of the stmcture reads  

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Figure 20. Schematic representation of untwisting of the cholesteric helix by a magnetic field [1].

The phenomenon of untwisting of the cholesteric helix near the transition into the smectic phase is especially clearly manifested in homopolymer 2.3 (Table 7.4) with a decrease in the temperature the temperature region of existence of the cholesteric mesophase in this polymer does not exceed 5 C. For this polymer, the values of the S -Ch and CA-rf transition temperatures increase with an increase in the molecular weight [84], which results in a shift in the region of the existence of the cholesteric mesophase for the different firactions along the temperature scale. A sharp difference in the pitch of the cholesteric helix for fractions with a different molecular weight is the consequence of this (Fig. 7.17). 

The guest host effect realized in polymers on addition of a dichroic dye and untwisting of the cholesteric helix open up certain prospects for the construction of solid optical elements based on LC polymers such as dichroic polaroids and selective filters. The important possibility of obtaining ferroelectric polymeric LC materials was recently demonstrated in [67]. 

FIGURE 6.15. Illustration of the field-induced untwisting of a cholesteric helix in a thin cell with a planar orientation by the walls. 

The absence of a significant effect of the chain structure of the macromolecules on the twist elasticity constant K i was also found in [13] in studying the thresholds of untwisting of the cholestoic helix of comb-shaped copolymers of the acrylic series (Vm, IX). Changing the degree of polymerization within the limits of SO to ISO has almost no effect on the value of Kj2, [ (4-7) 10 dyne], which coincides in order of magnitude with the twist elasticity constants of low-molecular-weight nematic-cholesteric mixtures. 

The optical properties of cholesteric liquid crystals are very specific and are determined by the pitch and arrangement of the axis of the helix and the polarization of the incident light. In an external field changes occur both in the direction of the axis of the helix (texture transitions) and in its pitch (untwisting of the helix). Before considering these field variations let us give a brief account of the optical properties of cholesteric liquid crystals in the absence of a field. Comprehensive reviews of the topics have been given recently in [1, 2]. 

Field untwisting of a helix for thin cells with planar boundary conditions occurs differently from the case of an infinite cholesteric medium. For a field perpendicular to the axis of a cholesteric helix in a planar texture, a stepwise change in the pitch with an increase in the field is predicted... 

Stepwise untwisting of the helix, by an electrical field perpendicular to its axis, has been observed for the case of a planar cholesteric texture with As > 0, and with strong anchoring of the molecules to the limiting surfaces... 

Figure 22 Photoinduced untwisting of (a) the cholesteric helix in the films of (b) an LC copolymer containing chiral-photochromic monomer units and (c) a mixture of nematic homopolymer and chiral-photochromic...

Field untwisting of a helix for thin cells with planar boundary conditions occurs differently from the case of an infinite cholesteric medium. For a field perpendicular to the axis of a cholesteric helix in the planar texture, a stepwise change in the pitch with increase in the field is predicted [128]. The size of the step increases with a decrease in the ratio 2electric field perpendicular to the helix axis has been observed for the case of planar cholesteric texture with a>0 and with strong anchoring of the molecules to the limiting surfaces [129]. Under these conditions the relaxation of the field-induced (i.e. untwisted) state is accompanied by the formation of spatially modulated structures in the form of strips or grids. 

If the cell walls are treated to produce a homeotropic orientation in a cholesteric liquid crystal with As < 0, for a particular relation between the thickness and the helical pitch (1 < Po/d < 2) a new texture appears under the influence of the electric fleld. These are the bubble domains [77] mentioned in Section 6.1.1. When there is no field present the liquid crystal has a homeotropic nematic structure, since the helix is untwisted by the walls. The application of a low-frequency field induces an electrohydrodynamic instability. After the removal of the field a new stable texture appears in the form of cholesteric bubbles dispersed through the homeotropic nematic phase. Thus a memory is created, while erasure of the information can be performed either by a high-frequency field or by the mechanical... 

The linear-in-field fiexoelectric coupling, discussed in Section 4.5, for nematics can modity the threshold field for helix untwisting in cholesterics. The flexo-effect stabilizes the helical structure, thus, it results in a decrease of an apparent dielectric anisotropy [40]... 

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