Cholesteric helix

The sense of the cholesteric helix must be positive in the case of CELLOH and negative for CTA. The reason for the hi er optical rotations for the CELLOH solutions compared to the CTA solutions is not obvious based on the number of chiral centers per structural unit, but may be related to the tightness of the pitch. While some data (17) exists on the pitch of CTA in TFA-CH2CI2. none is available for CELIXIH in TFA-CH2Q2 due to the small domain size of the mesophase, that is, a fingerprint pattern is not observed in the case of CELLOH. 

The straight-rod model predicts a right-handed cholesteric helix for 96 and a left-handed one for PBLG and schizophylan, which is in agreement with experimental results.280 In the threaded EFJC model, the flexibility of the macromolecular helix can be freely chosen. The handedness of the cholesteric phase is based on entropic hard core repulsion phenomena between the helices and an enthalpic chiral dispersion force. Right-handed mesophases were predicted for solutions of 96, 97, and schizophylan. However, only for 96 this was in agreement... 

Fig. 5.17 Thermal (helix-inverting) relaxation of CLC doped with overcrowded alkene dopant, as followed by UV/Vis spectroscopy. The data points correspond to the right edge of the selective reflection band. The top panel shows the reflection colors and pictograms of the cholesteric helix. Reproduced with permission from [106]. Copyright 2013 Royal Society of Chemistry...

The expected preference of a statistical distribution of the mesogenic side chain has so far been only realized by the copolymerization in which n = 2 n.p = 12 and only if the monomer ratio is 1 1. Other compositions also led to smectic phases. The best proof for its cholesteric structure is its selective reflection of left-circular polarized light in the visible which indicates a left-handed cholesteric helix of the polymer. The structure has been established also by x-ray investigations (8). This copolymer is the first enantiotropic cholesteric polymer. 

If an electric field is applied perpendicular to the helical axis, the helix starts to unwind and, for a sufficiently high value of the field, will be completely unwound. The unwinding of a cholesteric helix is a dramatic and spectacular event and this probably masked the less spectacular event that takes place long before in the same geometry, namely that the field tilts the helix axis in a plane perpendicular to the field. This is the same as saying that the optic axis (the axis of the oblate cholesteric indicatrix) tilts in that plane. The effect is linear in the electric field and therefore arises from a... 

V/pm above which the structure became degraded by the field. At these field strengths the brightness was still relatively small. This device would need compensation foils to ensure an acceptable viewing angle in the dark state. We have found that on top of the indium-tin-oxide (ITO) electrodes, where the electric field lines are normal or tilted to the cell plane instead of parallel to it, the cholesteric helix can be reoriented into... 

For cholesteric liquid crystals, the wavelength of selective light reflection Xj is related to the pitch of the cholesteric helix P in the following manner Xj =nP, where n is the refractive index. It is evident that for a cholesteric mesophase with selective reflection of the... 

The cholesteric phase is similar to that of the nematic phase on a local scale. As in the nematic phase, the molecules can be described by a director. However, the director in the cholesteric phase is twisted about an axis normal to the molecular orientation, following a helical path (Figure 1.3). The distance over which the molecular director rotates by 2tt along the helix axis is defined as the length of the cholesteric helix pitch, P. The twist is right-handed or left-handed depending on the molecular conformation. Iridescent colors are characteristic of cholesteric phases [1,2]. 

The wavevectors of the incident light and the cholesteric helix have the same amplitude, kj = q. ... 

Now we would like to understand why only one diffraction maximum is observed in the normal reflection from the cholesteric helix and why the reflected light is circularly polarized. Therefore, at first, we write the Bragg condition on account of possible higher diffraction orders ... 

The appearance of the high harmonics in the director distribution results in considerably faster electro-optical switching. The dynamics of the cholesteric helix in the electric field is described by the balance of viscous, elastic and electric torques in the infinitely thick sample is given by... 

For instance, the third harmonic of the distorted helix relaxes nine-times faster than the first one and this agrees with experimental data showing submillisecond response times of the cholesteric helix in the external electric field. 

Blinov, L.M, Belyayev, S.V., Kizel , V.A. High-order reflections Irom a cholesteric helix induced by an electric field. Phys. Lett. 65A, 33—35 (1978)... 

Fig. 6. Computed dependence of perceived contrast ratio on cell thickness for a reflective display with three different guest-host dyes having the indicated dichroic ratios R. Dye concentration adjusted to maintain an on-state brightness of 50%. Concentration of chiral dopant adjusted to maintain 3 turns of the cholesteric helix in the cell.

Fig. 8. Dependence of contrast ratio upon the number of turns of the cholesteric helix in the layer for different host birefringences An. The three curves are computed for a hypothetical neutral dye with R=6.7 dissolved in different liquid crystal hosts. Indicated birefringence values are typical for the cyclohexylcyclohexane (CCH), phenyl-cyclohexane (PCH) and phenylpyrimidine (PPYR) liquid crystal substance classes. Values used for the computation nQ=1.50, d=10.0 ym and on-state brightness=50%.

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