Pitch of cholesteric

The unique properties of liquid crystals have also provided opportunity for study of novel nonlinear optical processes. An example involves the ability to modify the pitch of cholesteric liquid crystals. Because a pseudo-wave vector may be associated with the period of pitch, a number of interesting Umklapp type phasematching processes (processes in which wave vector conservation is relaxed to allow the vector addition to equal some combination of the material pseudo-wave vectors rather than zero) are possible in these pseudo-one-dimensional media. Shen and coworkers have investigated these employing optical third harmonic generation (5.) and four-wavemixing (6). 

The Helfrich-Prost model was extended in a pair of papers by Ou-Yang and Liu.181182 These authors draw an explicit analogy between tilted chiral lipid bilayers and cholesteric liquid crystals. The main significance of this analogy is that the two-dimensional membrane elastic constants of Eq. (5) can be interpreted in terms of the three-dimensional Frank constants of a liquid crystal. In particular, the kHp term that favors membrane twist in Eq. (5) corresponds to the term in the Frank free energy that favors a helical pitch in a cholesteric liquid crystal. Consistent with this analogy, the authors point out that the typical radius of lipid tubules and helical ribbons is similar to the typical pitch of cholesteric liquid crystals. In addition, they use the three-dimensional liquid crystal approach to derive the structure of helical ribbons in mathematical detail. Their results are consistent with the three conclusions from the Helfrich-Prost model outlined above. 

In the 1960s, there was already a forerunner of photochemically induced phase transition in LC (20). When mixtures of cholesteryl iodide and cholesteryl bromide with cholesteryl nonanoate were exposed to UV irradiation, the helical pitch of cholesteric LC changes as a result of photodecomposition of the halides. The reflected color shifts gradually to red with progression of photodecomposition. Pattern-wise imaging was demonstrated but the image was blurred within 15 min. since LC of small molecules is a viscous fluid. 

This technique has been applied to measure the pitch of cholesteric liquid crystals. 

PBLG solution shows the finger-print texture, seen in Figure 6.20. A pair of neighboring dark-bright stripes corresponds to a half period of the helix, P/2, which is about a few microns. It is a practical means of estimating the pitch of cholesteric liquid crystals. 

Sagisaka T, Yokoyama Y. 2000. Reversible control of the pitch of cholesteric liquid crystals by photochromism of chiral fulgide derivatives. Bull Chem Soc Jpn 73(1) 191 196. 

The Cano-wedge method is an experimental technique to measure the pitch of cholesteric Uquid crystals. It consists of a flat substrate and a hemisphere with a cholesteric Uquid crystal sandwiched between them as shown in Figure 1.22(a). At the cento, the spherical surface touches the flat surface. On both the flat and spherical surfaces there is a homogeneous alignment layer. The intrinsic pitch of the Uquid crystal is Pg. Because of the boundary... 

The liquid crystal mesophases provide various opportunities for thermal reorientation for instance, heating alters the pitch of cholesteric helices. Reference 14 considered nonlinear optical properties of C smectics associated with changes in the molecular orientation angle during heating. In this section we show that thermal orientation effects are also present in nonuniformly oriented nematics. 

Cholesteric liquid crystals (CLCs) show very distinctly that molecular structure and external fields have a profound effect on cooperative behavior and phase structure (see also Chapters 2 and 3). CLCs possess a supermolecular periodic helical structure due to the chirality of molecules. The spatial periodicity (helical pitch) of cholesterics can be of the same order of magnitude as the wavelength of visible light. If so, a visible Bragg reflection occurs. On the other hand, the helix pitch is very sensitive to the influence of external conditions. A combination of these properties leads to the unique optical properties of cholesterics which are of both scientific and practical interest. 

Small concentrations of guest molecules may induce dramatic changes in the pitch of cholesteric liquid crystals. The corresponding (reflection) color response may be exploited in analytical chemistry as described in Section 6. 

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