Liquid crystals pitch length

In particular most of the early studies on CPL were based on the incorporation of a luminescent achiral chromophore in a chiral nematic or cholesteric liquid crystal. Chiral nematic liquid crystals (CNLC) are intrinsically birefringent and exhibit a helical supramo-lecular architecture, which is characterized by the pitch length p (Figure 5.11). 

FIGURE 5.11 Supramolecular, helical architecture and definition of pitch length p of chiral nematic liquid crystals. 

Schuster et al. reported that the photochromism of a fulgide could change the helical pitch length of a cholesteric liquid crystal. 27 They added an indolylfulgide 3 (5.2 % w/w) to a cholesteric liquid crystal composed of 4-cyano-4 -pentylbiphenyl 26 (5CB) and 1.35 % (w/w) of a chiral cyclic ether (R)- 27, prepared from (R)-binaphthol. The cholesteric pitch length could be changed reversibly between 30 and 42 pm, after UV and visible light irradiation, respectively. 

The terminus of chirality induction is used for processes, in which the structural information of a chiral molecule is transferred to an initially achiral collective which then will form a superstructural chiral phase. One of the most prominent examples can be found in the field of liquid crystals The doping of a nematic LC phase with chiral mesogenes (dopants) can lead to a twisted, helical cholesteric phase. Noteworthy is the fact that the length scales of the chiral information that characterizes the involved species can differ by several orders of magnitude a few Angstrpms in a single chiral molecule, but the pitch of a helical cholesteric phase amounts typically a few microns. 

Although the control of the phase and pitch length of a liquid crystal using a fulgide dopant has also been reported [92], no asymmetric induction is described for this system. 

Fig. 4.1.15. First and second order reflexion spectra of a cholesteric liquid crystal film (0.45 0.55 mole fraction mixture of 4 -bis(2-methylbutoxy)-azoxybenzene and 4,4 -di-n-hexoxyazoxybenzene) 15 pitch lengths or 11.47 on thick. Angle of incidence 45°. Polarizer and analyser are parallel to the plane of reflexion for and normal to it for measurements. The small oscillations are interference fringes from the two cholesteric-glass interfaces. (After Berreman and Scheffer. )...

It is well known that a nematic liquid crystal readily adopts a helical configuration if a small amount of a cholesteric is added to it. For low concentrations of the cholesteric, the inverse pitch is a linear function of the concentration, but at higher concentrations the linear law is not obeyed. 44 The curve attains a maximum at a certain concentration, beyond which it decreases. It turns out, for example, that the twist per unit length of pure cholesteryl propionate is actually less than that of its... 

FIGURE 5.2 Liquid crystals, (a) Smectic crystals the ends of the molecules are on a plane, (b) Nematic crystals the ends of the molecules do not match, (c) Cholesteric crystals the molecules in each layer are arranged in a manner similar to nematic crystals, but the angle changes from plane to plane of the molecules, forming a helix of pitch length p. 

Figure 11.19 Variation of pitch length with temperature for a thermochromic chiral nematic liquid crystal.

Use the tensor representation to numerically calculate the hquid crystal director configuration of a cholesteric liquid crystal in a hybrid ceU. The ceU thickness and length arc = 10 pm and = 20 pm, respectively. The director is only a function of x (paraUel to the cell surface) and z (perpendicular to the ceU surface). On the top surface of the ceU the hquid crystal is anchored homeotropicaUy, whUe at the bottom of the ceU the hquid crystal is anchored homogeneously. The pitch P of the hquid crystal is 5 pm. InitiaUy the hquid crystal in the cell is in the isotropic state. The parameters of the hquid crystal are j = 6 x 10 N, K22 = 3 X 10 N, and AC33 = 10 x 10 N. Using flie periodic boundary condition in the X direction, plot the director configuration in the xz plane. 

The pitch of a chiral nematic phase is the distance along the hehx over which the director rotates by 360°. It should be noted, however, that the stmcture repeats itself every half pitch due to the equivalency of and -ft Interesting optical effects occur when the wavelength of light in the liquid crystal is equal to the pitch. These will be described at length in Chapter 11. The pitch of a chiral nematic phase can be as short as 100 nm. Mixing the two optical isomers in various proportions allows the pitch to be increased from the pilch of either of the two pitre optical isomers. A racemic mixture (equal parts of each optical isomer) possesses an infinite pitch and is therefore nematic. Finally, the chiral nematic phase is often ealled the cholesteric phase, since many of the first compounds that possessed this phase were derivatives of cholesterol. 

A cholesteric liquid crystal contains both nematic and chiral moieties in a single molecular entity or as a binary mixture. Consisting of a helical stack of quasinematic layers, a well-aligned cholesteric film can be characterized by handedness and helical pitch length, p, as depicted in Figure 5 ... 

The second living system feature we select is that they are chiral. We take this to mean broken mirror symmetry. In liquid crystals, chirality is expressed as a macroscopic helix with a pitch, />(,. In cholesteric liquid crystals, 1500 A < Pq < oo, and qo, its wavevector (wavenumber qo = 2it/po), is perpendicular to n, the direction of orientational order. The existence of this intrinsic equilibrium length has several implications of which we mention two particularly insightful ones [1], [2]. 

Arguments for the minimal model system being the traveling cholesteric liquid crystal-isotropic liquid phase boundary are given in this section. The sample is prepared so that the length scale imposed on it by the non-equilibrium driving forces is comparable to the cholesteric liquid crystal s equilibrium length, its pitch. In a pattern formation context, knows time ... 

Figure 7-18 Chiral cholesteric (nematic) liquid crystal structure. The dotted line shows a helical path within the medium. Pitch length p = 360 rotation.

Figure 6. Mid-cell tilt angle versus voltage for a range of cells having different twist angles, showing the increase in slope and onset of bistability resulting from the supertwist effect. The liquid crystal is E7 in each case, with the pitch length matched to the twist angle.

The Helmholtz free energy represented in this equation is extremal in configurations adopted by the liquid crystal director [14], The symbols have their usual meaning 9 and (j) are, respectively, the tilt (measured from the cell normal) and twist angles of the nematic director P is the pitch length of the chiral nematic fluid and D is the dielectric displacement, which is constant through the... 

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