Helical axis, cholesterics

The transfer of the nomenclature of isotropic optical activity is surely acceptable where it evidently yields a descriptive picture of the experimental observations. However, precautions are necessary as to apparently self-evident implications, this is all the more important since the anisotropic nature of the sample is by no means obvious when observing parallel to the optical and thus helical axis. An unbiased and complete record of how a cholesteric sample acts on the measuring radiation can be obtained by el-lipsometry. This method (compare Sec. 6.4) yields a comprehensive description of the state of polarization including the degree of polarization (Rbseler, 1990). An adequate simulation can be based on the Berreman formalism (1972) rendering possible a study of particularities observed, such as pronounced depolarization related to the selective reflection band (Reins et al., 1994). 

Molecules that contain a chiral center can form chiral liquid crystalline phases, where the orientation direction rotates in a helical fashion as one moves along the helical axis, which is perpendicular to the locally preferred direction of orientation. Both nematic and smectic phases can be chiral. In a chiral nematic phase, also known as a cholesteric, as one moves along the helical axis, the director rotates sinusoidally (see Fig. 10-31. Thus, if z is... 

Figure 2. Schematic representation of the cholesteric and chiral smectic C phase. The repeating distance along the helical axis (pitch) is between 200 nm to some pm.

A sheet of cholesteric liquid crystal (pitch is / q) is sandwiched between two glass plates with the gap d being ten microns. The helical axis of cholesteric liquid crystals in the absence of a magnetic field is defined along the Z axis, shown in Figure 6.4, and 6 is the deformation angle between... 

Berreman used a 4x4 matrix multiplication method. Assuming the incident and reflected wavevectors to be in the xz plane, z being along the helical axis of the cholesteric, the dependence on the y coordinate may be ignored altogether. Writing exp [i( ut—etc., it is easily verified... 

As or Ts of opposite signs occur in pairs to form dislocations and pincements (fig. 4.2.6). Such pairing can be observed directly in the fingerprint textures which are exhibited by cholesterics of large pitch when the helical axis is parallel to the plates (figs. 4.2.7 and 4.2.8). 

Fig. 4.5.4. Helfrich s model of permeation in a cholesteric liquid crystal. At low shear rates flow takes place along the helical axis without the helical structure itself...

Fig. 4.5.5. Theoretical variation of the apparent viscosity with pitch P = 2n/q for flow normal to the helical axis of a cholesteric (or twist nematic) at low shear rates. Plot of versus P for twisted PAA. The separation between the...

Magnetic field normal to the helical axis the cholesteric-nematic... 

Fig. 4.6.3. Deformation of a planar structure due to a magnetic field acting along the helical axis of cholesteric liquid crystal composed of molecules of positive diamagnetic anisotropy. A similar deformation superposed in an orthogonal direction results in the square-grid pattern (see fig. 4.6.4). (Helfrich. )...

We next examine the effect of a magnetic field acting along the helical axis of a cholesteric film having a planar texture. If > 0 and boundary constraints are absent, there is a possibility of a 90° rotation of the helical axis because > Xi- on the other hand, boundary effects are... 

Dependence of pitch on temperature applications to thermography In most pure cholesteric materials, the pitch is a decreasing function of the temperature. An elementary picture of the temperature dependence of the pitch can be given in analogy with the theory of thermal expansion in crystals. " Assuming anharmonic angular oscillations of the molecules about the helical axis, the mean angle between successive layers... 

The local order in a cholesteric may be expected to be very weakly biaxial. The director fluctuations in a plane containing the helical axis are necessarily different from those in an orthogonal plane and result in a phase biaxiality . Further, there will be a contribution due to the molecular biaxiality as well. It turns out that the phase biaxiality plays a significant role in determining the temperature dependence of the pitch. Goossens has developed a general model taking this into account. The theory now involves four order parameters the pitch depends on all four of them and is temperature dependent. However, a comparison of the theory with experiment is possible only if the order parameters can be measured. 

When an electric field E is applied normal to the helical axis, the helix gets distorted in a manner somewhat analogous to that depicted in fig. 4.6.1 for the cholesteric case. Above a critical field given by... 

The nematic phase (N, ) is exhibited by relatively few compounds examples are hexakis((4-octylphenyl)ethynyl)benzene (fig. 6.1.1(A)) and the hexa-n-alkyl and alkoxybenzoates of triphenylene (fig. 6.1.1(e)). The Nd phase has an orientationally ordered arrangement of the discs with no long-range translational order (fig. 6.1.2(f)). Unlike the usual nematic of rod-like molecules, is optically negative, the director n now representing the preferred axis of orientation of the disc normal. The properties of this phase will be discussed in greater detail in 6.5. A twisted nematic (or cholesteric) phase, with the helical axis normal to the director, has also been identified. ... 

Static measurements of the change in sample thickness, ALILq (with Lq the thickness in the mechanically loaded state, but without external electric field), as a function of an applied electric field (parallel to the helical axis of a cholesteric monodomain sample) have been carried out [72]. To eliminate effects that are quadratic in the electric... 

Though this type of periodic structure with multiple arches of the director is difficult to generate in a nematic, it is already present in a cholesteric liquid crystal when viewed in a plane whose normal makes an oblique angle with the helical axis. The flexoelectric effect changes the periodicity of this structure under a DC field applied normal to the helical axis, effectively rotating the latter. This can be used in tmn to measure (ei — 63). ... 

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... 

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.

Kent Display is a pioneer of cholesteric liquid crystal displays (ChLCDs) in which the director of the liquid crystal twists around a helical axis [3]. The remarkable property is that the cholesteric material reflects light of certain wavelengths depending on the pitch over which the director rotates. When an electric held is applied. 

Cholesteric liquid crystal (ChLC)-driven electronic paper has been investigated mainly by Kent Display [2], Since ChLCs are chiral molecules, the particular color of light depends on the pitch denoted as P, where the pitch is the distance along the helical axis for ChLC to twist 360 and is determined by the amotmt and type of chiral additive within the liquid crystal mixture. ChLCDs are driven by switching the different textures of the ChLC electrically [1, 3], as shown in Fig. 4. 

More recently, it has been theoretically predicted by Brand [81] that elastomeric networks that have chiral nematic or smectic C mesophases should have piezoelectric properties. The non-centro-symmetric material responds to the deformation via a piezoelectric response. Following this prediction, both Finkelmann and Zental have reported the observation of piezoelectricity. In one case, a nematic network was converted to the cholesteric form with the addition of CB15, 2 -(2-methylbutyl)biphenyl-4-carbonitrile [82]. By producing a monodomain, it is possible to measure the electro-mechanical or piezoelectric response. Compression leads to a piezoelectric coefficient parallel to the helical axis. Elongation leads to the perpendicular piezoelectric response. As another example, a network with a chiral smectic C phase that possesses ferroelectric properties can also act as a piezoelectric element [83]. Larger values of this response might be observed if crosslinked in the Sc state. 

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