Anisotropy and Birefringence

Liquid crystal phases are anisotropic, and the c director is used to indicate the direction of molecular orientation. In the case of the (a) columnar discotic, (b) nematic, and (c) smectic C phases, make a sketch of the molecular arrangement and indicate the c director. 

Which of the following liquid crystal samples will be birefrin-gent when viewed on the polarizing microscope between crossed polarizers (a) homeotropically aligned nematic phase, (b) the isotropic phase, (c) a planar-aligned smectic A phase, (e) the cholesteric phase with a focal conic texture, (d) the isotropic phase of a discotic material  

A thin slab of nematic liquid crystal is filled between two glass parallel plates for use as a quarter-wave plate with a 488 nm laser. If the liquid crystal has a birefringence of 0.22, calculate the thickness of the liquid crystal slab. 

When a planar-aligned liquid crystal slab with a birefringence An and a uniform director is placed between crossed polarizers and the slab rotated between the polarizers, the total transmitted intensity varies as sin 20, where 6 is the angle between the polarization direction of the first polarizer and the direction. Starting with an incident wave with intensity /q, show that (a) the ordinary and extraordinary waves have a phase shift 

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An ordered packing of macromolecules may also cause an optical anisotropy and birefringence, which are characteristic, for instance, of polymer spherulites. Because of the radial anisotropy of a spheruHte and the convergence of beams in the spherical structure, the interference picture represents the so-caUed Maltese cross, the center of which is located in the center of spherulite. No calculations are performed using such a picture but the photoelasticity method is very efficient in revealing qualitatively the presence of any spherulites, or a mesomorphic or ordered sate of polymeric chains. 

To get the best results with dye-doped TN displays the liquid crystal fluid must have low viscosity, appropriate dielectric anisotropy, and birefringence. The dyes must have all the advantages already discussed in the Sec. 3.4.8 on Heilmeier displays. 

Understand the concepts of anisotropy and birefringence as they apply to liquid crystals. 

Optical Properties. When light falls on an object, it is either partially absorbed, reflected, or transmitted. The behavior of the object as it relates to each of these three possibiUties determines visual appearance. Optical properties of fibers give useful information about the fiber stmcture refractive indexes correlate well with fiber crystalline and molecular orientation and birefringence gives a measure of the degree of anisotropy of the fiber. 

There has been an increasing interest in liquid crystals containing fluorine atoms because fluorination produces important changes in the melting temperatures, viscosity, birefringence, dielectric anisotropy and mesophase stability. This why structure-mesomorphism relationship studies were carried out in mono- and... 

The optical apparatus used in this work was described in section 8.6 and has the capability of providing both Raman scattering and birefringence measurements simultaneously. The Fourier expansion of the overall Raman scattering signal is given by equation (8.51), and the coefficients are given by equations (8.52) to (8.54). In these expression, a simple, uniaxial form for the Raman tensor was assumed. From these coefficients, the anisotropies in the second and fourth moments of the orientation distribution can be solved as... 

The major difference between the configuration of the OMI sandwich cell and other STN-LCDs is that the optical path difference (5 = And 1 pm) is much lower. There is no requirement for a significant pretilt (0 < 0 < 5°), the twist angle of the chiral nematic layer is lower (180°), the front polariser is parallel to the nematic director (a = 0°) and the polariser and analyser are crossed (P = 90°). The 180° twist gives rise to strong interference between the two elliptically polarised rays. If the optical path difference is small, e.g. 0.4 m, a bright, white, non-dispersive off-state is produced. The chiral nematic mixture should be of positive dielectric anisotropy, low birefringence and exhibit a low cell gap to pitch ratio dip 0.3). 

As to infrared spectroscopy - and the same holds good for other spectral ranges -the orientational order is readily observable in form of dichroism Being related to the molecular shape, the molecular polarizability is anisotropic as well. By the alignment of the molecules this anisotropy is transferred to the sample, however damped due to the imperfect order as described by the order parameters. As a consequence, the dielectric function and furthermore the (complex) refractive index are anisotropic, so that eventually (linear) dichroism and birefringence occur. 

Dependence of Flow Birefringence on Molecular Weight, Anisotropy and Chain Rigidity... 

The relationship between stress and polymer orientation implies that there is a proportionality between the polymer stress tensor optical anisotropy or birefringence. This proportionality is called the stress-optic law (Janeschitz-Kriegl 1983) and is expressed as (Section 1.6.3)... 

Figure 7.5. Correlation between indentation anisotropy AH and birefringence An for injection-moulded oriented PE. AH and An were measured at the centre of the PE bar along the z axis (Fig. 7.2). (After Rueda et al, 1989.)...

Saito, H., Inoue, T. (1987). Chain orientation and intrinsic anisotropy in birefringence-free polymer blends,25, 1629-1636. 

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