Nematic liquid crystals optical anisotropy

Note 1 The nematic liquid crystal must have a negative dielectric anisotropy (Af < 0), and a positive anisotropy (Aa > 0). The optical texture corresponding to the flow pattern consists of a set of regularly spaced, black and white stripes perpendicular to the initial direction of the director. These stripes are caused by the periodicity of the change in the refractive index for the extraordinary ray due to variations in the director orientation. 

The application of an electric field above the threshold value results in a reorientation of the nematic liquid crystal mixture, if the nematic phase is of negative dielectric anisotropy. The optically active dopant then applies a torque to the nematic phase and causes a helical structure to be formed in the plane of the display. The guest dye molecules are also reoriented and, therefore, the display appears coloured in the activated pixels. Thus, a positive contrast display is produced of coloured information against a white background. The threshold voltage is dependent upon the elastic constants, the magnitude of the dielectric anisotropy, and the ratio of the cell gap to the chiral nematic pitch ... 

The use of birefringence to determine the behavior of 5( 7) is a natural choice since the principal characteristic of the nematic phase is optical birefringence i.e., the refractive index differs for light polarized parallel (/ n) or perpendicular (%) to the axis of molecular alignment. Eor a nematic liquid crystal, the director n specifies this optical z axis and / n = and = Dg are called the extraordinary and ordinary refractive indices, respectively. In general, rig > rig and the difference is the refractive index anisotropy (birefringence)... 

Blinov, L. M., Barberi, R., Kozlovsky, M. V., Lazarev, V. V., and de Santo, M. P. Optical anisotropy and four possible orientations of a nematic liquid crystal on the same film of a photochromic chiral smectic polymer. / Nonlinear Opt. Phys. Mat. 9, 1 (2000). 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

Besides aligning liquid crystals, external electric fields can also change the orientational order and thus the electro-optical properties of liquid crystals. When the long molecular axis of a liquid crystal molecule, whose anisotropy of polarizability is positive, is parallel to the applied field, the potential of the molecule is low. Thus the applied field suppresses the thermal flue-mation and increases the order parameter. Now we discuss how the orientational order of a nematic liquid crystal changes with applied fields. Using the Landau-de Gennes theory, the free energy density of a liquid crystal in an electric field (when the liquid erystal director is parallel to the field) is [4]... 

The two indices of refraction in a nematic liquid crystal equal the square root of the corresponding relative permittivities. Therefore it is not the optical anisotropy or birefringence that is most directly related to the order parameter but the difference in the... 

Planar-aligned nematic liquid crystals also display a nonlinear birefringence which has been used to produce switches in both transmitted power and polarization state. This, allied with their dielectric anisotropy and thus sensitivity to applied electric fields, permits their application to a wide range of optical/optoelectronic devices. 

TABLE 2.1. Optical anisotropy correlation with molecular structure of nematic liquid crystals [28]. 

However, it is well known that a mechanical deformation of a conventional, isotropic polymer network causes anisotropy. Under deformation the chain segments become oriented according to the symmetry of the external field and the state of order of the network can be characterized by an order parameter similar to that of nematic liquid crystals. Very early mechanical experiments on nematic polydomain elastomers actually demonstrate that a uniaxial deformation of a nematic elastomer converts the polydomain structure into a macroscopically xmi-formly ordered monodomain network [44]. This is shown in Fig. 2, where the opaque polydomain becomes optically transparent and converts into a monodomain... 

A nematic liquid crystal with a uniform alignment of the director n behaves like a uniaxial crystal with positive optical anisotropy > <, (where He = i is the refraction index for the extraordinary beam and <, = is the refraction index for the ordinary beam). We can consider the cholesteric structure as a special case of a nematic structure when the director n describes a helix. As is shown in Figure 6.1, the optical anisotropy in CLCs is negative, i.e., rioh > K /i, where tiei, = np and n h = xa are the refractive indices for the extraordinary and ordinary beams, respectively. The index h indicates that the macroscopic optical axis corresponds to the direction of... 

When an electric or magnetic field is applied to a liquid crystal cell, a texture transition occurs to minimize the free energy of the system. These texture changes in cholesteric liquid crystals are physically similar to the Frederiks transition in a nematic liquid crystal and result in a significant change in the optical properties of the layer. Texture transitions have been reviewed previously [8, 9] with allowance made for the sign of the dielectric or diamagnetic anisotropy, the initial texture, and the direction of the applied field. Here, we consider only the instability of the planar cholesteric texture, which has been widely discussed in recent literature. 

One of the most striking anisotropic properties of nematic liquid crystals is their optical anisotropy, which is manifested as birefringence. It was this property of liquid crystals that led to their discovery about 100 years ago, and early in the history of liquid crystals attempts were made to determine their birefringence. The first rough estimation was made by Lehmann in 1905 [1], who placed the nematic phase of 4,4 -bis(methoxy)azoxybenzene between a plane glass plate and a lens with a large radius of curvature. The birefringence... 

Equation (11.149) shows that G is independent of the optical anisotropy As of the NLC, and determined mainly by the elastie eonstant 2 of the NLC. This is due to the fact that, in Equation (11.148), we have the faetor (n — in the denominator that cancels the factor el=(nl—nlf (n +ngf in the numerator. is therefore dependent only on the elastie eonstant of NLCs. This inverse dependence of the gain on the elastic constant K suggests that for nematic liquid crystals with lower elastic constant, the effective gain constant will be proportionately larger. 

Apart from high strength materials formed from nematic polymer fibres, most applications of nematic liquid crystals depend on their anisotropic optical properties. As a consequence the refractive indices of nematics are of prime importance in the development of materials for applications. The refractive indices are determined by the molecular polarisability coupled to the mientational order of the mesogens in the liquid crystal phase, so refractive indices can provide a direct probe of the order parameter. Furthermore the optical properties of liquid crystal films are frequently used to determine phase behaviour, identify phase types through characteristic optical textures or explore the properties of defects, and such experiments rely on the anisotropy in the refractive index of the material. The first tool of a liquid crystal scientist is the polarising microscope, which emphasises the importance of optical properties in general and refractive indices in particular to the stufy of liquid crystals. 

The optical anisotropy (i.e. the birefringence) of a nematic liquid crystal is a very important property for the contrast ratio and viewing angle in liquid crystal displays. The optical anisotropy of the nematic is caused by the anisotropy of the molecular polarisability of the constituent anisometric molecules (rod-like molecules) and their long range orientational ord. ... 

---