Nematic director

FIG. 13 A colloidal liquid crystal. The rod-like particles point to a preferred diree-tion, called the nematic director. The solvent is disordered. 

The transition moment of the dye should align well with the nematic director -the order parameter... 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

A cholesteric, or chiral nematic (N ) phase. This is a positionally disordered fluid in which the constituent molecules align on average their axes along a common direction called the nematic director. Being the DNA helices chiral, the orientational order develops an additional macro-helical superstructure with the twist axis perpendicular to the local director. The phase thus consists of local nematic layers continuously twisted with respect to each other, with periodicity p/2 (where p is the cholesteric pitch see Fig. 8a) [27,28]. For 150-bp helices, the N phase appears at a concentration around 150 mg/mL in 100 mM monovalent salt conditions. This LC phase is easily observed in polarized optical microscopy. Since the N pitch extends to tens of micrometers (that is, across... 

In a hard-rod system, at sufficiently high volume fraction a transition is usually expected from the nematic to the smectic A phase [37], a lamellar phase with layers perpendicular to the nematic director. However, as elegantly demonstrated by Livolant [29], in DNA the smectic phase is replaced by columnar ordering this behavior can easily be explained on the basis of strand flexibility [38] or length polydispersity [39], both favoring the COL phase over smectic. 

The nematic director n, which describes the local average orientation of the molecular long axes... 

The nematic free energy density describes the energy associated with the spatial variation in the nematic director ... 

The free energy density terms introduced so far are all used in the description of the smectic phases made by rod-like molecules, the electrostatic term (6) being characteristic for the ferroelectric liquid crystals made of chiral rod-like molecules. To describe phases made by bent-core molecules one has to add symmetry allowed terms which include the divergence of the polar director (polarization splay) and coupling of the polar director to the nematic director and the smectic layer normal ... 

The first term in (7) describes the coupling between the polarization splay and tilt of the molecules with respect to the smectic layer normal. This coupling is responsible for the chiral symmetry breakdown in phases where bent-core molecules are tilted with respect to the smectic layer normal [32, 36]. The second term in (7) stabilizes a finite polarization splay. The third term with positive parameter Knp describes the preferred orientation of the molecular tips in the direction perpendicular to the tilt plane (the plane defined by the nematic director and the smectic layer normal). However, if Knp is negative, this term prefers the molecular tips to lie in the tilt plane. The last term in (7) stabilizes some general orientation (a) of the polar director (see Fig. 7) which leads to a general tilt (SmCo) structure. 

Fig. 12 Layer and director structure in 2D phases which occur due to the preference of the system to polarization splay. Upper line, side view on the layer lower line, top view on the layer. Red arrows show the polar director. Blue nails show the projection of the nematic director to the smectic plane. There is no blue nail in the centre of the wall, meaning that the cone angle is reduced to zero...

Finally, dispersions of MWCNT in chiral nematic liquid crystals were studied as well. These experiments suggested no change in the helical twisting characteristics of the chiral nematic phase. However, the MWCNTs were thought to disrupt the translational order in the SmA phase (decrease of the SmA-N phase transition) yet follow the twist of the nematic director in the chiral nematic phase [498]. 

Let us briefly review the essential ingredients to this procedure (for more details of the method see [30] and for our model [42]). For a given system the hydrodynamic variables can be split up into two categories variables reflecting conserved quantities (e.g., the linear momentum density, the mass density, etc.) and variables due to spontaneously broken continuous symmetries (e.g., the nematic director or the layer displacements of the smectic layers). Additionally, in some cases non-hydrodynamic variables (e.g., the strength of the order parameter [48]) can show slow dynamics which can be described within this framework (see, e.g., [30,47]). 

In the previous section we have shown that a minimal set of variables supports our picture of the physical mechanism. But neglecting the coupling between velocity field and nematic director and vice versa is a rather crude approximation since it is well known, that this coupling plays an important role in nematohydrodynamics [29, 30]. So the natural next step is to include this coupling and to perform a linear... 

The spatial and temporal response of a nematic phase to a distorting force, such as an electric (or magnetic) field is determined in part by three elastic constants, kii, k22 and associated with splay, twist and bend deformations, respectively, see Figure 2.9. The elastic constants describe the restoring forces on a molecule within the nematic phase on removal of some external force which had distorted the nematic medium from its equilibrium, i.e. lowest energy conformation. The configuration of the nematic director within an LCD in the absence of an applied field is determined by the interaction of very thin layers of molecules with an orientation layer coating the surface of the substrates above the electrodes. The direction imposed on the director at the surface is then... 

Figure 2.12 Orientation of the nematic director at substrate. (f>o is the preferred azimuthal angle, 6q, is the preferred polar angle and 6 is the tilt angle commonly used.

Therefore, switch-off times are independent of the field strength and directly dependent on material parameters, such as viscosity coefficients and elastic constants, and the cell configuration. Therefore, they are often three or four orders of magnitude larger than the switch-on times. However, sophisticated addressing techniques can produce much shorter combined response times ( on + off The nematic director should be inclined, e.g. 1° pretilt,... 

A standard TN-LCD consists of a nematic liquid crystal mixture of positive dielectric anisotropy contained in a cell with an alignment layer on both substrate surfaces, usually rubbed polyimide, crossed polarisers and a cell gap of 5- 0fim, see Figure 3.7. The nematic director is aligned parallel to the direction of rubbing in the azimuthal plane of the device. The alignment layer induces a small pretilt angle (6 1-3°) of the director in the zenithal plane. The... 

The super birefringent effect (SBE-LCD) reported by Scheffer and Nehring from Brown Boveri in Baden, Switzerland, uses the optical interference of two normal, elliptically polarised modes of transmitted light generated by a high-tilt, highly-twisted nematic structure viewed between two polarisers set in an unusual way, i.e. the input polarisation direction is not parallel to the nematic director at either substrate surface and the polarisers are not crossed at 90°, see Figure 3.10. 

---