Splay nematics

Figure C2.2.11. (a) Splay, (b) twist and (c) bend defonnations in a nematic liquid crystal. The director is indicated by a dot, when nonnal to the page. The corresponding Frank elastic constants are indicated (equation(C2.2.9)).

Fig. 6. The three basic curvature deformations of a nematic Hquid crystal bend, twist, and splay. The force constants opposing each of these strains are...

Electric polarization resulting from a splay or bend deformation of the director of a nematic liquid crystal. 

Fig. 32. Schematic representation of the flexo-electric effect, (a) The structure of an undeformed nematic liquid crystal with pear- and banana-shaped molecules (b) the same liquid crystal subjected to splay and bend deformations, respectively.

For a nematic LC, the preferred orientation is one in which the director is parallel everywhere. Other orientations have a free-energy distribution that depends on the elastic constants, K /. The orientational elastic constants K, K22 and K33 determine respectively splay, twist and bend deformations. Values of elastic constants in LCs are around 10 N so that free-energy difference between different orientations is of the order of 5 x 10 J m the same order of magnitude as surface energy. A thin layer of LC sandwiched between two aligned surfaces therefore adopts an orientation determined by the surfaces. This fact forms the basis of most electrooptical effects in LCs. Display devices based on LCs are discussed in Chapter 7. 

It has been shown 65,68) that the threshold voltage is a function of the dielectric anisotropy Ae and the elastic constants of splay (ku), twist (k22) and bend (k33) deformation of the nematic phase (Fig. 17) ... 

Fig. 17a-c. Elastic constants for a splay b twist c bend deformations of a nematic phase. The full lines represent the director... 

Fig. 24. Three principal types of orientational effects induced by electric (E) and magnetic (H) fields in nematic low molecular liquid crystals. At the top of the figure the initial geometries of molecules are shown. Below the different variants of the Frederiks transition — splay-, bend- and twist-effects are represented...

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. 

Let us first consider the case where the preferred orientation of the polar director is perpendicular to the tilt plane (K > 0). The spatial variation of the layer normal and the nematic and polar directors is shown in Fig. 12. We see that regions of favorable splay (called blocks or layer fragments in Sect. 2) are intersected by regions of unfavorable splay (defects, walls). In the region of favorable splay the smectic layer is flat. In the defects regions the tilt angle decreases to reduce energy... 

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...

Sathyanarayana P, Mathew M, Sastry VSS, Kundu B, Le KV, Takezoe H, Dhara S (2010) Splay bend elasticity of a bent-core nematic liquid crystal. Phys Rev E (Rapid) 81 010702(R)-... 

The three elastic constants are the Frank elastic constants, called after Frank, who introduced them already in 1958. They originate from the deformation of the director field as shown in Fig. 15.52. A continuous small deformation of an oriented material can be distinguished into three basis distortions splay, twist and bend distortions They are required to describe the resistance offered by the nematic phase to orientational distortions. As an example, values for Miesowicz viscosities and Frank elastic constants are presented in Table 15.10. It should be mentioned that those material constants are not known for many LCs and LCPs. Nevertheless, they have to be substituted in specific rheological constitutive equations in order to describe the rheological peculiarities of LCPs. Accordingly, the viscosity and the dynamic moduli will be functions of the Miesowicz viscosities and/or the Frank elastic constants. Several theories have been presented that are more or less able to explain the rheological peculiarities. Well-known are the Leslie-Ericksen theory and the Larson-Doi theory. It is far beyond the scope of this book to go into detail of these theories. The reader is referred to, e.g. Aciemo and Collyer (General References, 1996). 

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 2.9 Schematic representation of the elastic constants for splay, twist and bend, ku, k22 und kjs, respectively, of a nematic phase.

Here u is the position of a layer plane and z is the position coordinate locally parallel to the director n, where n is parallel to the average molecular axis, which is assumed to remain normal to the layer plane, du/dz = e is the compressional (or dilational) strain. Thus, layer bending and layer compression are characterized by a splay (or layer-bend) modulus K and a compression modulus B. Other kinds of distortion present in nematics, such as bend or twisting of the director n, are not compatible with layers that remain nearly parallel, and hence are forbidden. Equation (10-36) is not invariant to rotations of frame, and its validity is limited to weak distortions a rotationally invariant expression has been given by -Grinstein and Pelcovits (1981).---------------------------------------------------------... 

Problem 10.8 You are measuring the elasticities and viscosities of a room-temperature nematic at reduced temperatures and you find that below about 10°C the twist and bend constants K2 and become very large, while the splay constant Ki retains a modest value. Also, the Miesowicz viscosity t], becomes enormous while r) goes up only modestly. What could explain this behavior ... 

Because of the difficulty with which polymeric nematic monodomains are prepared, there are few measurements of Leslie viscosities and Frank constants for LCPs reported in the literature. The most complete data sets are for PBG solutions, reported by Lee and Meyer (1990), who dissolved the polymer in a mixed solvent of 18% dioxane and 82% dichloromethane with a few percent added dimethylformamide. Some of these data, measured by light scattering and by the response of the nematic director to an applied magnetic field, are shown in Figs. 11-19 and 11-20 and in Table 11-1. While the twist constant has a value of around K2 0.6 x 10 dyn, which is believed to be roughly independent of concentration and molecular weight, the splay and bend constants ATj and K3 are sensitive to concentration and molecular weight. 

Figure 4.9 Elastic deformations of calamitic, rod-like liquid crystals in the nematic phase. The corresponding elastic elasticity constants are K, (splay), /<2 (twist), and Kj (bend). K, has the largest influence on the threshold voltage, of TN cells [23f].

Here nd are elastic constants. The first, is associated with a splay deformation, K2 is associated with a twist deformation and with bend (figure C2.2.11). These three elastic constants are termed the Frank elastic constants of a nematic phase. Since they control the variation of the director orientation, they influence the scattering of light by a nematic and so can be determined from light-scattering experiments. Other techniques exploit electric or magnetic field-induced transitions in well-defined geometries (Freedericksz transitions, see section (C2.2.4.1I [20, M]. 

Fig. 3. Bend and splay deformations in nematic liquid crystals...

Here K, K2 and iTs are elastic moduli associated with the three elementary types of deformations splay, twist and bend, respectively. Though the three elastic moduli are of the same order of magnitude the ordering K2 < K < K3 holds for most nematics. As a consequence of the orientational elasticity a local restoring torque (later referred to as elastic torque) acts on the distorted director field which tends to reduce the spatial variations. 

Similar expressions are obtained for the splay and twist elastic constants. The temperature dependence of the elastic constants of simple nematics is represented well by (2.3.35). >... 

Fig, 3.13,1 Meyer s model of curvature electricity. The nematic medium composed of polar molecules is non-polar in the undeformed state ((a) and (< )) but polar under splay (b) or bend ([Pg.206]

Fig. 5.5.1. The temperature dependence of the splay and bend elastic constants, (crosses) and (circles) respectively, in the nematic phase of CBOOA prior to the...

Very few quantitative measurements of the physical properties have been reported. The Frank constants for splay and bend have been determined using the Freedericksz method. Interestingly the values are of the same order as for nematics of rod-like molecules. The twist constant has not yet been measured. The faet that the diamagnetic anisotropy is negative makes it somewhat more difficult to measure these constants by... 

Figure 1. Distortions in nematics, (a) Pure splay, (b) pure twist and (c) pure bend [19],...

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