Director alignment

Note 4 Director alignments for point defects with different values of 5 are illustrated in Fig. 23. 

Fig. 22. (a) Identification of the angles and 6 used to describe a disclination. (b) Director arrangement of an 5 = I/2 singularity line. The end of the line attached to the sample surface appears as the point s = + V2 (points P). The director alignment or field does not change along the z direction. The director field has been drawn in the upper and the lower surfaces only. 

Fig. 23. Schematic representation of the director alignments at disclinations with different values of s and (J)o,s 72 correspond to two-brush defects and s = 1 to four-brush...

Fig. 31. Scheme of director alignment in the shear flow of velocity u of a nematic phase and... 

Note 1 In DSM the Williams Kapustin) domains become distorted and mobile, and macroscopic director alignment is completely disturbed. 

Twisted nematic liquid crystal sandwiched between two glass plates, with the director aligned parallel to the plates, with one of the plates turned in its own plane about an axis normal to it. 

A nematic liquid crystal of negative dielectric anisotropy is aligned with the director aligned orthogonal to the cell walls by means of a surfactant orientation layer, see Figure 3.4. One or two linear, elliptical or circular polarisers are... 

The negative Ni is the result of the coupling of molecular tumbling under flow and the local molecular-orientation distribution. At low shear rates, the director tumbles with the flow and Ni will be positive. At intermediate shear rates, nonlinear viscoelastic effects are important. The director tumbling competes with the steady director alignment along... 

In most experiments (and applications) a nematic layer is sandwiched between two solid (glass) surfaces supporting transparent electrodes. Special surface coatings and/or treatments allow control of the director alignment at the bounding plates. There are two basic geometries the planar one where n is parallel to the surfaces (usually along x) and the homeotropic one where n... 

Table 1. Eight different combinations (labelled A to H) of initial director alignments and the sign of anisotropies a, ffa- The EC pattern species are characterized in the last column CH stands for patterns, which are compatible with the Carr-Helfrich mechanism, in contrast to the remaining, nonstandard ones (ns-EC).

For a/e > 0.0057 EC occurs superimposed onto the Freedericksz state (secondary instability) at a higher voltage Uc > Upi- The standard model can also be applied here by carrying out numerical linear stability analysis of the Freedericksz distorted state, and one is faced with similar modifications and difficulties as mentioned in case C before. The ea-dependent Uc and Qc, presented by the dotted hnes in Fig. lO(a-b), have been calculated numerically. It should be noted that the convection rolls are now oriented parallel to the initial director alignment, contrary to the normal rolls in case A or C. 

The critical wavevector is perpendicular to, or subtends a large angle with the initial director alignment (contrary to normal rolls) thus, the rolls are parallel (longitudinal) or strongly oblique (see Fig. 13). 

In this paper we have reviewed the structures appearing at onset of electro-convection in nematic liquid crystals. The influence of the relevant material parameters (ca and ao) and the role of the initial director alignment were explored. Our calculations using a linear stability analysis of the standard model of electroconvection (performed for zero frequency) revealed that four different scenarios characterized by different ranges of the wavenumber q can be identified (1) the Qf= 0 mode (a homogeneous deformation known as the Freedericksz transition) predicted and observed in cases C, D, E and H, which is... 

As a test of the revised theory, further experiments were conducted [Zhao et al., 2005] on nematic solutions of a SCLCP. ER measurements indicated, via application of the Brochard hydrodynamic model, a slightly prolate conformation, R /R = 1.17 0.02, consistent with small-angle neutron scattering measurements, which indicated, that= 1.12 0.06. Observations of the shear stress transient response of a homeotropic monodomain indicated that at a concentration between 0.01 and 0.02 g/mL, the solution exhibited a transition from director-aligning to director-tumbling behavior. The latter result is inconsistent with the original Brochard model [see Eq. (1.94)], which predicts such a transition (i.e., Sas > 0) only for a polymer with an oblate shape but agrees with the modified theory [Eq. (1.96)]. 

Preedericksz transition in planar geometry is uniform in the plane of the layer and varies only in the z direction. However, in some exceptional cases, when the splay elastic constant Ki is much larger than the twist elastic constant K2 (e.g., in liquid crystal polymers), a spatially periodic out-of-plane director distortion becomes energetically favourable. The resulting splay-twist (ST) Freedericksz state is manifested in experiments in the form of a longitudinal stripe pattern running parallel to the initial director alignment no x. 

As already stated, electroconvection cannot be explained by the standard model for < 0 and Ca < 0. Surprisingly, EC has been observed also for this parameter combination in certain calamitic nematics.These EC patterns differ clearly from the standard EC patterns the rolls are dominantly parallel to the initial director alignment (see Fig. 4.6a). They are not observable using the common shadowgraph technique (single polarizer) but are by using crossed polarizers (plus sometimes an additional... 

Fig. 5.21 Nematic phase. Typical photo [6] of a diffiaction pattern for a ncanatic liquid crystal with the director aligned vertically (a) and the scheme explaining this pattern (b)...

Fig. 5.27 Smectic C phase in the magnetic flhn along the vertical direction, Hlln. Typical diffractogram (a) and its scheme (b) showing the four-point picture of reflections from the smectic layers and blurred nematlc-llke arcs corresponding to sketch (c) of the uniform director alignment with broken smectic layers [16]...

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