Bend Frederiks transition

This effect is a version of the splay-bend Frederiks transition, but it is observed in liquid crystals doped with dyes. The liquid crystalline matrix (the host) is subjected to the influence of a field the function of the dye (the guest) is to enable the effect to be seen with only one polarizer or even without any. 

Figure 11. The geometry of the bend Frederiks transition (a) and the profile of the director deviation, induced by an external field (b).

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...

Fig. 11.15 Three basic configurations of the director and the magnetic field for the Frederiks transition onset, namely, splay (a), bend (b) and twist (c)...

The oscillations of I (U) are well seen in the experimental plot. Fig. 11.21. The measurements were made at 27°C on 55 nm thick cell filled with a mixture having ta = 22. From the I (U) curve, the field dependence of the phase retardation 8(17) and the Frederiks transition threshold Uc were obtained. In mm, from Ec = UJd and Fq. (11.56) the splay elastic constant Ku was found. The bend modulus "33 was calculated from the derivative dbldU. The same material parameters may be found for the whole temperature range of the nematic phase. 

FIGURE 4.4. Crossed electric and magnetic fields, (a, b) Magnetic field stabilizes director orientation, the first-order Frederiks transitions in an electric field are possible, (c, d, e) Both magnetic and electric fields are destabilizing (c) twist, (d) splay-bend, and (e) twist-splay-bend distortions are possible dependent on the value of the electric and magnetic fields. 

Twist relaxation of splay and bend is a general phenomenon in materials with small K2. Chiral structures can occur in defective nematic samples even when there is no azimuthal anchoring at all. Twisted brushes observed by Press and Arrott in textures of lens-shaped nematic droplets floating on the water surface are one example [15]. Another well-known illustration of twist relaxation is the periodic pattern of stripes that occur in the geometry of splay Frederiks transition in polymer nematics with a small (less than 0.33) ratio K2/K [16]. A field applied normally to the planar nematic cell causes stripe structures composed mostly of twist rather than the uniform splay response observed in regular materials. 

Les us consider the splay Frederiks transition (all the expressions are also valid for the bend effect if, and y are replaced by K32 and 7x, respectively). In the case of the uniform orientation of the director in the plane of the sample (thex,y-plane, wavevec-... 

At present, at least three types of steady-state dielectrically driven pattern are known for nematics. The electric-field-induced periodic bend distortion in the form of parallel stripes has been observed in a homeotropi-cally oriented layer of 5-CB ( a= 13) in the presence of a stabilizing magnetic field [75, 76]. The stripes with a wavevector q were parallel to the electric field E and stationary at low fields. It was shown that a stable periodic pattern of the director minimizes the free energy of the cell when the ela.stic moduli and A 33 are similar to each other. In these experiments the Frederiks transition is of first order, the nonde-formed and deformed areas coexist at a given voltage, and the front between them may propagate along the direction y perpendicular to both fields [77]. 

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