Freedericksz cell

The experimental set-up used for the Freedericksz cell as well as for the TN-cell is described elsewhere... 

Figure 1. Director configuration and associated elastic distortion in a Freedericksz cell below (a), slightly above (b), considerably above (c) the threshold voltage.

Figure 2. Tilt angle versus voltage profiles for Freedericksz cells containing E7, and two fictitious liquid crystal (LC) materials. LCA has the 33/ 11 ratio reduced from 2.7 to 0.8 LCB also has the dielectric constant ratio 8eIe reduced to 0.3.

Figure 10. Effective birefringence and optical transmission calculated for a Freedericksz cell operated in the tunable birefringence mode (cell thickness 10 pm, wavelength 633 nm, liquid crystal E7).

The use of birefringent polymer layers has subsequently been applied to other types of display. These include compensated versions of the bend Freedericksz cell operat-... 

Before giving analytical expressions for the director deformations in Freedericksz cells, we will summarize the magnetic and electrical methods. The advantage of electro-optical measurements is that the cell thickness does not enter the equations and is therefore ruled out as an error source. Furthermore, the electric field can always be considered strictly perpendicular to the sample plane. On the other hand, in the electric method conductivity effects can influence the measurements and exact knowledge of and is required to extract the second elastic constant from the birefringence or capacitance characteristics. Moreover, the electric measurement is restricted... 

The one-dimensional deformations in Freedericksz cells and their optical characteristics are now well understood. A comprehensive theoretical treatment of the one-dimensional director patterns in electro-magnetically driven cells can be found in publications by Thurston [25], who has also considered the stability of configurations in pretilted cells. Ong [26] has calculated the optical properties when the splay/... 

Fig. 6—Local nematic directors in a Freedericksz cell when H > Hp. Dotted lines indicate the equivalent tiK configuration of the directors. TiH angle 6 is defined as shown.

Fig. 8—Tilt angle of the directors at the center of Freedericksz cell, plotted as a function of reduced field H/Hp, For H/Hp slightly greater than 1, behaves as...

Rg. 9—TW angle of (he directors plotted as a function of posHlon In a Freedericksz cell for three different magnetic Held strengths. 

If we compare with figure C2.2.I I, we can see that this defonnation involves bend and splay of the director field. This field-induced transition in director orientation is called a Freedericksz transition [9, 106, 1071. We can also define Freedericksz transitions when the director and field are both parallel to the surface, but mutually orthogonal or when the director is nonnal to the surface and the field is parallel to it. It turns out there is a threshold voltage for attaining orientation in the middle of the liquid crystal cell, i.e. a deviation of the angle of the director [9, 107]. For all tliree possible geometries, the threshold voltage takes the fonn [9, 107]... 

H. Qi, B. Kinkead, T. Hegmann, Unprecedented dual alignment mode and Freedericksz transition in planar nematic liquid crystal cells doped with gold nanoclusters. Adv. Funct. Mater. 18, 212-221 (2008)... 

The liquid crystal parameters K2, K3/Kx> na and cell design parameters 3g OCg, d and the orientation of polarizers were varied one at a time. The ratio K3/KX was chosen as a parameter in order to keep the Freedericksz transition threshold voltage constant while varying the elastic constants. Variations in the threshold voltage due to the natural cholesteric pitch were not compensated for. Several calculations were also conducted for the case of infinite cholesteric pitch (no cholesteric compound in the liquid crystal mixture). 

Although the dynamics of Freedericksz transition in splay geometry, bend geometry, and twisted geometry is more complicated, the response time is still of the same order and has the same cell thickness dependence. The rotational viscosity coefficient is of the order O.IN - s/m. When the elastic constant is 10 "N and the cell thickness is 10pm, the response time is of the order 100 ms. Faster response times can be achieved by using thinner cell gaps. 

Strictly speaking, when the mbbing angle <1> is not equal to zero the Freedericksz transition threshold is smeared. However, in a normally black IPS mode, the transmittance is proportional to the phase retardation 8 = Ind rdX of the LC cell asT sin 8/2). In the small voltage regime, the phase retardation is small and transmittance exhibits a threshold-like transition. 

The spectral response of a holographic PDLC to applied electric fields is shown in Figure 11.27, where white incident hght is used [37]. At 0 V, due to the periodic refractive index, the cell has a high narrow reflection peak. When the applied voltage is increased, the liquid crystal is ahgned toward the layer normal direction. The amplitude of the oscillation of the refractive index decreases and the reflection of the cell also decreases. The drive voltage is approximately equal to the product of the field threshold of the Freedericksz transition of the liquid crystal layer and the cell thickness. 

Note that the threshold field here is smaller than the threshold field of the Freedericksz transition in the regular liquid crystal cell consisting of two parallel substrates with the same cell gap, for the following reason. In the regular cell the hquid crystal is anchored by the two-dimensional surface of the substrate, while in the polymer-stabilized hquid crystal cell here, the liquid crystal is anchored by the one-dimensional polymer fiber. 

The simplest display application of a nematic polymer liquid crystal, using polarized light, involves the splay Freedericksz transition shown in Fig. 5(a) for a material with positive Ac and planar surface alignment. The device is constructed using two polarizers crossed with each other, placed above and below the cell, with their polarization direction at 45° to the director of the planar texture. Above a threshold voltage given by... 

The Freedericksz transition is also the basis of operation for most liquid crystal displays. In a twisted-nematic display cell, the surface anchoring at the two substrates is incommensurate, inducing a twist to the director field that rotates light polarization. Application of an electric field sufficiently strong to align the director... 

The optical reorientation processes discussed up to now were qualitatively similar to the corresponding low-frequency field effects. As mentioned earlier this is not always the case. A breakdown of the analogy with static fields was first reported by Zolotko et al. who observed in a homeotropic layer a drastic increase of the Freedericksz threshold power for an o-ray as the angle of incidence was increased. Durbin et al. mentioned that in a planar cell Freedericksz transition cannot be induced by a light beam polarized perpendicularly to the director. From a simple analogy one would expect for these cases a threshold not deviating significantly... 

An experimental investigation was made of aberration self-focusing due to orientational deformation of a nematic with a hybrid orientation subjected to the held of an incident ordinary optical wave. When the radiation was incident on a sample from the homeotropic substrate side, the reorientation occurred at intensities higher than the threshold for a photoinduced Freedericksz transition in a homeotropic cell of the same thickness, and it depended strongly on the angle of incidence of the ordinary wave on the sample. The effect was not observed when light was incident from the planar substrate side. 

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