The Clark-Lagerwall Effect

The variation of the azimuthal director angle (p in the Clark-Lagerwall effect (Figs. 7.11, 7.14) is described by the equation of the torque equilibrium, which comes from the condition for the minimum of the FLC free energy (7.39) 

For typical values of polarizations Ps — 20 nC/cm, the driving fields E 10 V///m, and the dielectric anisotropy Ae 1, we have 

For AeE/47r Pg the FLC switching times r are approximately governed by the field squared, r = 47r7 /AeP, as in the Frederiks effect in nematics. FLC mixtures with negative Ae 0 are also used for the dielectric stabilization of the initial orientation in FLC displays [55, 80]. 

References [81] show that two regimes of switching exist in the Clark-Lagerwall effect, separated by the threshold field Pth 

The optical transmittance I in the Clark-Lagerwall effect is calculated as follows [50, 73]  

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The space charge accumulated due to the spontaneous polarization also influences the switching properties of the Clark-Lagerwall effect [83-91]. If we take into account the electron (hole) charge density (r(t), which is accumulated at the interface between the orienting layer and the FLC medium [83, 84]... 

The DHF effect is also less sensitive to the surface treatment and more tolerant to the cell gap inhomogeneity. As follows from experiment and qualitative estimations [22, 98-101, 104] the effective birefringence value Arieff is approximately twice as low as An = n — nx in the Clark-Lagerwall effect. The insensitivity of DHF cells to the surface treatment enables us to utilize successfully the same aligning technique which has been developed for nematic hquid crystals. 

The DHF effect seems to be successfully competing with the Clark-Lagerwall effect in such applications as Light Valves or Optically Addressed Light Modulators, operating at low controlling voltages with a suflSciently fast response time [98-100, 104]. Recently bistable states were found in FLC with the small values of helix pitch [177]. 

An unusual effect was observed in an antiferroelectric liquid crystal (AFLC) [116-125]. The switching is associated with the appearance of the third state, in addition to the two bistable up and down states known for the Clark-Lagerwall effect. The corresponding hysteresis of electrooptical switching is shown in Fig. 7.23. We can see that the third state at the zero field is stable, and can be transformed either into up or down states if not applying a rather high switching field. 

The existence of two or more thermodynamically stable states with different optical transmission is a very important feature of FLC cells. As mentioned above, bistable switching or bistability is realized in the Clark-Lagerwall effect. In this section, we will consider the influence of physical parameters and cell configuration on the appearance of the phenomenon. Reliable reproduction of bistability conditions is very crucial for technological applications. 

The Clark-Lagerwall Effect. This effect is observed in thin surface-stabilized FLC (SSFLC) cells where the smectic layers are perpendicular to the substrates, the thickness is less than the helical pitch (delectric field of opposite polarity switches the direction of the spontaneous polarization between the UP and... 

Figure 23. The Clark-Lagerwall effect. In a thin SSFLC cell the electric field of opposite polarity. switches the spontaneous polarization between the UP and DOWN positions, which correspond to the LEFT and RIGHT positions of the director.

The variation in the azimuthal direetor angle in the Clark-Lagerwall effect is described by the equation for the torque equilibrium, which follows from the minimization of the free energy (Eq. 71) ... 

Here the elastic modulus Kis defined in such a way that it includes 6 (see e.g. [7]). In the absence of backflow and at not very high voltages, the response times in the Clark-Lagerwall effect are determined by... 

A third, field-off, state, in addition to the two stable states known for the Clark-Lagerwall effect, has also been shown to be stable, and a layered structure with alternating tilt has been established by optical [205, 206] and scanning tunneling microscopy [207] techniques. 

Fig. 13.12 Clark-Lagerwall effect in thin SSFLC cell. Application of the electric field E between the ITO electrodes causes up-down switching of spontaneous polarization accompanied by conical motion of the director n. The projection of the n-vector on plane xy is C-director forming an angle

Let us point to certain advantages of the DHF electrooptical effect for applications as compared with the Clark-Lagerwall mode. 

Table 8.7 shows that the parameters of the prototype light valve (CdS-nematic) are much worse than that of the a Si-FLC device. The operation speed of the latter comes closer to the solid electrooptical crystal modulator (PROM), but with a considerably higher resolution. Liquid crystal light valves on a Si-FLC operate using the Clark-Lagerwall mode [21], the electroclinic eflFect [22], or the deformed helix ferroelectric effect [24]. The operation speed in the two mentioned cases could be 10-100 times faster than mentioned in Table 8.7. 

However, due to the helical super structure of the SmC phase, the spontaneous polarization Pg of the individual smectic layers is averaged out. Therefore, the formation of the helix has to be suppressed in order to achieve a macroscopic ferroelectricity of the SmC phase. This can be done effectively by surface stabilization in very thin samples, as demonstrated by Clark and Lagerwall in 1980 [14]. They showed that under these conditions only two states may occur and that it is possible to switch between the two states within the range of microseconds by reversing the direction of the applied electric field. A sketch of this is given in Fig. 1.4. 

Until the mid-1990s and after 20 years of intense research on nematic field-effect LCDs it was still uncertain whether LCDs and LC materials could indeed meet the short response time requirements and the optical quality required for LCD television. Therefore, parallel to nematic LCD research, strong efforts were made to find effects based on the inherently faster responding ferroelectric liquid crystals (FLCs). Unfortunately, FLCs proved to be difficult to surface-align, rendering them up to now commercially applicable only for niche products such as electronic eye shutters or time sequential LCD projection. FLC examples are the surface-stabilized ferroelectric (SSF)-LCD of Clark and Lagerwall [40] which initiated FLC-LCD development and the deformed helix ferroelectric (DHF)-LCD of Beresnev et al. [41], In 1995 a TFT-addressed black-white DHF-LCD television prototype with 20 ps response time and broad field of view was developed by the author and coworkers in collaboration with Philips [42] (Fig. 6.5a). 

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