Dielectric biaxiality

For instance, let the field be parallel to the y-axis, where 6, (p are director angles in the FLC layer (similar to that shown in Fig. 7.1). Then the contribution to FLC free energy in the case of dielectric biaxiality gives [56]... 

As shown in [59], the dielectric biaxiality l g — t, in some cases, is comparable with the dielectric anisotropy e — t of an FLC, and should be taken into account as a factor of the dielectric stabilization of a director configuration [9, 44-56]. 

It was, however, found to be possible to realize a high contrast ratio from a material in the C2 state when it was combined with the r-Vmin mode [21] by using a FLC material with a negative dielectric anisotropy and/or a large positive dielectric biaxiality [22]. In addition, the C2U state has several advantages over the CIU state and bookshelf state. The C2U state provides faster response times... 

The r-Vmin behaviour is an unusual behaviour that shows a minimum in the response (t)-voltage (V) curve. The behaviour is exhibited by FLC materials that have modest values of spontaneous polarization to balance the dielectric restoring torque [22]. Therefore, to operate in the r-Vmin mode, FLC materials must have low Pg values and large positive dielectric biaxiality ( ). A typical r-Vmin characteristic is shown in Fig. 6.1.10. The C2U orientation in combination with the... 

In Eq. (291) we derived an expression for the director equation of motion with dielectric and ferroelectric torques included. If the origin of the dielectric torque is in the dielectric biaxiality, the equation (with the elastic term skipped) will be the closely analogous one... 

Phases having biaxial symmetry (tilted smectic phases) exhibit dielectric biaxiality in particular. At frequencies of 1 MHz and below, the biaxiality becomes important and critically influences the electrooptic switching behavior of the SmC phase. It is therefore important to be able to measure the biaxiality at these frequencies. Being a symmetrical second rank tensor, the dielectric permittivity can always be diagonalized in a proper frame and described by three components along the principal directions. The three principal values can then be expressed by a single subscript and can be determined by three independent measurements performed at three different orientations of the director relative to the measuring electric field. In practice, this may not be that... 

Figure 85. The dielectric biaxiality of the nonchiral smectic C mixture M4851 (Hoechst), measured by the long pitch method (from Buivydas [155]).

Each of the models serving as basis for the dielectric biaxiality measurements has been derived using certain assumptions. The method described by Gouda et al. [157] assumes an undisturbed ferroelectric helix, and this assumption is best fulfilled in short pitch substances. Actually, the pitch/cell thickness ratio is the important parameter. For measurement convenience, the cells cannot be made very thick, hence the method works well for materials with a helical pitch of up to about 5 pm. This includes practically all cases of single smectic C substances. The method cannot be applied to nonchiral materials. 

Experiments on SmC and SmC material indicate that the dielectric biaxiality is not necessarily negligible with respect to the dielectric anisotropy. An example for the temperature dependence of the dielectric constants for a commercially available ferroelectric SmC material is shown in Figure 8.3. 

A large positive dielectric biaxiality 6c if AC stabilization is required... 

Vbry little information exists about further physical parameters such as the helical pilch p. the dielectric biaxiality 6c, the dielectric anisotropy Ac, and the optical birefringence An of FLC polymers. 

J. C Jooci. M. i. Ibwier, and J. R. Hughes, Fast, high-contrast fetroelectric liquid crystal displays and the role of dielectric biaxiality. Displays 14M (1993). 

The above formulation assumes that the dielectric biaxiality de of the SmC liquid crystal may be neglected. However, it should be pointed out that although in some instances it can be acceptably negligible compared to the uniaxial approximation Ca (especially, in some materials, near the transition temperature to SmA [158, p.212]), it may nevertheless have a dominant role to play and has been incorporated into many models of cell switching, for example by Maltese, Piccolo and Ferrara [191] and Brown, Dmm and Jones [28]. Measurements of dielectric biaxiality for several SmC materials have been reported by Jones and Raynes [139]. Convenient references on the definition of these parameters for SmC may be found in the text by Lagerwall [158, p.l87] or the article by Jones and Raynes [139]. 

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