Electrooptical viscosity

A central part of the application-oriented evaluation of liquid crystals are so-called virtual clearing temperatures, electrooptic properties, and viscosities. These data are obtained by extrapolation from a standardized nematic host mixture. 7 Af, An, and jy are determined by linear extrapolation from a 10% iv/iv solution in the commercially available Merck mixture ZLI-4792 (Tfji = 92.8°C, Af = 5.27, An = 0.0964). For the pure substances the mesophases are identified by optical microscopy and the phase transition temperatures by differential scanning calorimetry (DSC). The transition temperatures in the tables are cited in °C, numbers in parentheses denote monotropic phase transitions which occur only on cooling the sample C = crystalline, S = smectic A, Sg = smectic B, S = smectic G, S> = unidentified smectic phase, N = nematic, I = isotropic. 

As there is no appropriate method to measure directly the rotational viscosity of ferroelectric liquid crystals, y is generally deduced from the electrooptic response time measurements [ 12,18,44]. The relationship between fio 9o and t is not straightforward and requires the use of a theoretical model for the optical transmission based on the bookshelf geometry briefly summarized in the following. 

The coefficient y is rotational viscosity of the director similar to coefficient yi for nematics. In fact, it does not include a factor of sin cp and, in the same temperature range, can be considerably larger than the viscosity ytp for the Gold-stone mode. This may be illustrated by Fig. 13.10 the temperature dependence of viscosities y and have been measured for a chiral mixture that shows the nematic, smectic A and smectic C phases [15]. The pyroelectric and electrooptic techniques were the most appropriate, respectively, for the measurements of ya and ytp describing the viscous relaxation of the amplitude and phase of the SmC order parameter. The result of measurements clearly shows that y is much larger than y and, in fact, corresponds to nematic viscosity yj. 

The switching time in the electrooptical effects in FLCs is defined by the rotational viscosity which characterizes the energy dissipation in the director reorientation process [6, 10, 31-34]. According to the FLC symmetry, two viscosity coefficients should be taken into account, and 7, which determine the corresponding response rates with respect to the director angles 9 and p (Fig. 7.5). The relevant dynamic equations take the form [4, 20]... 

The rotational viscosity 7 is determined in accordance with (7.13b) for a sufficiently high electric field E [31-37]. In [31, 34] it was shown that 7< could be estimated from the experimental dependence of the electrooptical response as follows ... 

The helix pitch value Ro is easily controlled by varying the concentration of a chiral dopant in a smectic C matrix. To provide variation of the helix pitch from 0.1 fim to 100 m and more, we should have a chiral dopant with a high twisting power and good solubility. At the same time, the chiral dopant should not depress the smectic C temperature range [11]. Moreover, the growth of polarization should be more pronounced than that of the rotational viscosity 7<, with an increasing concentration of the chiral dopant. Various types of chiral dopants are presented in [11], and some of them were used to reveal the novel electrooptical modes in FLCs [22]. 

FIGURE 7.6. Different methods for measurements of the rotational viscosity 7< (a) dynamics of transmission I t) in the electrooptical cell (b) the repolarization current ip versus time t and (c) the repolarization current for the special (triangular) form of field E t). 

Today the electrooptical properties of liquid crystals form well-developed branches both in the physics and technology of liquid crystals. In addition, electrooptical measurements are the basis of a number of precise methods for determining the physical parameters of a material, such as its elastic and viscosity coefficients, optical anisotropy, spontaneous polarization, flexoelectric coefficients, anchoring energies at interfaces, etc. 

The viscosity parameters associated with the electrooptic effect, and the increased torque that can be exerted on the liquid crystal by an applied electric field due to the spontaneous polarization, result in an electrooptic effect that can be several orders of magnitude faster than in nematics. Switch-... 

The switching time of a liquid crystal display is proportional to the rotational viscosity. Therefore and due to its strong temperature dependence, y, is one of the most important material constants of liquid crystals for electrooptical applications. 

In Sec. 2.6.4 we derived the scaling law for the cone mode viscosity with respect to the tilt angle 6. In this section we want to penetrate a little deeper into the understanding of the viscosities relevant to the electrooptic switching dynamics. Let us therefore first review the previous result from a new perspective. With 0 = const, an electric torque will induce a cone motion around the z axis (see Fig. 75a). We can describe this motion in different ways. If we choose to use the angular velocity of the c director, that is, with respect to the z axis, then we have to relate it to the torque component... 

The first experimental determination of the cone mode viscosity was made by Ku-czyfiski [147], based on a simple and elegant analysis of the director response to an AC field. Pyroelectric methods have been used by the Russian school [136, 148], for instance, in the measurements illustrated in Fig. 67. Later measurements were normally performed [149] by standard electrooptic methods, as outlined earlier in this chap-... 

In the smectic C phase, the rotational viscosity Yq> can be estimated by observing the polarization reversal or the electrooptic properties of the cell, as described in Sec. 2.7.6. The estimation may, for instance, be based on the approximation mentioned there, using the elastic torque [137]... 

---