Electrooptical Response

If a nematic liquid crystal has negligible conductivity the results of Sections 11.2.1-11.2.5 for the Frederiks transition induced by a magnetic field may be directly applied to the electric field case. To this effect, it suffices to substitute H by E and all components of magnetic susceptibility tensor Xij hy correspondent components of dielectric permittivity tensor s,y. From the practical point of view the electrooptical effects are much more important and further on we discuss the optical response of nematics to the electric field. 

We discuss the splay-bend distortion induced by an electric voltage applied to a cell similar to that shown in Fig. 11.16 using two transparent electrodes at z = 0 and z = d. The distortion is easy to observe optically for the cell birefringence. The splay-bend cell behaves like a birefringent plate discussed in Section 11.1.1 but now the plate birefringence is controlled by the field. The optical anisotropy 

The corresponding phase retardation is obtained by integrating (11.70) over the ceU thickness  

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. 

11 Optics and Electric Field Effects in Nematic and Smectic A Liquid Crystals 8/2JC 

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Materials that exhibit photoconductivity and/or electrooptical response can be found in large numbers among molecular glasses (Fig. 3.40). Dihydropyridines with Tg 25 C and low tendency of crystallization have been used (e.g., 2BNCM, 73), adding only a small fraction of a binding polymer (<10%), and 2,4,7-trinitro-9-fluorenone (TNF) as a sensitizer [310]. A common strategy is... 

Figure 3.38. Principle of the photorefractive effect By photoexcitation, charges are generated that have different mobilities, (a) The holographic irradiation intensity proHle. Due to the different diffusion and migration velocity of negative and positive charge carriers, a space-charge modulation is formed, (b) The charge density proHle. The space-charge modulation creates an electric Held that is phase shifted by 7t/2. (c) The electric field profile. The refractive index modulation follows the electric field by electrooptic response, (d) The refractive index profile.

Recently, it was theoretically shown, on the basis of standard density-matrix formalism of nonlinear optics, that chiral isotropic media can possess an electrooptic response [174]. Such materials would be inherently stable and could therefore be extremely useful for the development of electro-optic devices. Contrary to usual electro-optic materials, index (absorption) modulation in such media is due to the imaginary (real) part of the electro-optic susceptibility. The response relies on the damping of the material response. 

Figure 4.6 Working principle of a twisted nematic (TN) cell in the normally white" configuration (left), and the change of transmission with increasing applied voltage (right). In the cell configuration sketched above the threshold voltage (V,, ) for the electrooptical response corresponds to approximately V90 for 90% of maximum transmission.

Moreover, after removal of the poling field, the electrooptical response of the material should be stable over time. For this reason, the glass transition temperature (Tg) of the polymer should be high enough for the chromophore acentric order to be kept frozen over device operation. 

An advance that has extended the application of LCDs to full page computer terminals and other high information content displays without having to resort to TFTs is the supertwisted nematic device. It makes use of the fact that the electrooptic response of the nematic gets progressively steeper as the twist angle is increased, until at a certain... 

On the other hand, it has been shown on LMWLCs that the well-known SmC, where the molecules are tilted with respect to the layer normal, is no longer the only possibility to obtain a fluid biaxial phase [63], As a consequence, a strict determination of the chiral smectic phase structure requires not only a careful analysis of the X-ray diagrams obtained on powder as well as on aligned samples, but also a study of the electrooptic response, which allows discrimination between the ferroelectric, the antiferro-electric, and the ferrielectric behavior. 

Knowledge of the electrooptic behavior of the FLCPs is of the utmost importance for display device applications. One relevant parameter in this respect is the response time. As for the spontaneous polarization, the determination of the response time requires a uniformly aligned sample. The test cell is placed between crossed polarizers so that one tilt direction is parallel to the direction of one polarizer. The electrooptic effect is achieved by applying an external electric field across the cell, which switches the side chains from one tilt direction to the other as the field is reversed. A photodiode measures the attenuation of a laser beam when the cell is switched between the two states. Generally, the electrooptical response time is defined as the time corresponding to a change in the light intensity from 10 to 90% when the polarity of the applied field is reversed ( 10-9o)-... 

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. 

G. Basappa and N.V. Madhusudana, New type of high field electrooptic response in nematics, Proc. SPIE 4147, 116 125, (2000). 

Kang, H., A. Facchetti, H. Jiang, P. Zhu, and T.J. Marks. 2004. Synthesis and unprecedented electrooptic response properties of twisted ir-system chromophores. Mater Res Soc Symp Proc. 833 151-156 Facchetti, A., G.R. Hutchison, S. Keinan, and M. Ratner. Control mechanisms for transport and nonlinear optical response in organic materials a tale of twists and barriers. Inorg Chim Acta 357 3980-3990. 

Pereverzev, Y.V, O.V. Prezhdo, and L.R. Dalton. 2003. Structural origin of the enhanced electrooptic response of dendrimeric systems. Chem Phys Lett 373 207-212. 

Yu and coworkers describe a technique to retain stability and maximize the electrooptic response. They preformed the imide structure with an aryl dihalide monomer and incorporated highly efficient chromophore groups before polymerization. This highly functionalized monomer was subjected to a Pd-catalyzed coupling reaction with 2,5-bis(tributyltin)thiophene to give the polymer... 

Fig. 11.22 Dynamic of the electrooptical response of a planar nematic cell the voltage pulse U (upper plot) and the transient intensity of transmitted monochromatic light I (lower plot)...

We can use Eqs. (13.13) and (13.14) and find parameters a, %j and p in the SmA phase. For this we need slow, automatically made temperature scans through the A —> C phase transition with simultaneous measurements of SSFLC cell capacitance, i.e. Xsm(T) and the electrooptical response i.e., field induced angle 9(7 at frequency 0.1-1 kHz. Then the asymptotic behaviour of capacitance at temperature T > provides us the value of dielectric constant and susceptibility Xx = (e - and the ratio XsJ c = PX us the coupling constant p in... 

By a proper treatment of the electrodes, one can obtain a texture with a uniform orientation of the smectic normal in one direction within the cell plane. Between the crossed polarizers such a cell will be black if a polarizer is installed parallel to the smectic normal. Upon application of the electric field, the antiferroelectric structure becomes distorted. At low voltages of any polarity, the electrooptic response is proportional to E the bottom part of the curves has symmetric parabolic form [35] shown in Fig. 13.24b. Above the AF-F transition, the director acquires one of the two symmetric angular positions ( 9 on the conical surface) typical of the SmC phase. At these two extreme positions the transmission is maximum. With increasing temperature from T toTi the AF-F threshold decreases due to a decrease of the potential barrier separating structures with alternating and uniform tilt. It is natural because within the SmC A phase T1 is closer to the range of the SmC phase than T2 or T3. 

At fields below E f, the macroscopic polarization is absent due to alternating Po, the first order term in polarization is absent and the distortion is controlled by a higher order term proportional to PqE - This explains the parabolic form of the electrooptical response at the fields below AF-F threshold. 

Multiplexed twisted nematic liquid crystal devices (TN-LCDs) are the mainstay of low power, medium information content displays. At present, the voltage threshold and the nonlinearity of the electrooptic response intrinsic to the twisted nematic structure are used to achieve multiplexing. The multiplexing level achievable using this technology is limited by the sharpness of the electrooptic response and by the variations of this response with viewing angle. ... 

The calculations of the electrooptic response of TN-LCDs are usually conducted on high speed computers with large memories. 

FIGURE 13 Schematic plot of hysteresis in the electrooptic response of a cholesteric phase-change device. 

Based on the director distribution we can derive the electrooptical response of a nematic liquid crystal cell (such as birefringence), rotation of the polarization plane of the incident light, total internal reflection, absorption, or some other important characteristics of the cell. In this chapter we will consider in detail these particular features of the electrooptical phenomena in uniform structures. Special attention will be paid to their possible applications. Electrooptics of the isotropic phase and polymer nematics, including Polymer Dispersed Liquid Crystals (PDLC), are also discussed. 

This effect has been observed experimentally in comparatively thick cells (d 50 /xm) [113]. In cells with d 20 /xm, the final twisted state (in the field) proves to be insufficiently stable and the nematic liquid crystal layer is gradually transformed into a planar structure. The addition of small quantities of cholesteric liquid crystals to the initial nematic mixture enables a stable twisted structure to be achieved with the application of a field and improves the electrooptical characteristics of the device. The electrooptical response of electrically induced twist nematic cells includes intensity oscillations observed both in the switching on and switching off regimes [114]. These oscillations take place due to the variation of birefringence, which are not important in the usual twist effect. 

When supertwisted, i.e., twisted up to an angle exceeding 90, liquid crystal cells were known [31], but the importance of these structures for display applications was not clear. It was shown that the electrooptical response of supertwisted cells almost always revealed a hysteresis behavior due to the appearance of transient light scattering domain structures [119, 120]. When studying the early works devoted to the electrooptics of cholesteric structures we could imagine that domain appearance is their intrinsic feature and cannot be avoided [121]. However, this is not true and might have been discovered before 1980 if the results of [119, 120] could have been analyzed more carefully. 

A special case was considered in [21]. The dielectric instability was investigated in the hybrid [4] or so-called corkscrew texture. A wedge-form cell was prepared with the planar and homeotropic orientation of a cholesteric mixture at opposite boundaries. It was shown that the Cano-Grandjean disclinations are not observed in this case and the electrooptical response... 

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 process of the director reorientation in polymer ferroelectrics, as in their low-molecular counterparts, involves changes in the tilt 0) and azimuthal (f) angles. These two modes are characterized by quite different rates. The 6 process corresponds to the soft-mode distortion, and the corresponding time To diverges at the C A phase transition point. The process means the motion of the director over the conical surface around the normal to the smectic layer (the Goldstone mode). In the helical structure the latter involves the twisting-untwisting mode, tq and differ considerably from each other, because backbones participate in those modes to a different extent. This can be seen in the dielectric spectra [172], and in the pyroelectric and electrooptical response. 

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