Nematic liquid crystals typical values

Equation (6) predicts that 5 values at low temperatures will decrease as T increases, heading toward the value 5 at P. But when 7 reaches 7j (a temperature below P ), 5 will undergo a first-order jump from 5j to 0 since the isotropic phase is the stable phase for all 7 > 7j. The observed variation of 5(7) for a typical thermotropic nematic liquid crystal is shown in Fig. 4. For the simplified case where the sixth-order coefficient cin Eq. (5) is set equal to zero, it can be shown that... 

In a liquid crystal phase, the system remains a colloidal liquid, but the arrangement of the particles becomes ordered and periodic, and exhibits many of the attributes of a traditional solid crystal, despite having an order parameter far lower than that in a solid crystal. This difference can be seen in the latent heat of crystallisation, with a typical value for solid crystals of 250 J g , while liquid crystals have 5 J g . Understanding the control of these systems allows us to exploit chiral nematic liquid crystals to create artificial structural colour with biopolymers. 

These three different modes of deformation are demonstrated in Figure 2.21 for a nematic liquid crystal. The fluid-like nature of the nematic phase allows these deformations to take place with relatively little energy cost (compared with a crystalline solid). In these equations, the constants K, K22. and K33 are known as the Frank elastic constants and typically take a value around N/m. Measurement of the elastic constants is often carried out to characterize the switching capabilities of liquid crystal materials (i.e., how well they will perform in a device under the application of an electric field). 

There are five independent viscosities which describe the viscosity of the nematic phase depending on the position of the director with respect to the direction of flow, but only two are relevant to the flow in most nematic liquid crystal displays (Figure 2.8). In practice, it is difficult to determine the absolute value for any of them. The Meisowiscz viscosity q, which describes the shear viscosity along the director direction (Figure 2.8), can be determined approximately by a capillary flow method (Ostwald viscometer) and is useful in characterizing the decay time in TN displays. Typical values at 20°C are between 5 and 200 cSt (or mPa-s). As with isotropic liquids, the temperature dependence approximates to Arrhenius behavior. 

Table 9.1 Typical Values for Some Nematic Liquid Crystal...

Chiral nematic liquid crystals possess a helical structure, the pitch P of which is defined to be the distance along the helbr over which the director rotates through 2n radians. Since n and -n are indistinguishable the poiod of repetition L is half that of the pitch (see FIGURE 2). Typical values for L are in the range 300 nm [5, p.l5]. For chiral nematics one additional term, linear in the... 

The constants iFi=i-3 are the Frank elastic constants and correspond to the three fundamental deformations of the director field splay, twist and bend. Then-magnitude is of the order of 10 N, which is a fairly small value, meaning that on a length scale of several hundred microns (a typical size of a bulk sample), the nematic liquid crystal can easily deform or be deformed. It should be added that the Frank elastic constants depend on the order in the liquid crystal, being approximately proportional to 5. Consequently, the Frank constants Ki are temperature dependent and increase with decreasing temperature. 

Anisotropic molecules show optically isotropic behavior in the bulk when they are disordered and randomly oriented, for instance in solutions or liquid crystal above the transition temperature. Under the influence of a strong beam, the induced dipole moment of the molecules feels a torque that tends to orient the molecule. The reorientation of the molecular dipoles induces a change in the refractive index. The typical values for molecular susceptibilities and the time-responses vary depending on the type of systems. For small anisotropic molecular systems, x 10 esu, with a time response 10 s. However, in the nematic phase, liquid crystal molecules are strongly correlated, resulting in much higher values, x 10 esu,... 

Here, 6 represents the angle between an individual molecule and the director, and this is summed over all molecules. Typically, for a nematic phase, 0.7 >S> 0.4 note that the transition from the isottopic liquid to the nematic phase is discontinuous and so at the transition, S will jump from a value of zero to about 0.3-0.4. While beyond the scope of this chapter, it is important to note that it is the nematic phase of liquid crystals that is the basis for almost all display applications. 

An isotropic liquid crystal is partially ordered close to the orienting solid surface. The surface induced perturbation of the order in an isotropic phase is localized in a thin layer with the thickness of the nematic correlation length Since the values of the nematic correlation length in the isotropic phase are typically only a few nanometers, ellipsometry represents a perfect tool for the study of interfacial order. 

In a typical Lyot filter, crystals are often selected so that transmission has its maximum value at the wavelength determined by the thickest crystal retarder, with other stages in the filter serving to block the transmission of unwanted wavelengths. The spectral region passed by the LCTF is dependent on the choice of polarizer, optical coating, and the liquid crystal characteristics (nematic, cholesteric, smectic, etc.). In practice, a Lyot LCTF may have as many as 11 polarizers and 10 liquid crystalline layers and is sometimes equipped with an internal microprocessor to tune all of the stages. 

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