Birefringence elastic constants

Table 3.10 Transition temperatures (°C). elastic constant ratio kjj/kj ). birefringence (A j, dipole moment (pD), Kirkwood-Froehlich factor (g) and dielectric anisotropy (As) for the compounds (106-109)... 

Table 3.14 Transition temperatures (°C), elastic constants fk/y, k22 kjj, 10 N), dielectric anisotropy ( e), dielectric constant measured perpendicular to the molecular long axis (e ), birefringence ( n), refractive index measured perpendicular to the director (noJ, rotational viscosity (y. Poise) and bulk viscosity (r, Poise) for tr ns-l-(4-cyanophe-nyl)-4-pentylcyclohexane (41), iTSins-l-(4-cyanophenyl)-4-[(E)-pent-l-enyl]cyclohexane (74) andtra.ns-l-(4-cyanophenyl)-4-[(E)-pent-3-enyI]cyclohexane (78) extrapolated to 100% at 22°...

The order parameter S is a very important quantity in a partially ordered system. It is the measure of the extent of the anisotropy of the liquid crystal physical properties, e.g., elastic constants, viscosity coefficients, dielectric anisotropy, birefringence, and so on. S is temperature dependent and decreases as the temperature increases. The typical temperature dependence of S is shown in Figure 1.16. 

Fig. 3.4.2. Raw recorder traces of interference oscillations due to the change in the sample birefringence with deformation for hexyloxyazoxybenzene at various temperatures. Polarizer and crossed analyser are inclined at 45° to the principal axes of the specimen. The sudden onset of oscillations occurs at the threshold field. The increase in the threshold for the successive traces illustrates the rapid temperature variation of the elastic constant. Sample thickness 45 m. T, = 128.5 °C. (After Gruler, Scheffer and Meier.

Since the simplest oil-in-water (O/W) and water-in-oil (W/O) microemulsions are ternary systems in which the particles are swollen direct and reverse micelles, respectively, the examples given for the application of electrical birefringence will include both microemulsions and micelles. As the studies reveal, the experiments are usually carried out to find answers to specific questions instead of the complete physical characterization of the particles. Often, however, interesting additional information is derived such as the mechanism of phase separation or the elasticity constant of the monolayer in W/O microemulsions. 

Recently Wright et al. have obtained room temperature values of all five elastic constants for uniaxially drawn polymethylmethacrylate (Perspex) and polystyrene (Carinex) by measuring the critical angle for total reflection of an ultrasonic beam incident on immersed samples. The specimens were stretched by similar extents at different temperatures, with orientation assessed by measurements of optical birefringence. 

The Determination of Elastic Constants in Weakly Birefringent Liquid... 

THE DETERMINATION OF ELASTIC CONSTANTS IN WEAKLY BIREFRINGENT LIQUID CRYSTALS... 

A procedure is described that can measure optical phase retardations of birefrigent materials with a resolution 2x10-4 radians. The method relies on phase modulation with alternate right and left handed circularly polarized light. Phase sensitive detection is employed to reduce noise and thermal fluctuations in the optics and light source. The method is useful in Frederik s transition measurements to determine the elastic constants of weakly birefringent polymer liquid crystals with long equilibration times. 

The cell parameters thickness (d), twist (3o)> capacitive threshold voltage (Vc) and the liquid crystal material parameters birefringence (n ), dielectric anisotropy (Ea)> pitch (P), bend to splay elastic constant ratio (K3/KX) and twist elastic constant (K2) were varied one at a time over a wide range of values. Transmission versus voltage curves were calculated at 0 and 40 incidence in the principal viewing plane and values for M0, My,... 

Parameters varied are the thickness of the layer, the wavelength of the light, the indices of refraction, the birefringence, the pretilt, the elastic constants and the dielectric anisotropy. 

For a thermotropic liquid crystal, its physical properties, such as birefringence, viscosity, dielectric anisotropy, and elastic constant, are all dependent on the operation temperature -except at different rates. Polymer-stabilized BPLC is no exception [45]. Figure 14.10 shows... 

To investigate the temperature effects quantitatively, here we analyze the temperature and frequency effects on Kerr constant. Based on Gerber s model (Equation (14.2)), Kerr constant is governed by the birefringence (An), average elastic constant (k), dielectric anisotropy (Ae) and pitch length (P) of the chiral LC host. The temperature effects on An, k, and As are described by the following relations [46]... 

The preconditions for the use of polymer liquid crystals in display applications are that they exhibit bulk optical properties dependent on the molecular orientation in the mesophase and that this orientation may be altered on application of an external field. In this chapter we shall be concerned with electric or optical fields only. The particular optical property, i.e. (a) the birefringence, (b) the dichroism or (c) the scattering power, defines the display construction in terms of the use of polarized (a and b) or non-polarized (b and c) light, whereas the ability to switch from one orientation to another depends on the anisotropic electric permittivity and the orientational elastic constants. The dynamics of the induced orientation will depend, additionally, on the viscosity constants of the material. 

In a comprehensive study at room temperature, Hadley, Pinnock and Ward [20] determined the five independent elastic constants for oriented filaments of polyethylene terephthalate, nylon 6 6, low and high-density polyethylene and polypropylene. The orientation was determined in terms of draw ratio and optical birefringence. Subsequent studies indicated that it would have been appropriate to record not only the overall orientation, as derived from birefringence, but also the crystal orientation, obtainable from X-ray measurements. The results are summarized in Table 7.1 and Figures 7.9-7.13 (see Section 7.5 for discussion of the aggregate theory predictions). 

Kuhn, W. and Griin, F. (1942) Relations between elastic constants and the strain birefringence of high-elastic substances. Kolloidzitschrift, 101, 248. 

Figure 8.29 Stiffness constants of uniaxially drawn amorphous polymers, measured at room temperatures, as a function of birefringence (a) polymethylmethacrylate, (b) polystyrene. (Redrawn from Wright, H., Faraday, C.S.N., White, E.F.T. et al. (1971) The elastic constants of oriented glassy polymers. ]. Phys. D, 4, 2002. Copyright (1971) Institute of Physics.)...

Before giving analytical expressions for the director deformations in Freedericksz cells, we will summarize the magnetic and electrical methods. The advantage of electro-optical measurements is that the cell thickness does not enter the equations and is therefore ruled out as an error source. Furthermore, the electric field can always be considered strictly perpendicular to the sample plane. On the other hand, in the electric method conductivity effects can influence the measurements and exact knowledge of and is required to extract the second elastic constant from the birefringence or capacitance characteristics. Moreover, the electric measurement is restricted... 

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