Splay measurement

In a study where both peripheral and central nervous system effects were measured in rats co-exposed to u-hexane and toluene (Pryor and Rebert 1992), toluene exposure at 1,400 ppm for 14 hours a day for 9 weeks prevented the peripheral neurotoxicity (decreased grip strength and nerve conduction velocities) caused by exposure to 4,000 ppm 77-hcxanc alone. There was no reciprocal action of 77-hexane on the motor syndrome (shortened and widened gait and widened landing foot splay) and hearing loss caused by toluene. Brainstem auditory response amplitudes were decreased by 77-hcxanc, co-exposure to toluene did not block this effect. 

Table 7. Measurements of the Fredericks transition in the magnetic field 71) (H = critical field, r = relaxation time, kn = splay elastic constant, yl = twist viscosity coefficient...

What are typical values for the parameters k and kl The bending rigidity of surfactant films is typically of the order of 1-20 kBT at room temperature. Factors that reduce k are short alkyl chains, cosurfactants, double-chain surfactants with unequal chains, and cis-unsaturated bonds. For the saddle-splay modulus only few measurements have been done. It tends to be negative with an amount much smaller than the bending rigidity for the same system. 

Table 3.13 Transition temperatures (°C) and some values for the dielectric anisotropy (Ae), the ratio of the dielectric anisotropy and dielectric constant measured parallel to the director fAe/ej. and the ratio of the bend (kjj) and splay (kjj) elastic constants for the nitriles 36, 41, 53, 39,49 and 50... 

Measurement of the critical field for this transition is therefore a convenient method for measuring the splay elastic constant K. ... 

Problem 10.8 You are measuring the elasticities and viscosities of a room-temperature nematic at reduced temperatures and you find that below about 10°C the twist and bend constants K2 and become very large, while the splay constant Ki retains a modest value. Also, the Miesowicz viscosity t], becomes enormous while r) goes up only modestly. What could explain this behavior ... 

Because of the difficulty with which polymeric nematic monodomains are prepared, there are few measurements of Leslie viscosities and Frank constants for LCPs reported in the literature. The most complete data sets are for PBG solutions, reported by Lee and Meyer (1990), who dissolved the polymer in a mixed solvent of 18% dioxane and 82% dichloromethane with a few percent added dimethylformamide. Some of these data, measured by light scattering and by the response of the nematic director to an applied magnetic field, are shown in Figs. 11-19 and 11-20 and in Table 11-1. While the twist constant has a value of around K2 0.6 x 10 dyn, which is believed to be roughly independent of concentration and molecular weight, the splay and bend constants ATj and K3 are sensitive to concentration and molecular weight. 

Figure 3 Illustration of the hind-limb splay procedure the hind paws of the mouse are dipped in ink, the animal is then dropped from a fixed height onto a piece of paper and the distance between some parameter of the hindlimbs is measured. (Reproduced from Cory-Slechta DA (1989) Behavioral measures of neurotoxicity. Neurotoxicology 0 . 271-296, with permission.)...

Fig. 3.13.3. A hybrid aligned cell for the determination of the anisotropy of the flexoelectric coefficients. In this geometry, the director has a splay-bend distortion which gives rise to a flexoelectric polarization P. On applying an electric field E, the director is twisted by an angle (j> cc — which can be measured optically.

Very few quantitative measurements of the physical properties have been reported. The Frank constants for splay and bend have been determined using the Freedericksz method. Interestingly the values are of the same order as for nematics of rod-like molecules. The twist constant has not yet been measured. The faet that the diamagnetic anisotropy is negative makes it somewhat more difficult to measure these constants by... 

This form for the free energy per unit area was discussed by Helfirich and states that the mean curvature which minimizes the free energy has a value Co, termed the spontaneous curvature of the membrane. The energy cost of deviating from the spontaneous curvature is the bending or curvature modulus, k. The parameter k, known as the saddle-splay modulus, measures the energy cost of saddlelike deformations. 

A comment should be added on the rotational viscosity of the sample in the experiment. It can easily be shown that in the case of azimuthal anchoring measurements, the viscosity entering the analysis equals the rotational viscosity 71. When measuring the zenithal anchoring coefficient, the effective viscosity has to be corrected according to the scattering geometry. However, in first approximation the pure splay mode viscosity is sufficient. 

This chapter is concerned with experimental measurements of flexo-electric coefficients. After a brief introduction to flexoelectricity in nematic liquid crystaJs, some applications exploiting the flexoelectric effect and the influence of this effect on electrohydrodynamic instabilities are pointed out. Flexoelectricity axises in samples with a splay-bend distortion in the director field and as such its measurement is not as direct as for dielectric constants. The theoretical background needed to analyse electro-optic experiments and extract the flexocoefficients is outlined in Section 2.2. Various experimental techniques that have been developed are described in Section 2.3. These involve cells in which the alignment of the nematic director is homeotropic, or planar or hybrid. In the first case, the interdigitated electrode technique is particularly noteworthy, as it has been used to establish several features of flexoelectricity (1) the effect can arise purely from the quadrupolar nature of the medium, and (2) the dipolar contribution relaxes at a relatively low frequency. 

It is clear that the two polar vectors respect the apolar nature of n. There is also an obvious analogy of the above mechanism with the orientation polarization of a liquid dielectric, which was used by Helfrich to relate the two flexocoefficients with molecular properties. The intrinsic splay or bend can be related to an appropriate angle and molecular dimensions. The relevant component of the electric dipole moment and the curvature elastic constant, viz., and the splay constant Ki or /ux and the bend constant It s figure in the estimation of the flexocoefficients. Nematic liquid crystals made of banana-shaped molecules have been studied only recently, and a comparison of the experimental measurements with the Helfrich formula leads to interesting inferences, as will be mentioned later in this chapter, and covered more thoroughly in the companion Chapter 3 by Jakli et al. ... 

Practically aU other methods developed for the measurement of flexo-coefficients are indirect . These exploit the fact that the polarization resulting from the splay-bend distortion couples linearly with an applied electric field E. This contributes to the total free energy of the sample, and hence alters the distortion of the director field compared to that in the absence of flexoelectric polarization. An external electric field of course acts on the dielectric anisotropy (As) of the nematic, which, like the orientational or-... 

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