Measurement of the Director Tilt

Derived from molecular modeling with the software ChemSD Pro 13.0 hy CambridgeSoft on the AMI level. 

In case of the sample with 13 wt% of formamide, the tilt angle rises abruptly to a quiet high, almost constant value of 9opt = 27°. Here the phase transition towards the SmC analog phase does not take place from the lamellar L phase but from the Coll phase. 

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Temperature-dependent X-ray diffraction measurements of the layer spacing of the lyotropic SmC analog phase in mixtures with different concentrations of formamide revealed that the layer spacing increases approximately linearly with the amount of solvent. The maximum solvent layer thickness which stiU allows the correlation of the director tilt direction between succeeding surfactant layers, was estimated to be about 2.7 nm. 

Extensive measurements of the Prederiks transition in various smectic C liquid crystals have been carried out by the Halle group [117, 118]. In experiments, the conventional sandwich cells with optically transparent electrodes were used. The director was oriented uniaxially by rubbing the electrodes and the smectic layers were tilted with respect to the cell plane (a bookshelf geometry). An electric field applied along the cell normal ( -direction), due to positive dielectric anisotropy, induces the director rotation around the normal to the smectic layers. Fig. 6.32. Two optical effects are observed ... 

Like in the magneto-optical method, optical detection may be applied in the electrically driven case as well. As an alternative, the cell capacitance C is a convenient measure of the transition threshold and the tilt deformation of the director field. The capac-itanee versus voltage curves can be used to determine the dielectric and elastic constants and the surface tilt angles [ 19]. A", is given by the critical field and 33 is obtained from the slope of the C U) curve. In the... 

Phases having biaxial symmetry (tilted smectic phases) exhibit dielectric biaxiality in particular. At frequencies of 1 MHz and below, the biaxiality becomes important and critically influences the electrooptic switching behavior of the SmC phase. It is therefore important to be able to measure the biaxiality at these frequencies. Being a symmetrical second rank tensor, the dielectric permittivity can always be diagonalized in a proper frame and described by three components along the principal directions. The three principal values can then be expressed by a single subscript and can be determined by three independent measurements performed at three different orientations of the director relative to the measuring electric field. In practice, this may not be that... 

Let us now extract the physical consequences contained in all these relations and start with the last one. As numerical examples we will use the data from Rieker and Clark [168] on the mixture W7-W82, for which the tilt angle 0 saturates at about 21° at low temperature, and the corresponding saturation value for the chevron angle 5 has been measured as 18°. To begin with we see that Eq. (412) sets an upper limit to the layer kink p, because of the requirement of uniqueness of the director n at each chevron interface. Figure 96a illustrates the fact... 

Fig. 5—Tilt angle (deviation from the field direction) of the director field plotted as a function of distance from the wall. The distance is measured in units of magnetic coherence length, which is the characteristic iength of magnetic phenomena in nematic iiquid crystais.

The formula presented in Eq. 3 indicates the threshold voltage at which the director starts to reorient. Gerritsma, DeJeu, and Van Zan-ten 4 have measured the magnetic threshold by both capacitive and optical techniques and found that the capacitive threshold is lower than the optical one. Van Doorn has shown that this difference is to be expected, since the fluid starts to reorient by the tilting of the director toward the applied magnetic field before the twist has appreciably changed. Consequently the capacitive threshold, which occurs when the director starts to tilt toward the applied field, is lower than the optical threshold, which occurs when the twist becomes sufficiently nonuniform that the optical vector of the light does not Tol-low the twist. A similar difference has been observed in twisted nematic devices excited with electric fields. Berreman s explanation of the static characteristics of electric-field-excited devices is similar to that of Van Doorn. ... 

The viscous properties of a smectic A are characterized by the same five independent viscosities that characterize the nematic. As we shall see, however, the elastic properties of the smectic are very different from those of a nematic, and some flows permitted to the nematic are effectively blocked for the smectic. For smectic C, for which the director is tilted with respect to the layers, there are some 20 viscosities needed to characterize the viscous properties (Leslie 1993). Formulas for these, derived using a method analogous to that used for nematics by Kuzuu and Doi (1983, 1984) can be found in Osipov et al. (1995). The smectic phase for which rheological properties are most commonly measured is smectic A, however, and hereafter we will limit our discussion to it. 

It is interesting to notice how much more sudden the optical transition is than the tilt response. Transmission gives a very indirect measure of director behavior. 

Fig. 5.28 Optically measured director tilt angle 6opt of different C50/formamide mixtures in dependence of the temperature T - Tc relative to the lamellar L to lyotropie SmC analog phase transition (adapted from [17]. Cop5oight 2015 Wiley-VCH Verlag GmbH Co. KGaA. Reproduced with permission) (See Footnote 6)...

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