Frequency domain reorientation

For spin-f nuclei, dipolar interactions may be modulated by intramolecular (DF, reorientation etc.) and/or intermolecular (TD) processes. In general, the intra- and inter-molecular processes can produce quite different Tj frequency dispersion curves. In practice, NMR field cycling experiments are often needed to extend the frequency domain from those employed in conventional spectrometers to a lower frequency range (i.e., the kHz regime) for unambiguous separation (and identification) of different relaxation mechanisms. The proton spin relaxation by anisotropic TD in various mesophases has been considered by Zumer and Vilfan.131 133,159 In the nematic phase, Zumer and Vilfan found the following expression for T ... 

Experiments described in this section are suited to investigate ultraslow motion with correlation times in the millisecond-to-second range. Here, the NMR spectra are given by their rigid-lattice limit and one correlates the probability to find given NMR frequencies at two different times separated by the so-called mixing time tm [11,72]. A two-dimensional (2D) spectrum results, being a function of two NMR frequencies at t = 0 and t = tm, respectively. Since the NMR frequency reflects the orientation of the molecule, 2D spectra provide a visual representation of the reorientational process. Time- and frequency-domain... 

Variable frequency proton Ti studies were first used to detect the characteristic dependence of Ti due to director fluctuations [6.20] in liquid crystals. It was recognized soon after that besides the director fluctuations, relaxation mechanisms, which are effective in normal liquids such as translational self-diffusion and molecular reorientation [6.24], also contribute to the proton spin relaxation in liquid crystals. Though the frequency dependences of these latter mechanisms are different from the relaxation, the precise nature of proton Ti frequency dispersion studied over a limited frequency range using commercial NMR spectrometers often may not be unambiguously identified. Furthermore, because of a large number of particles involved in collective motions, the motional spectrum has much of its intensities in the low-frequency domain far from the conventional Larmor frequencies. The suppression of director fluctuations in the MHz region due... 

Fig. 4—Retardation as a function of voltage. The continuing reorientation of the structure (left side) with increasing voltage results in an ever increasing retardation, i.e., birefringence. The retardation A0 continues to increase unless another electro-optic regime ensues viz, below the dielectric relaxation frequency, domains, and above, chevron distorions (M. Hareng, et al ).

Block copolymers with dielectrically active segments can provide insight into more local chain motions. A block polymer with a central active segment and dielectrically-silent wings shows relaxations in two frequency domains the relaxations are plausibly interpreted as local segmental motion and whole-body reorientation. 

Equation (10-4), the well-known dielectric response equation in the frequency domain, is equivalent to Eq. (10-1) if the assumption (2) holds. However, the assumption (2) is generally not vaUd for a reorienting NLC, when n(r ) const. 

A reorientation or depolarization of the domain is also effected by mechanical stress (e.g. 20... 50 N/mm for PZT). Influencing factors besides the stress magnitude are its direction and frequency as well as the kind of electrical circuit (e.g. open circuit, load or short circuit). If the electrical field induced by a force is in the polarization direction, the nonlinearities are essentially smaller than those of a generated field in the opposite direction or in the case of short circuit. 

Many relaxation processes influence the dielectric spectra of FLCs. Apart from the usual l.f. and h.f. modes characterizing the reorientations of molecules around their principal axes, the Sm C phase shows at least two collective processes. One collective mode, the Goldstone mode (GM), is associated with the fluctuations of the azimuthal angle (the cone motion) it is observed in Sm C phase at low frequencies and is not an activated process. The second mode, the soft mode (SM), is connected with the tilt fluctuations its critical frequency falls in the kilohertz range, from ca. 50 to ca. 500 kHz. The soft mode shows a decrease of frequency in Sm A phase on approaching the transition Sm A -Sm C, but it survives to the lower temperature phase. In special conditions (e.g., after applying an appropriate strength of the bias field ) yet another collective mode can be observed (domain mode). 

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