Fluctuations chiral nematics

In contrast to nematics, a helical twist of the molecular director takes place in the chiral nematic phase. Studies of the spin-lattice relaxation in chiral nematics have shown that the relaxation mechanisms are essentially the same as in pure nematics [141, 142]. At high Larmor frequencies the relaxation is diminished by molecular self-diffusion and by local molecular rotations, whereas director fluctuations determine the relaxation rate at low Larmor frequencies. This can be easily understood because the spin-lattice relaxation rate in the MHz region is dominated by orientational fluctuations with wavelength much smaller than the period of the helix. The influence upon the rotating frame spin-lattice relaxation time Tip of the rotation of the molecules due to diffusion along the helix, an effect specific for twisted structures, has not been observed in COC [143]. 

F re 3. Schematic diagram of selective reflection from a right-handed chiral nematic planar texture for A= inside the liquid ciystal. The linearly polarized input light may be considered as counter-propagating right-handed (RH) and left-handed (LH) circular components. The RH component in which the E field matches the sense of the helicoidal structure is back reflected due to director fluctuations, whilst the LH component is almost totally transmitted. By convention, the handedness is delined in terms of the progression of the E field vector in time relative to the observer. The RH rotating wave therefore has the same spatial structure as the chiral nematic at any time. 

The simplest case of Bragg diffraction is shown in Fig. 20 a for an ideal planar chiral nematic. If is the scattering vector, arising from the structure in, and local fluctuation of, e r), the dielectric tensor, then... 

The result obtained has very interesting consequences (i) to have well aligned SmA samples, very flat glasses without corrugation are needed (ii) even small dust particles or other inhomogeneities create characteristic defects in the form of semispheres (see Fig. 8.29b below) and weU seen under an optical microscope (iii) layers are often broken (not bent) by external factors in particular, strong molecular chirality may result in the formatimi of defect phases like twist-grain-boimdary phase (iv) the thermal fluctuations of director in smectic A phase are weak and the smectic samples are not as opaque as nematic samples. In fact there is a critical cell thickness for short-wave fluctuations. 

Non-chiral liquid crystal transforms directly from the isotropic phase into the nematic phase. If there is a spatial fluctuation in these phases (i.e. spatial non-uniformity) a physical property / (F) can be expressed in terms of a set of Fourier components / ( ) exp (- / r), where q is... 

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