Thermally excited orientational director fluctuation

In a uniaxial nematic liquid crystal, the spatial orientation of the optical axis is determined by the orientation of the director. Due to thermally excited orientational director fluctuations, the spatial direction of the optical axis is not constant in time. As a result, any light illuminating the sample is... 

Proton, deuteron and carbon spin relaxation measurements of liquid crystals have provided detailed information about the molecular motions of such anisotropic liquids (anisotropic rotation and translation diffusion of individual molecules), and about a peculiar feature of liquid crystalline phases, namely collective molecular reorientations or order fluctuations. Spin relaxation in liquid crystalline mesophases has challenged NMR groups since the early 1970s, shortly after the publication of theoretical predictions that order fluctuations of the director (OFD, OF), i.e. thermal excitations of the long-range orientational molecular alignment (director), may play an important unusual role in nuclear spin relaxation of ordered liquids. Unique to these materials, which are composed of rod-like or disc-like (i.e. strongly anisotropic molecules), it was predicted that such thermal fluctuations of the director should, at the frequencies of these fluctuation modes, produce rather peculiar Ti(p) dispersion profiles. For example in the case of uniaxial nematic... 

Strong scattering of light. Similar to the phonon collective excitations in 3D solids, orientational normal modes in liquid crystals can be considered as plane-wave-like, spatially coherent excitations of the director field n (r, f), which determines the mean orientation of the long molecular axis. In contrast to phonons in solids, the excitations in liquid crystals are always overdamped because of the viscosity. De Gennes [27] considered the effect of such a thermally excited and overdamped orientational plane wave dnir,t) = 5n (t) on the optical properties of nematic and found that it is directly reflected in the fluctuation of the dielectric tensor field 5e(r, t) ... 

For the description of the long-wave-length elastic excitations in liquid crystals, we introduce a director field n(r, t), which describes the local orientation of the long axes of liquid crystalline molecules. For finite temperatures, this director field will fluctuate because of thermal excitations... 

The orientation of the director is not constant in time and fluctuates due to thermal excitations. Because the energy associated with the local perturbation of the director is small, the amplitude of the thermal fluctuations is large. With the director, also the optic axis fluctuates and with it the optical dielectric constant, which results in strong scattering of light. This feature is most prominently observed in the opaque appearance of liquid crystals. 

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