Dynamic Properties of Nematic Liquid Crystals

For finite wavelengths, the collective dynamics of bulk nematics can be described within the hydrodynamic equations of motion introduced by Ericksen [4-8] and Leslie [9-11]. A number of alternate formulations of hydrodynamics [12-18] leads essentially to the equivalent results [19]. The spectrum of the eigenmodes is composed of one branch of propagating acoustic waves and of two pairs of overdamped, nonpropagating modes. These can be further separated into a low- and high-frequency branches. The branch of slow modes corresponds to slow collective orientational relaxations of elastically deformed nematic structure, whereas the fast modes correspond to overdamped shear waves, which are similar to the shear wave modes in ordinary liquids. 

In the long-wavelength limit, the relaxation rates for both modes are proportional to which is characteristic of hydrodynamic modes. Here q is the wave-vector of the overdamped mode. 

In 1968 de Gennes introduced the concept of orientational normal modes in nematic liquid crystals that could successfully clarify the nature of this extraordinarily 

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)  

Here and j are the eigenvalues of the dielectric constant for optical frequencies in a direction parallel and perpendicular to the equilibrium director o  

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