Spectrum of Light and Orientation Fluctuation Dynamics

Just as the scattered light is distributed over a spectmm of wave vectors ky for a given incident wave vector k the frequency of the scattered light is distributed over a spec-tram of frequencies (Hf, for a given incident light frequency cd,. This spread in frequency Ao)= ay-co, is inherently related to the fact that the director axis fluctuations are characterized by finite relaxation time constants. 

In general, if the relaxation dynamics is in an exponential form [eg., An(f) = the frequency spectrum associated with this process, which is 

As shown in Chapter 3, the dynamics of the orientational fluctuations depends on the distortion modes involved and the corresponding viscosity coefficient. 

For a pure twist-type distortion, the equation of motion governing the elastic restoring energy and the viscous force is of the form 

The dynamics of the other two types of orientation distortions, bend and splay deformations, are more complicated because such distortions are necessarily accompanied by flow (i.e., physical translational motion of the liquid crystal) this phenomenon is sometimes called the backflow effect, which may be regarded as the reverse effect of the flow-induced reorientation effect discussed in Chapter 3. A quantitative analysis of these processes shows that the half-widths of the spectra associated with pure splay and pure bend deformations are given, respectively, by 

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