Scattering in SmA Liquid Crystals

Light-scattering processes in SmA liquid crystals are governed by fluctuations in the layer displacement they are analogous to scattering in nematics, which will be discussed in detail in the next chapter. In terms of the Fourier Ug components of the layer displacement, the free energy in the absence of an external field is given by  

Following the derivation given in Chapter 5, the intensity of the scattered wave is given by 

This is the usual case involving the transmission of light through a smectic film the scattering is much smaller than in the nematic phase. 

Case (2), however, corresponds to large scattering. If = 0, Equation (4.64) becomes 

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The threshold voltage (or field) for dynamic scattering in SmA liquid crystals was predicted in 1972 [Eq. (2)] by Geurst and Goosens [67] who extended the Carr-Helf-rich model [64] for dynamic scattering in nematics. 

The maximum scattering occurs at some resonance values of the wavevector q = m l qc. In fact, hght propagating along z probes different q modes with the number m. However, in comparison with nematics, well aligned, defect-free SmA liquid crystals are weakly scattering. 

There are very few structural studies of thermotropic side-chain polymers under shear flow. Recent work [54] describes the neutron scattering by the liquid crystalline polymethacrylate labelled PMAOC4H9 (Sect. 4.1) in the SmA phase. Typical liquid crystal behavior was observed in which the layers orient... 

Forced Rayleigh scattering experiments on smectic liquid crystals measured the binary mass diffusion constants parallel and perpendicular to the director (D and Dj ), finding that D is larger than Dj in both the smectic and nematic phase of 8CB [104]. Measure-ments for the SmB, SmA and N phases of p-butoxybenzylidene-p-n-octy-laniline show Z>n to be much smaller than Dx in the SmB phase (see Fig. 9) due to the different activation energies between the phases [105]. 

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