Observation of Fluctuations Using Light Scattering

Fluctuations in the order parameter are reflected in various physical properties of a liquid crystal material. In this section we will focus on the elastic (Rayleigh) scattering of light by such fluctuations in the isotropic phase of nematic and cholesteric materials near Tc. 

We begin by expressing the dielectric constant at an arbitrary point r in terms of the order parameter 

At a point fi far from the scattering volume the radiation from a volume d r around r due to the induced oscillating dipole moment P(f) 

Since 23(9) and 12(9) are independent, the cross terms in Eq. [117] average to zero, leaving 

Substituting Eq. [118] into Eq. [115] and using the results of Eq. [86] we have, finally, that the Rayleigh ratio for the scattering geometry of Fig. 11 is 

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