Permittivity of Isotropic Liquids

Liquid crystals are anisotropic fluids and the discussion of their dielectric properties is based on the fundamental ideas obtained for isotropic liquids. We recall the relevant results. 

The Maxwell equations for the electromagnetic field in conductive materials such as organic liquids read  

Here E and H are vectors of electric and magnetic field strength, (o)) and p(co) are frequency dependent dielectric and magnetic permittivities, ct is permanent conductivity. In the second equation, the two terms describe the displacement and Ohmic current, respectively. 

In the limit of co = 2nf oo no dynamic process in medium can foUow the field the electric polarization P = x E vanishes (i.e. dielectric susceptibility X 0) and the displacement vector D = (1 + 4jtx )E coincides with E, that is = 1 + 47tx 1. With decreasing frequency, fast electronic processes have enough time to follow the field and, at optical fi-equencies, e = (n is refraction index) shows peculiarities related to electronic absorption bands (normal and abnormal dispersion). With further decreasing frequency other processes such as molecular rotations and vibrations begin to contribute to the electric polarization and s = again increases, see Fig. 7.3. 

On the other hand, since for the sine-form field dE/dt oc caE the role of permanent conductivity ct decreases with increasing frequency, in the high frequency limit (0 1/tm = 47ta/ a material can be considered as non-conductive. The time Tm = /4tict is called Maxwell dielectric relaxation time. Later we shall meet it again under another name space charge relaxation time . 

---