Dipole Dynamics of an Isotropic Liquid

To set the stage for discussion of frequency dispersion of liquid crystal permittivity we turn back to the isotropic liquids. First we shall find a characteristic relaxation time for molecular dipoles and then discuss real and imaginary components of the permittivity [10]. 

An applied electric field reduces the symmetry of an isotropic liquid from to Coov and creates anisotropy in the angular distribution function of dipoles the 

S is the decreasing with time angle between the dipole and E and is a fricti(Mi coefficient for a change of angle [g.cm s ]. Usually, due to high viscosity of a liquid, the inertial term may be neglected. Then 

Since the crnitribution of the considered dipole to the field-induced polarization is given by its projection on the -axis, pf = p .cos9, the rate of the increase of this projection is 

From here the kinetic equation may be written for the electric field induced polarization in the system of v dipoles in a unit volume with initial arbitrary orientation  

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