Nonlinear dielectric relaxation and dynamic Kerr effect in a strong dc electric field suddenly switched on: Exact solutions for the three-dimensional rotational diffusion model

Abstract

The infinite hierarchy of differential-recurrence relations for ensemble averages of the spherical harmonics pertaining to the noninertial rotational Brownian motion of an ensemble of polar and anisotropically polarizable molecules in a strong external dc electric field is derived by averaging the underlying Langevin equation. This procedure avoids recourse to the Fokker-Planck equation, the solution of which involves complicated mathematical manipulations. Exact analytic solutions for the spectra of the relaxation functions and relaxation times for nonlinear dielectric relaxation and dynamic Kerr effect of symmetric top molecules are calculated for two limiting cases, namely, pure induced dipole moments and pure permanent moments, using the continued fraction method. The general case where both types of moment are taken into account is then considered by using matrix continued fractions. Exact expressions for the dielectric and Kerr effect relaxation times are also derived as functions of the parameters j and s characterizing the field-off and the induced dipole moments. Plots of these relaxation times are presented for various values of j and s. The nonlinear relaxation behavior is emphasized in figures showing how the real and imaginary parts of the spectra of the relaxation functions deviate from the Lorentzian profiles.