Reorientational dynamics of an electric dipole in fluctuating electric fields

Abstract

The depolarization of rotating dipoles in a fluctuating electric field is discussed. When the random field is weak, a Fokker–Planck equation is derived from a stochastic model for dipole rotation. In particular, the coefficients in the Fokker–Planck equation showing coupling between random fields and an external field are derived for the first time for dielectric relaxation. This Fokker–Planck equation reduces to the simple rotational diffusion equation of Debye’s theory when the random electric field is white noise and isotropic but not otherwise. The early part of the dipole relaxation is found to be Gaussian in time although in the present paper the discussion is restricted to to the time regime after the initial inertial motion. The results also indicate that the relaxation time along the static external field, T1, gets longer as the static external field increases; this is in agreement with recent molecular dynamics simulation findings.