Inertial effects in the nonlinear transient relaxation of rigid rodlike molecules in a strong dc electric field

Abstract

A method of calculation of nonlinear transient responses of an assembly of noninteracting polar linear molecules due to sudden changes in a strong external dc electric field is presented. The infinite hierarchy of differential-recurrence relations for the decay functions describing the relaxation of the system is derived by averaging the underlying inertial Langevin equation. The solution of this hierarchy is obtained in terms of matrix continued fractions. The integral relaxation time and the spectrum of the electric polarization for various nonlinear transient responses ͑step-on, step-off, and rapidly rotating field͒ are calculated for typical values of the model parameters. The nonlinear transient responses exhibit pronounced nonlinear effects due to the strong dc field. Analytical equations for the quantities of interest are presented in the overdamped limit. Furthermore, the linear response relaxation function and linear dynamic susceptibility are obtained as a particular case of a general nonlinear theory.

Inertial effects in the orientational relaxation of rodlike molecules in a uniaxial potential

“…The advantage in computational labor that the direct averaging method based on the Langevin equation has over the solution by the Fokker-Planck method is considerable because neither the derivation of that equation nor a knowledge of the intricate transformations used to effect separation of the variables in it is required. These advantages have been highlighted in a recent paper 22 in the context of the three-dimensional rotational Brownian motion in a potential.…”

“…Here we shall use a recently developed method 22 for the evaluation of the inertial response of systems of polar molecules in a double-well uniaxial potential, Eq. ͑1͒, with dynamics described by the inertial Langevin equation, which is based on an exact solution of the associated recurrence relations for the spectra of the statistical moments using matrix continued fractions and which also allows one to derive approximate analytic solutions by utilizing the concepts of the integral relaxation ͑correlation͒ time, escape rate, and the effective eigenvalue.…”