Rotational Brownian Motion and Nonlinear Dielectric Relaxation of Asymmetric Top Molecules in Strong Electric Fields: The Langevin Equation Approach

Abstract

fields. The linear theory of electric polarization of dielectric fluids was formulated originally by Debye [11], who calculated the linear dielectric response in the context of the noninertial rotational diffusion model of spherical molecules. That response has a well-known representation in terms of the Debye equation for the complex dielectric permittivity and of the Cole-Cole diagram, which is a perfect semicircle. Linearresponse theory was further extended by Perrin [12] and others [13,14] to asymmetric top molecules when the dielectric response becomes more complicated, as rotation about each molecular axis may contribute to the dielectric spectra. The permittivity in linear response is independent of the applied electric field strength. Many attempts have been made to generalize the Debye theory in order to take into account the nonlinear aspects of dielectric relaxation of polar fluids in high electric fields, however only symmetric top molecules have been usually treated (see [15] and [16] and references cited therein for a review). The theory of rotational Brownian motion of asymmetric tops in an electric field (in the low field strength limit) has been developed by Wegener et al. [17-19] in a particular application to the Kerr effect relaxation (the results of Wegener et al. [17-19] were reproduced recently by Hosokawa et al. [20]). A theory of nonlinear dielectric relaxation of asymmetric top molecules in strong electric fields was developed in Ref. [21]. Here, this theory is presented in details. As a particular example, the theory is used to evaluate the nonlinear dielectric relaxation in superimposed ac and strong dc bias electric fields for a system of rodlike molecules, where the dipole moment vector may be directed at an arbitrary angle to the long molecular axis. In an experimental context, this technique has been recently proposed by Hellemans et al. [7