Inertial effects in the theory of dielectric and kerr effect relaxation. III. Assemblies of nondipolar anisotropically polarizable molecules in alternating and pulsed fields

Abstract

Exact expressions, in the low-field limit (where linear response theory applies), for the Kerr effect response (KER) including inertial effects, of nondipolar anisotropically polarizable molecules are given. These expressions (which are the generalisation of the Peterlin and Stuart theory for induced dipoles to include inertia) are obtained by adapting the inertia-corrected Debye theory of dielectric relaxation, due to Gross and Sack, to cover Kerr effect relaxation. The expressions in general have the form of continued fraction expansions in the frequency domain. This allows the amplitude of the in-phase and quadrature components of the ac response to be calculated to any desired degree of accuracy by taking successive convergents of the continued fractions. It is shown that taking the second convergent of the continued fraction is equivalent to using a modified Smoluchowski equation (MSE). This is equivalent to taking a 2 × 2 truncation of the n-matrix in the perturbation method already described by us. It is further shown that this equation provides an adequate description of the KER for induced dipoles for very small inertial effects. The inclusion of inertial effects causes the phase angle of the KER to show a sharp discontinuity at ▪ (where I is the moment of inertia of a molecule and ω the frequency of the applied field), rather than the linear increase predicted by the Peterlin and Stuart theory. In the case of rotation in two dimensions the continued fractions may be inverted exactly into the time domain to yield a closed-form expression for the KER to a rectangular pulse. In general the realization that linear response theory applies in the low-field limit means that the existing results of models for the permanent-dipole dielectric response may be carried over the induced-dipole KER with a few simple parameter changes.