Rotational Brownian motion and dielectric relaxation of polar molecules subjected to a constant bias field: Exact solution

The longitudinal and transverse components of the complex dielectric susceptibility tensor and dielectric correlation times are calculated exactly for a system of noninteracting polar molecules placed in a constant external electric field. The calculations are carried out in the context of the rotational diffusion model. The theoretical results are compared with experimental data on both the magnetic relaxation of colloidal suspensions of single domain ferromagnetic particles (ferrofluids) and the dielectric relaxation of dilute solutions of polar macromolecules in a bias field. There is good agreement with the experimental data on both of these systems. It is shown that previous analytic results for the correlation time based on the effective eigenvalue method are in general an acceptable approximation to the exact solutions.