Influence of the anisotropic polarizability on the anomalous dielectric relaxation spectra

The nonlinear dielectric response due to the application of a strong dc bias electric field superimposed on a weak ac electric field is considered in the context of the anomalous diffusion (subdiffusion). A perturbation procedure is used to derive analytical expressions for the first three harmonic components of the electric polarization of an assembly of both polar and anisotropically polarizable symmetric-top molecules. To accomplish that, an infinite hierarchy of multiterm (21) differential-recurrence equations of noninteger order for the moments is established and solved for the stationary regime. The results so obtained are illustrated in the form of Argand diagrams and three-dimensional relaxation spectra for the complex nonlinear dielectric increment extracted from the first harmonic component of the electric susceptibility. These plots show the role and importance played by the fractional exponent α and the parameter P measuring the influence of the dipole moment over the permanent one.