Nonlinear harmonic components of the electric polarization of symmetric-top molecules

The nonlinear dielectric relaxation of an assembly of polar molecules submitted to the action of a dc field superimposed on an ac electric field is studied theoretically in the framework of the noninertial rotational diffusion model. It is also assumed that the permanent dipole moment vector makes an arbitrary angle with respect to the long molecular axis of each rodlike molecule. By calculating the ensemble averages of two Wigner rotation matrix elements 〈D0,01(Ω)〈(t) and 〈D0,11(Ω)〉(t), it is possible to express the first three harmonic components of the electric polarization varying in ω, 2ω and 3ω in analytic form, together with the steady-state frequency-dependent component. Three-dimensional dispersion and absorption plots are presented in order to show the influence of the diffusion anisotropy parameter Δ. Cole–Cole diagrams of the second and third harmonic components are also presented allowing one to distinguish two relaxation processes along the short and the long molecular axes, respectively.