Steady state response of the nonlinear dielectric relaxation and birefringence in strong superimposed ac and dc bias electric fields: Polar and polarizable molecules

Abstract

Both nonlinear dielectric relaxation and dynamic Kerr effect responses of an assembly of polar and anisotropically polarizable molecules acted on by strong superimposed external dc E0 and ac E1(t)=E1 cos ωt electric fields are evaluated in the context of the rotational diffusion model in the noninertial limit. The relaxation functions fn(t) (the expectation value of the Legendre polynomials Pn), which are appropriate to describe these nonlinear relaxation phenomena, are calculated by expanding them as a Fourier series in the time domain. An infinite hierarchy of recurrence relations for these Fourier amplitudes of fn(t) is obtained, the solution of which is expressed in terms of an infinite matrix continued fraction, so allowing us to evaluate the dynamic characteristics of the electric polarization and birefringence. For a weak ac field, the results predicted by the theory are in complete agreement with previous solutions obtained by perturbation methods. The solutions for the particular cases, where only either permanent or induced dipole moments are taken into account, can easily be extracted from the general solution. Diagrams of the frequency behavior of the in-phase and out-of-phase components of the electric birefringence and polarization are presented showing pronounced nonlinear effects due to the high ac field.