Nonlinear dielectric relaxation of polar molecules in a strong ac electric field: steady state response

The nonlinear dielectric relaxation ac stationary response of an assembly of rigid polar molecules acted on by strong superimposed external dc E0 and ac E1(t)=E(1) cos omegat electric fields is evaluated in the context of the noninertial rotational diffusion model. The calculation proceeds by expanding the relaxation functions f(n)(t) (the expectation value of the Legendre polynomials P(n)), which describe the nonlinear relaxation of the system, as a Fourier series in the time domain. Hence, an infinite hierarchy of recurrence equations for the Fourier components of f(n)(t) is obtained. The exact solution of this hierarchy can be obtained in terms of a matrix continued fraction, so allowing us to evaluate the ac nonlinear response. For a weak ac field our results are in complete agreement with previous solutions obtained by perturbation methods. Diagrams showing the behavior of the in-phase and out-of-phase components of the electric polarization are presented.