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

Both nonlinear dielectric relaxation and dynamic Kerr effect responses of a n assembly of polar and anisotropically polarizable molecules acted on by s trong superimposed external dc E-0 and ac E-1(t)=E-1 cos omega t electric f ields are evaluated in the context of the rotational diffusion model in the noninertial limit. The relaxation functions f(n)(t) (the expectation value of the Legendre polynomials P-n), which are appropriate to describe these nonlinear relaxation phenomena, are calculated by expanding them as a Fouri er series in the time domain. An infinite hierarchy of recurrence relations for these Fourier amplitudes of f(n)(t) is obtained, the solution of which is expressed in terms of an infinite matrix continued fraction, so allowin g us to evaluate the dynamic characteristics of the electric polarization a nd 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 permanen t or induced dipole moments are taken into account, can easily be extracted from the general solution. Diagrams of the frequency behavior of the in-ph ase and out-of-phase components of the electric birefringence and polarizat ion are presented showing pronounced nonlinear effects due to the high ac f ield. (C) 2000 American Institute of Physics. [S0021-9606(00)51006-X].