ON THE NONLINEAR BEHAVIOR OF DIELECTRIC-RELAXATION IN ALTERNATING-FIELDS .2. ANALYTIC EXPRESSIONS OF THE NONLINEAR SUSCEPTIBILITIES

Starting from the rotational diffusion equation of Smoluchowski, the e nsemble average of the first Legendre polynomial appropriate to dielec tric relaxation is calculated. The corresponding response is given up to the third order in the applied electric field by considering a cons tant field on which is superimposed an alternating field. Moreover, th e polar molecules are assumed to be anisotropically polarizable. Thus, we obtain three harmonic components of the electric susceptibility wh ere nonlinear coupling effects appear between the unidirectional field and the alternating field together with permanent and induced dipole moments. Dispersion plots are presented for some values of the paramet er P which measures the ratio between induced and permanent moments. A lso, for some values of this parameter P, the variations of phase angl es with frequency are considered and it is shown how they are interest ing in the treatment of experimental data by application of Kramers-Kr onig relations.