ON THE TRANSIENTS OF THE NONLINEAR DIELECTRIC-RELAXATION RESPONSE

Transients of dielectric relaxation for an assembly of noninteracting rigid molecules acted on by a pure alternating stimulus of the form E( t)=E(O) cos omega t are calculated up to the third order in the electr ic field strength. Both permanent and induced dipole moments are consi dered which leads to a nonlinear response characterized by a mixture o f harmonics in omega, 2 omega, and 3 omega, and of exponential terms s uch that exp(-2Dt) and exp(-6Dt), where D represents the rotational di ffusion constant. The time-dependent behavior of the electric polariza tion which is given by the expected value of the first Legendre polyno mial < P-1(u)>(t) is obtained from solving the Smoluchowski equation. When one restricts up to terms in E(3), it is shown that the nonlinear dielectric response depends on the ensemble average of the second Leg endre polynomial (appropriate to Kerr effect relaxation) whose only te rms proportional to E(2) are retained. The evolution of < P-1(u)>(t) i s presented in some figures for different values of omega and the para meter P which reflects the balance between permanent and induced dipol ar moments. All these curves are compared with the corresponding linea r responses in order to emphasize their differences in the establishme nt of the phenomenon and in the stationary regime.