On the calculation of field-dependent relaxation times from the noninertial Langevin equation

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Abstract
The problem of the dielectric relaxation of an assembly of noninteracting rigid dipoles subjected to a strong direct current field superimposed on which is a weak alternating field is treated by averaging of the noninertial Langevin equation regarded as a Stratonovich stochastic differential equation. The hierarchy of differential-difference equations so obtained is linearized in the alternating current (ac) field. It is then closed by assuming that the ratio of the Fourier–Laplace transforms of the ensemble averages of the first and second spherical harmonics may be replaced by its zero-frequency value. This allows one to obtain closed-form expressions in terms of the Langevin function for the relaxation times, complex susceptibility and loss tangent induced by the coupling between the direct current (dc) field and the weak ac field. The relaxation times produced by this closure procedure for ac fields applied parallel and perpendicular to the dc field are in good agreement with the results of a numerical solution of the secular equation of the problem and with available experimental data.