Relaxation Theory of Nonlinear Processes in the Smoluchowski Rotational Diffusion Approximation

Kinetic Theory of the Langevin Saturation in Dilute Solution of Dipolar Symmetric-Top Molecules in Spherical Solvents

“…(12), (15)- (20) split into two components -the first, time-independent, and the second, changing with the double frequency 2ω, which describes the generation of the second harmonic polarization in the presence of a strong dc electric field. Various third-order electric polarization phenomena for the spherical-top molecules were discussed in [9][10][11].…”

“…The approximate solution of Eq. (3), if p x , p y , p z 1, known as "the low molecular reorientation", is given in [10,22].…”

“…In the particular case of the spherical-top molecule ξ = 1 and Eq. (3) becomes the well-known Smoluchowski-Debye equation depending on the polar angle ϑ only [9][10][11], which is fundamental for the theories of linear and nonlinear dielectric relaxation [6,7], the dynamic Kerr effect [5], as well as many interesting magnetic relaxation phenomena [6]. The approximate solution of Eq.…”

“…The Smoluchowski-Debye rotational relaxation theory has been extended to non-linear effects by Kielich and his co-workers [9][10][11], and applied to describe the dispersional and absorptional behavior of the third-order electric polarization induced in liquids consisting of the spherical-top molecule by external reorienting electric fields. The nonlinear-Langevin type relaxation was succesfully measured, as the nonlinear dielectric effect on the frequency of the probe field, by De Smet, Hellemans, Jadżyn, Kȩdziora and co-workers in many papers [14][15][16][17][18].…”

“…The Smoluchowski-Debye model of rotational diffusion of noninteracting, spherical-top molecules in solutions has been successfully applied in description of linear dielectric relaxation [1][2][3], the optical Kerr effect [4][5][6], the light scattering [7,8], various phenomena connected with the third-order electric polarization in liquids [9][10][11] and especially the nonlinear dielectric effect (NDE) measured at the frequency of the probe field [12][13][14][15][16][17][18]. This last effect, named the Langevin saturation, is characterized by a negative contribution to the nonlinear electric susceptibility χ(−ω; ω, 0, 0), due to a decrease in the potential energy of the polar molecules in dc electric field.…”