Polar fluids Debye relaxation

Models 1 and 2 were applied to simple nonassociated polar liquids. Wideband Debye relaxation + FIR spectral dependencies of the permittivity s (v) and absorption ot(v) were successfully described. Usually only one quasiresonance absorption band (at v between 10 cm-1 and 100-200 cm-1) and one non-resonance Debye loss e" peak (at microwaves) arise in these fluids. Although a spatial model gives, unlike a planar one, a correct value of the integrated absorption J ° ve"(v)dv, the calculated spectral dependencies resemble those found for motion in a plane. 

The origin of the terms transverse and longitudinal dielectric relaxation times lies in the molecular theory of dielectric relaxation, where one finds that the decay of correlation functions involving transverse and longitudinal components of the induced polarization vector are characterized by different time constants. In a Debye fluid the relaxation times that characterize the transverse and longitudinal components of the polarization are T ) and rp = (ee/eslfD respectively. See, for example, P. Madden and D. Kivelson, J. Phys. Chem. 86, 4244 (1982). 

It is of interest to compare these results with those for the field dependencies of the relaxation times and for T for the longitudinal and for the transverse polarization components of a polar fluid in a constant electric field Eq. As shown in [52, 55] the relaxation times and T are also given by Eqs. (5.55) and (5.56), where = nEJkT, p. is the dipole moment of a polar molecule and is the Debye rotational diffusion time with = 0. Thus, Eqs. (5.55) and (5.56) predict the same field dependencies of the relaxation times Tj and T for both a ferrofluid and a polar fluid. This is not unexpected because from a physical point of view the behavior of a suspension of fine ferromagnetic particles in a constant magnetic field Hg is similar to that of a system of electric dipoles (polar molecules) in a constant electric field Eg. 

Debye obtained his result by solving a forced diffusion equation Ci.e., with torque of the applied field included) for the distribution of dipole coordinate p - pcosS, with 6 the polar angle between the dipole axis and tSe field, and the same result for the model follows very simply from equation (3) using the time dependent distribution function in the absence of the field (5). The relaxation time is given by td = 1/2D, which for a molecular sphere of volume v rotating in fluid of viscosity n becomes... 

This behavior is analogous to that of a polar molecule in a fluid under the influence of an electric field. This was studied by Debye [14], who obtained the relaxation time... 

---