Relaxation, Debye transverse

Even if we consider a single solvent, e g., water, at a single temperature, say 298K, depends on the solute and in fact on the coordinate of the solute which is under consideration, and we cannot take xF as a constant. Nevertheless, in the absence of a molecular dynamics simulation for the solute motion of interest, XF for polar solvents like water is often approximated by the Debye model. In this model, the dielectric polarization of the solvent relaxes as a single exponential with a relaxation time equal to the rotational (i.e., reorientational) relaxation time of a single molecule, which is called Tp) or the Debye time [32, 347], The Debye time may be associated with the relaxation of the transverse component of the polarization field. However the solvent fluctuations and frictional relaxation occur on a faster scale given by [348,349]... 

Here /jn(f) is the intensity of the incident radiation and 0 is the phase of the interferometer in the dark. The functions N(< >) and M(< >) relate the intensities of the transmitted and intracavity fields to that of the incident light. The function 7ref (0 corresponds to the intensity of radiation from an additional source, which is very likely to be present in a real device to control the operating point. This description is valid in a plane-wave approximation, provided that we neglect transverse effects and the intracavity buildup time in comparison with the characteristic relaxation time of nonlinear response in the system. It has been shown that the Debye approximation holds for many OB systems with different mechanisms of nonlinearity. 

The picture in terms of the decoupled Eangevin equations (98) and (99) (omitting the inertial term in Eq. (98) is that the orientational correlation functions of the longitudinal and transverse components of the magnetization in the axially symmetric potential, Kvm sin" . are simply multiplied by the liquid state factor, exp(—t/T ), of the Brownian (Debye) relaxation of the ferrofluid stemming from Eq. (99). As far as the fenomagnetic resonance is concerned, we shall presently demonstrate that this factor is irrelevant. 

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). 

In Section V we are concerned with Gilbert s equation as applied to the Debye relaxation of a ferrofluid particle with the inertia of the particle included. It is shown, by averaging Gilbert s equation for Debye relaxation corrected for inertia and proceeding to the noninertial limit, how analytic expressions for the transverse and longitudinal relaxation times for Debye relaxation may be obtained directly from that equation thus bypassing the Fokker-Planck equation entirely. These expressions coincide with the previous results of the group of Shliomis [16]. 

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. 

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