Debye relaxation electric fields

A finite time is required to reestabUsh the ion atmosphere at any new location. Thus the ion atmosphere produces a drag on the ions in motion and restricts their freedom of movement. This is termed a relaxation effect. When a negative ion moves under the influence of an electric field, it travels against the flow of positive ions and solvent moving in the opposite direction. This is termed an electrophoretic effect. The Debye-Huckel theory combines both effects to calculate the behavior of electrolytes. The theory predicts the behavior of dilute (<0.05 molal) solutions but does not portray accurately the behavior of concentrated solutions found in practical batteries. 

Debye and Falkenhagen predicted that the ionic atmosphere would not be able to adopt an asymmetric configuration corresponding to a moving central ion if the ion were oscillating in response to an applied electrical field and if the frequency of the applied field were comparable to the reciprocal of the relaxation time of the ionic atmosphere. This was found to be the case at frequencies over 5 MHz where the molar conductivity approaches a value somewhat higher than A0. This increase of conductivity is caused by the disappearance of the time-of-relaxation effect, while the electrophoretic effect remains in full force. 

Relaxation processes are probably the most important of the interactions between electric fields and matter. Debye [6] extended the Langevin theory of dipole orientation in a constant field to the case of a varying field. He showed that the Boltzmann factor of the Langevin theory becomes a time-dependent weighting factor. When a steady electric field is applied to a dielectric the distortion polarization, PDisior, will be established very quickly - we can say instantaneously compared with time intervals of interest. But the remaining dipolar part of the polarization (orientation polarization, Porient) takes time to reach its equilibrium value. When the polarization becomes complex, the permittivity must also become complex, as shown by Eq. (5) ... 

When a constant electric field is suddenly applied to an ensemble of polar molecules, the orientation polarization increases exponentially with a time constant td called the dielectric relaxation time or Debye relaxation time. The reciprocal of td characterizes the rate at which the dipole moments of molecules orient themselves with respect to the electric field. 

This longitudinal relaxation time differs from the usual Debye relaxation time by a factor which depends on the static and optical dielectric constants of the solvent this is based on the fact that the first solvent shell is subjected to the unscreened electric field of the ionic or dipolar solute molecule, whereas in a macroscopic measurement the external field is reduced by the screening effect of the dielectric [73]. 

S nuclear quadrupole coupling constants have been determined from line width values in some 3- and 4-substituted sodium benzenesulphonates33 63 and in 2-substituted sodium ethanesulphonates.35 Reasonably, in sulphonates R — SO3, (i) t] is near zero due to the tetrahedral symmetry of the electronic distribution at the 33S nucleus, and (ii) qzz is the component of the electric field gradient along the C-S axis. In the benzenesulphonate anion, the correlation time has been obtained from 13C spin-lattice relaxation time and NOE measurements. In substituted benzenesulphonates, it has been obtained by the Debye-Stokes-Einstein relationship, corrected by an empirically determined microviscosity factor. In 2-substituted ethanesulphonates, the molecular correlation time of the sphere having a volume equal to the molecular volume has been considered. 

University in Ithaca. Nobel Prize in 1936 for contributions to the knowledge of molecular structure based on his research on dipole moments, X-ray diffraction (Debye-Scherrer method), and electrons in gases. His investigations of the interaction between ions and electric fields resulted in the - Debye-Huckel theory. See also -> Debye-Falkenhagen effect, - Debye-Huckel limiting law, - Debye-Huckel length, - Debye relaxation time. 

Debye-Falkenhagen effect - Debye and - Falken-hagen predicted, that in - electrolyte solutions the ionic cloud may not be established properly and maintained effectively when the ion and the cloud are exposed to an alternating (AC) electric field in particular of high frequency. Thus the impeding effect of the ion cloud on the ion movement should be diminished somewhat resulting in an increased value of the ionic conductance. Above frequencies of v 107 to 108 s-1 this increase has been observed, see also - Debye relaxation time. 

Debye relaxation time — A stationary ion is surrounded by an equally stationary ionic cloud only thermal movement causes any change in the actual position of a participating ion. Upon application of an external electric field the ions will move. At sufficiently high frequencies / of an AC field (1// < r) the symmetry cannot be maintained anymore. The characteristic relaxation time r is called Debye relaxation time, the effect is also called... 

Electrophoretic effect — A moving ion driven by an electric field in a viscous medium (e.g., an electrolyte solution) is influenced in its movement by the - relaxation effect and the electrophoretic effect. The latter effect is caused by the countermovement of ions of opposite charge and their solvation clouds. Thus an ion is not moving through a stagnant medium but through a medium which is moving opposite to its own direction. This slows down ionic movement. See also -> Debye-... 

This result obtained by Debye [1] describes the frequency dependence of the permittivity . In the following discussion the relaxation time measured with the electrical field E as the controlled variable is called the Debye relaxation time and is given the symbol x. ... 

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... 

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. 

The Debye-Hbckel theory of electrolytes based on the electric field surrounding each ion forms the basis for modern concepts of electrolyte behavior (16,17). The two components of the theory are the relaxation and the electrophoretic effect. Each ion has an ion atmosphere of equal opposite charge surrounding it. During movement the ion may not be exacdy in the center of its ion atmosphere, thereby producing a retarding electrical force on the ion. 

The first process prevails at relatively low frequencies. The electric component E of radiation orients dipole moments p along the field direction, while chaotic molecular motions hinder this orientation p and E are the vectors, and the field E is assumed to vary harmonically with time t. Due to inertia of reorienting molecules the time dependence of the polarization lags behind the time dependence E(f), so that heating of the medium occurs (the heating effect is not considered in this work). The dielectric spectrum obeys the Debye relaxation, for which the absorption monotonically increases with frequency. 

The molecular origin of these relaxations has been established for dipolar molecular liquids by Debye [122] who has shown that the applied electric field perturbs the orientational distribution function for the dipolar molecules, leading to a static relative permittivity So greater than n, where n is the optical refractive index, and a dispersion for c (/) accompanied by a peak in c" f). 

In terms of the usual (constant electric field) dieleetrie relaxation time Tp, we have = Xj s /s. Let us assume that the whole relaxation kineties is exponential (the Debye model). Gaussian proeess with exponential eorrelation is Markovian [297]. In this case, the n-point distribution function G can be factorized into a product of two-point distribution functions G2, and the corresponding convolution-type perturbation series for the rate kernel can be summed up exactly [88] leading to Eq. (9.37), that is. 

---