Debye frequency effect

Debye-Falkenhagen effect physchem The increase in the conductance of an electrolytic solution when the applied voltage has a very high frequency. d3 bT fal-kon,hag-on i,fekt ... 

Compared with the momentum of impinging atoms or ions, we may safely neglect the momentum transferred by the absorbed photons and thus we can neglect direct knock-on effects in photochemistry. The strong interaction between photons and the electronic system of the crystal leads to an excitation of the electrons by photon absorption as the primary effect. This excitation causes either the formation of a localized exciton or an (e +h ) defect pair. Non-localized electron defects can be described by planar waves which may be scattered, trapped, etc. Their behavior has been explained with the electron theory of solids [A.H. Wilson (1953)]. Electrons which are trapped by their interaction with impurities or which are self-trapped by interaction with phonons may be localized for a long time (in terms of the reciprocal Debye frequency) before they leave their potential minimum in a hopping type of process activated by thermal fluctuations. 

DEBYE-FALKENHAGEN EFFECT. The variation of the conductance of an electrolytic solution with frequency. This effect, which is noted at high frequencies, is also called the dispersion of conductance,... 

The concentration dependence of ionic mobility at high ion concentrations and also in the melt is still an unsolved problem. A mode coupling theory of ionic mobility has recently been derived which is applicable only to low concentrations [18]. In this latter theory, the solvent was replaced by a dielectric continuum and only the ions were explicitly considered. It was shown that one can describe ion atmosphere relaxation in terms of charge density relaxation and the elctrophoretic effect in terms of charge current density relaxation. This theory could explain not only the concentration dependence of ionic conductivity but also the frequency dependence of conductivity, such as the well-known Debye-Falkenhagen effect [18]. However, because the theory does not treat the solvent molecules explicitly, the detailed coupling between the ion and solvent molecules have not been taken into account. The limitation of this approach is most evident in the calculation of the viscosity. The MCT theory is found to be valid only to very low values of the concentration. 

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-Falkenhagen effect. In the absence of a complete and perfectly shaped ionic cloud movement of the ions is less impeded by the ionic cloud, thus electrolytic conductivity should increase. Above frequencies / 107 to 108 s-1 this increase has been observed, accordingly the Debye relaxation time is r 10-8 s. 

If the electrolyte is of the uni-univalent type and has a concentration of 0.001 molar, the Debye-Falkenhagen effect should become evident with high-frequency oscillations of wave length of about 20 meters or less. The higher the valence of the ions and the more concentrated the solution the smaller the wave length, and hence the higher the frequency, of the oscillations required for the effect to become apparent. 

Utilize the results obtained in the preceding problem to calculate the relaxation times of the ionic atmospheres and the approximate minimum frequencies at which the Debye-Falkenhagen effect is to be expected. It may be assumed that Aqtjo has a constant value of 0.6. The viscosities of the solvents are as follows nitrobenzene (0.0183 poise) ethyl alcohol (0.0109) and ethylene dichloride (0.00785). 

The properties of a one-dimensional Fermi gas model with two characteristic energies, two bandwidth cut-offs, is studied. The direct electron-electron coupling and the phonon mediated effective coupling are cut off at energies Ea and <0,, respectively, where E is the bandwidth of the electron energy band and to is the Debye frequency. The model is treated in the framework of renormalization group approach. It is shown that this model can be mapped on the usual one cut-off model and the results obtained for that model can be applied. 

For the same reason the conductivity increases at high frequencies, 3 x 10 Hz (Debye-Falkenhagen effect). The ion changes its direction of motion so quickly that the more sluggish atmosphere cannot adjust and follow the motion of the ion. The ion moves as if it had no atmosphere, and the conductivity increases. At high frequencies both the asymmetry and electrophoretic effects are absent. 

The conductivity increases at high frequency (>3 to 30 MHz, Debye-Falkenhagen effect). It takes approximately 0.1—1 ns to form an ionic atmosphere, and the time is dependent on the ion concentration. The literature is not clear as to the conductivity frequency dependence of electrolytes such as NaCl, but Cooper (1946) found no variations in the concentration range of 1—4 wt% and frequency range of 1—13 MHz. 

While much of his reputation was based on nonpolymeric accompHshments, such as demonstrated by the Debye-Huckel theory, the Debye-Scherrer x-ray diffraction technique, the Debye-Sears effect in liquids, the Debye temperature, the Debye shielding distance, the Debye frequency and the Debye unit of electric moment, his development of the hght scattering technique for the determination of the molecular weight of polymers resulted in his also being recognized as a world class polymer scientist. 

The frequency effect of K mainly originates from Ac because the remaining parameters are all independent of frequency in the low frequency region. Based on Debye relaxation model, Ac has following form ... 

This relation provides an explanation for the isotope effect in its simplest form from our discussion of phonons in chapter 6, we can take the Debye frequency... 

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 Debye-Falkenhagen effect. In the absence of a complete and perfectly shaped ionic cloud movement of the ions is less impeded by the ionic cloud, thus electrolytic conductivity should increase. Above frequencies / --10 to 10 this increase has been observed, accordingly the Debye relaxation time is r 10 s. 

From Equation 26.3 the Tc depends linearly on the Debye frequency, which predicts the isotope effect since the Debye frequency is proportional to the inverse square root of the mass of the vibrating atoms. We shall examine some of the other predictions in the following section. 

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