Relaxation time Debye

Mozumder (1969b) pointed out that in the presence of freshly created charges due to ionization, the dielectric relaxes faster—with the longitudinal relaxation time tl, rather than with the usual Debye relaxation time T applicable for weak external fields. The evolution of the medium dielectric constant is then given by... 

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. 

A single Debye relaxation time td has been measured for a number of common liquids, called Debye liquids. However, for alcohols, three relaxation times (tDi > tD2 > TD3) are generally found ... 

The correlation function C(t) is purely phenomenological. Interpretation of its time evolution is often based on theory in which the longitudinal relaxation time, tl, is introduced. This time is a fraction of the Debye relaxation time ... 

Debye relaxation time phys chem According to the Debye-Hrickel theory, the time required for the ionic atmosphere of a charge to reach equilibrium in a current-carrying electrolyte, during which time the motion of the charge is retarded. da bT, re,lak sa-sh3n, tTm ... 

Table 8.2 Debye relaxation times of some liquids (in ps)...

For a reasonable set of the parameters the calculated far-infrared absorption frequency dependence presents a two-humped curve. The absorption peaks due to the librators and the rotators are situated at higher and lower frequencies with respect to each other. The absorption dependences obtained rigorously and in the above-mentioned approximations agree reasonably. An important result concerns the low-frequency (Debye) relaxation spectrum. The hat-flat model gives, unlike the protomodel, a reasonable estimation of the Debye relaxation time td. The negative result for xD obtained in the protomodel is explained as follows. The subensemble of the rotators vanishes, if u —> oo. 

The results of the calculations of the spectra are illustrated by Figs. 18 and 19. The first figure refers to the temperature T = 133 K, which is near the triple point (131 K for CH3F). In this case the density p of a liquid, the maximum dielectric loss t j( in the Debye region, and the Debye relaxation time xD are substantially larger than those for T = 293 K (the latter is rather close to the critical temperature 318 K) to which Fig. 19 refers. The fitted parameters are such that the Kirkwood correlation factor is about 1 at T = 293 K. 

As a second example, we consider liquid fluoromethane CH3F, which is a typical strongly absorbing nonassociated liquid. For our study we choose the temperature T 133 K near the triple point, which is equal to 131 K. The relevant experimental data [43] were summarized in Table IV. As we see in Table VIII, which presents the fitted parameters of the model, the angle p is rather small. At this temperature the density p of the liquid, the maximum dielectric loss and the Debye relaxation time rD are substantially larger than they would be, for example, near the critical temperature (at 293 K). At such small (5 the theory given here for the hat-curved model holds. For calculation of the complex permittivity s (v) and absorption a(v), we use the same formulas as for water. 

In Section V the reorientation mechanism (A) was investigated in terms of the only (hat curved) potential well. Correspondingly, the only stochastic process characterized by the Debye relaxation time rD was discussed there. This restriction has led to a poor description of the submillimeter (10-100 cm-1) spectrum of water, since it is the second stochastic process which determines the frequency dependence (v) in this frequency range. The specific vibration mechanism (B) is applied for investigation of the submillimetre and the far-infrared spectrum in water. Here we shall demonstrate that if the harmonic oscillator model is applied, the small isotope shift of the R-band could be interpreted as a result of a small difference of the masses of the water isotopes. 

The role of specific interactions was not recognized for a long time. An important publication concerning this problem was the work by Liebe et al. [17], where a fine non-Debye behavior of the complex permittivity (v) was discovered in the submillimeter frequency range. The new phenomenon was described as the second Debye term with the relaxation time T2, which was shown to be very short compared with the usual Debye relaxation time td (note that td and 12 comprise, respectively, about 10 and 0.3 ps). A physical nature of the processes, which determines the second Debye term, was not recognized nor in Ref. [17], nor later in a number works—for example, in Refs. 54-56, where the double Debye approach by Liebe et al. was successfully confirmed. 

Equations (281b) and (282) determine the frequency dependence of the reorienting complex permittivity e r(v). One can estimate the principal (Debye) relaxation time by using the relation... 

When the temperature rises, the Debye relaxation time Td and the fitted mean reorientation time xor decrease, since intermolecular interactions weaken and become more chaotic. 

Returning to our problem, we remark that the temperature dependences of such parameters as, for example, the Debye relaxation time td(7 ) (which determines the low-frequency dielectric spectra), or the static permittivity s are fortunately known, at least for ordinary water [17], As for the reorientation time dependence t(T), it should probably correlate with in(T), since the following relation (based on the Debye relaxation theory) was suggested in GT, p. 360, and in VIG, p. 512 ... 

The pre-exponential factor in this case includes the solvent longitudinal relaxation time tl, which will be discussed further on when the recent works concerned with the role of the solvent will be considered. This longitudinal relaxation time is related to the usual Debye relaxation time according to... 

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]. 

Before results from MD simulation were available, it was assumed that ML (k, t) would both be predominantly diffusive and that the characteristic decay time tl for 4>ml (k, t) would be related to the Debye relaxation time rD characterizing the Lorentzian width of e(m) by [1,62]... 

A comparison between experimental and simulated main Debye relaxation time is presented in Figure 16-7. Simulation and experimental results show excellent agreement for not so dilute systems (p > 0.4g/cm3). However, below this density the experimental Debye time increases with decreasing density, whereas simulation results for this quantity keep decreasing and approaching the limiting behavior of a collection of free rotors. The extent of the loss of dynamic correlation between... 

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... 

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. 

Recent theoretical treatments, however, suggest instead that the dynamics of solvent reorganization can play an important and even dominant role in determining vn, at least when the inner-shell barrier is relatively small [43-45]. The effective value of vos can often be determined by the so-called longitudinal (or "constant charge ) solvent relaxation time, rL [43, 44]. This quantity is related to the experimental Debye relaxation time, rD, obtained from dielectric loss measurements using [43]... 

Some solvents may be characterized by one Debye relaxation time, t, corresponding to the rotational diffusion in the case of alcohols and solvents, where hydrogen bonds are formed, more than one relaxation process is observed [10]. 

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