Relaxation, Debye

Although long-time Debye relaxation proceeds exponentially, short-time deviations are detectable which represent inertial effects (free rotation between collisions) as well as interparticle interaction during collisions. In Debye s limit the spectra have already collapsed and their Lorentzian centre has a width proportional to the rotational diffusion coefficient. In fact this result is model-independent. Only shape analysis of the far wings can discriminate between different models of molecular reorientation and explain the high-frequency pecularities of IR and FIR spectra (like Poley absorption). In the conclusion of Chapter 2 we attract the readers attention to the solution of the inverse problem which is the extraction of the angular momentum correlation function from optical spectra of liquids. 

In summary, the NFS investigation of FC/DBP reveals three temperature ranges in which the detector molecule FC exhibits different relaxation behavior. Up to 150 K, it follows harmonic Debye relaxation ( exp(—t/x) ). Such a distribution of relaxation times is characteristic of the glassy state. The broader the distribution of relaxation times x, the smaller will be. In the present case, takes values close to 0.5 [31] which is typical of polymers and many molecular glasses. Above the glass-to-liquid transition at = 202 K, the msd of iron becomes so large that the/factor drops practically to zero. 

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 ... 

Implicit in (9.40) is the assumption that co is small compared with lattice vibrational frequencies. The susceptibility in the frequency region where Debye relaxation is the dominant mode of polarization is therefore... 

Figure 9.15 Dielectric function of water at room temperature calculated from the Debye relaxation model with r = 0.8 X 10 11 sec, eQcl = 77.5, and e0l, = 5.27. Data were obtained from three sources Grant et al. (1957), Cook (1952), and Lane and Saxton (1952).

Fig. 1.1 Dielectric dispersion spectra for a polar solvent with a single Debye relaxation process in the micro-wave region and two resonant transmissions in the IR and UV ranges [5 b].

Fig. 7.6 Effect of sequential addition of the ultrafast component of the solvent orientational motion on the values in MeOH at 298 K. Closed circles are experimental results curves (1), (2) and (3) were obtained by the molecular theory by including the first (slowest) one, the first two, and all three Debye relaxations the dashed line is by the Zwanzig theory [30 b].

Considerable progress has been made in going beyond the simple Debye continuum model. Non-Debye relaxation solvents have been considered. Solvents with nonuniform dielectric properties, and translational diffusion have been analyzed. This is discussed in Section II. Furthermore, models which mimic microscopic solute/solvent structure (such as the linearized mean spherical approximation), but still allow for analytical evaluation have been extensively explored [38, 41-43], Finally, detailed molecular dynamics calculations have been made on the solvation of water [57, 58, 71]. 

Debye relaxation function was used for the solvent dielectric relaxation. From Ref. 32 with permission, from J. Chem. Phys. 90, 153 (1989). Copyright 1989, American Physical Society. 

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

In the experiments we have used two approaches. First, we have simulated the kinetics of a bistable optical system in the Debye relaxation appoximation for different forms of potential by means of electronic analog simulation. Secondly, we have investigated the kinetics of a double-cavity membrane system (DCMS) driven by two modulated laser beams at different wavelengths. This system is known to display optical bistability [111]. 

Agmon N. 1996. Tetrahedral displacement The molecular mechanism behind the Debye relaxation in water. JPhys Chem 100 1072-1080. 

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. 

It follows from Eq. (32) that the spectral function L(z) actually determines the absorption coefficient. At high frequencies,13 such thatx y, this coefficient is proportional to xlm[x (x)]. In other limit, at low frequencies, one may neglect the frequency dependence L(z) by setting L(z) = L(iy). In this approximation, Eq. (32) yields the Debye-relaxation formula (VIG, p. 194) ... 

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