Debye absorption region

In the so-called Debye absorption region, dipole vibrations occur at a frequency lower than kT/li = 10 s , i.e. the solvent behaves as a classical system. But not all types of solvent polarization behave classically. For example, the atomic polarization of water has frequencies above 4 kT/ti, i.e. it behaves in a quantum-mechanical way. Moreover, even a small fraction of the Debye polarization has high natural frequencies, > kT/ti. Naturally, only the classical part of the Debye polarization determines the activation energy. And it is these coordinates that should be used when plotting potential energy diagrams for ion + solvent systems. 

Here multiplier 2 approximately accounts for doubling of integrated absorption due to spatial motion of a dipole, which is more realistic than motion in a plane to which LCs(Z) corresponds. For representation (235), only one (Debye) relaxation region with the relaxation time rD is characteristic. At this stage of molecular modeling it was not clear (a) why the CS potential, which affects motion of a dipole in a separate potential well, is the right model of specific interactions and (b) what is physical picture corresponding to a solid-body-like dipole moment pcs. 

Figure 2. Spectrum plot for nitrobenzene in a 7.5 nm pore at T = —4 °C this plot yields two distinct dielectric absorption regions. The solid and the dashed curves are fits to the Debye dispersion relation.

Tn the critical region of mixtures of two or more components some physical properties such as light scattering, ultrasonic absorption, heat capacity, and viscosity show anomalous behavior. At the critical concentration of a binary system the sound absorption (13, 26), dissymmetry ratio of scattered light (2, 4-7, II, 12, 23), temperature coefficient of the viscosity (8,14,15,18), and the heat capacity (15) show a maximum at the critical temperature, whereas the diffusion coefficient (27, 28) tends to a minimum. Starting from the fluctuation theory and the basic considerations of Omstein and Zemike (25), Debye (3) made the assumption that near the critical point, the work which is necessary to establish a composition fluctuation depends not only on the average square of the amplitude but also on the average square of the local... 

We shall show below that the hybrid model gives a satisfactory description of the usual Debye relaxation at the microwave region and explains a quasiresonance absorption band in the FIR region. 

In Fig. 28a we show for T = 27°C the frequency dependence of e and s", which comprises the Debye and FIR regions. We see three maxima on the loss curve 2. The frequency dependences obtained from the empirical formulas (shown by lines) agree well the measurement data (to obtain such an agreement at the lowest frequency v = 20 cm-1 we changed a little the values of the optical constants [42] at this frequency). The evolution of the recorded quasi-resonance absorption spectra with temperature is illustrated by Fig. 28b. For the highest temperature (50°C), curve 3, there is some disagreement with the empirical... 

Figures 32d-f, placed on the right-hand side of Fig. 32, demonstrate a wideband dielectric-loss frequency dependence. This loss is calculated (solid lines) or measured [17, 42, 51, 54] (dashed lines) for water H20 and D20 at the same temperatures, as correspond to the absorption curves shown on the left-hand side of Fig. 32. Our theory gives a satisfactory agreement with the experimental data, obtained for the Debye region, R- and librational bands, to which three peaks (from left to right) correspond. However, in the submillimeter wavelength region (namely, from 10 to 100 cm ) the calculated loss is less than the recorded one. The fundamental reason for this difference will be discussed at the end of the next section.

Solvent strength in the critical region. All of the experiments were performed with the dye phenol blue which has been well-characterized both experimentally and theoretically in liquid solvents (20,21,22). Since the dipole moment of phenol blue increases 2.5 debye upon electronic excitation (8), it is a sensitive probe of the local solvent environment. For example the absorption maxima occur at 550 and 608 nm in n-hexane and methanol, respectively. The excited state is stabilized to a greater extent than the ground state as the "solvent strength" is increased, which is designated as a red shift. 

In Figs. 5a,b and 6a,b we have a good coincidence of the calculated and experimental absorption and loss spectra. In the far-IR range the Debye relaxation band is not revealed. Only three mechanisms (a-c) contribute to dielectric relaxation in this region. Mechanism d, depicted by the curves 4, plays a noticeable role only in the lower part of the THz region. 

The loss and absorption peaks at v 700 cm-1, located near the border of the IR region, arise due to mechanism a—that is, due to reorientation of a rigid (permanent) dipole in the hat well. This mechanism is also responsible for the microwave loss peak located between the frequencies 0.1 and 1cm-1. The complex permittivity s of the corresponding relaxation band is actually governed by Debye theory, which is involved formally in our calculation scheme. 

The Mossbauer spectra of powdered samples of the clathrate are shown in Fig. 1. The statistics of the spectra is very poor at high temperature due to a low Debye-Waller factor (the absorption is 0.4 % at 320 K) and a relaxation phenomenon(absorption becomes broad in the region of the releixation time of 120 ns. The accumulated counts are more than a million counts above 250 K. The low temperature spectra of this clathrate are quite normal The efg for ferrocene derivatives is known to be essentially of molecular origin and the QS values do not... 

It has been noted that the conditions for observation of this type of absorption are much more favourable in solid polymers than in liquids. The point is that the relaxation times of polar liquids are of the order of magnitude of 10 s this means that the peak of Debye relaxation process will occur in the 1-10 cm" region and the broad absorption will extend through the region in which the Poley band is found. For polymers, however, the relaxation times are commonly much longer, typically ca 10" s, and the peak frequency of the Debye process is moved to a lower frequency therefore, the probability of resolving it from the Poley absorption is much higher. 

In the X-ray region the recoil energy can be so large that the frequency of y quanta emitted by free nuclei is shifted out of resonance with the absorption profile of the same transition in absorbing nuclei of the same kind. The recoil can be avoided by implanting the nuclei into the rigid lattice of a bulk crystal below its Debye temperature. This recoil-free emission and absorption of Y quanta is called the mGhauer effect. 

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