High-frequency relaxations

A typical example referring to frequency domain measurements is shown in Figure 1.11, where e", recorded with poly(methylacrylate) at various temperatures, is plotted as a function of frequency. The two peaks, related to a relaxation (low-frequency) and relaxation (high-frequency) are shifted to higher frequencies with increasing temperature (details of this phenomenon were outlined in Section 1.1.2.2). It should be noted that the a-relaxation is... 

The previous subsection described single-experiment perturbations by J-jumps or P-jumps. By contrast, sound and ultrasound may be used to induce small periodic perturbations of an equilibrium system that are equivalent to periodic pressure and temperature changes. A temperature amplitude 0.002 K and a pressure amplitude 5 P ss 30 mbar are typical in experiments with high-frequency ultrasound. Fignre B2.5.4 illustrates the situation for different rates of chemical relaxation with the angular frequency of the sound wave... 

Turning from chemical exchange to nuclear relaxation time measurements, the field of NMR offers many good examples of chemical information from T, measurements. Recall from Fig. 4-7 that Ti is reciprocally related to Tc, the correlation time, for high-frequency relaxation modes. For small- to medium-size molecules in the liquid phase, T, lies to the left side of the minimum in Fig. 4-7. A larger value of T, is, therefore, associated with a smaller Tc, hence, with a more rapid rate of molecular motion. It is possible to measure Ti for individual carbon atoms in a molecule, and such results provide detailed information on the local motion of atoms or groups of atoms. Levy and Nelson " have reviewed these observations. A few examples are shown here. T, values (in seconds) are noted for individual carbon atoms. 

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. 

This is a rather general conclusion independent of the model of rotational relaxation. It is quite clear from Eq. (2.70) and Eq. (2.16) that the high-frequency asymptotic behaviour of both spectra is determined by the shape of g(co) ... 

Anderson J. E., Ullman R. Angular velocity correlation functions and high-frequency dielectric relaxation, J. Chem. Phys. 55, 4406-14, (1971). 

As we relax in preparation for and pass into sleep, the active desynchronised awake EEG characterised by the low-amplitude (5-10 pV) high-frequency (10-30 Hz) beta waves becomes progressively more synchronised giving larger (20-30 pV) and slower (8-12 Hz) alpha waves, and then even slower (1-4 Hz) and bigger (30-150 pV) delta waves. This so-called slow-wave sleep is interrupted at intervals of some 1-2h by the break-up and desynchronisation of the EEG into an awake-like pattern. Since this is accompanied by rapid eye movements, even though sleep persists and can be deeper, the phase is known as rapid eye movement, REM or paradoxical, sleep. It is a time when dreaming occurs and when memory may be secured. 

The discrepancy may also be caused by the approximations in the calculation of the EEDF. This EEDF is obtained by solving the two-term Boltzmann equation, assuming full relaxation during one RF period. When the RF frequency becomes comparable to the energy loss frequencies of the electrons, it is not correct to use the time-independent Boltzmann equation to calculate the EEDF [253]. The saturation of the growth rate in the model is not caused by the fact that the RF frequency approaches the momentum transfer frequency Ume [254]. That would lead to less effective power dissipation by the electrons at higher RF frequencies and thus to a smaller deposition rate at high frequencies than at lower frequencies. 

It is appropriate to focus on some general parameters that could characterize a relaxation and to see how these are reflected in the experimental data. These parameters would include an unrelaxed, low temperature, high frequency modulus, Ejj, and a relaxed, high temperature,... 

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

There are two kinds of damping that are considered within the strong anharmonic coupling theory the direct and the indirect. In the direct mechanism the excited state of the high-frequency mode relaxes directly toward the medium, whereas in the indirect mechanism it relaxes toward the slow mode to which it is anharmonically coupled, which relaxes in turn toward the medium. 

---