Dispersion frequency

It should be noted that there is a considerable difference between rotational structure narrowing caused by pressure and that caused by motional averaging of an adiabatically broadened spectrum [158, 159]. In the limiting case of fast motion, both of them are described by perturbation theory, thus, both widths in Eq. (3.16) and Eq (3.17) are expressed as a product of the frequency dispersion and the correlation time. However, the dispersion of the rotational structure (3.7) defined by intramolecular interaction is independent of the medium density, while the dispersion of the vibrational frequency shift (5 12) in (3.21) is linear in gas density. In principle, correlation times of the frequency modulation are also different. In the first case, it is the free rotation time te that is reduced as the medium density increases, and in the second case, it is the time of collision tc p/ v) that remains unchanged. As the density increases, the rotational contribution to the width decreases due to the reduction of t , while the vibrational contribution increases due to the dispersion growth. In nitrogen, they are of comparable magnitude after the initial (static) spectrum has become ten times narrower. At 77 K the rotational relaxation contribution is no less than 20% of the observed Q-branch width. If the rest of the contribution is entirely determined by... 

Figure 3 Frequency-dispersion curves of the longitudinal polarizability per unit cell of infinite periodic chains of hydrogen molecules according to the method used (RPA (bottom) and UCHF (top)). AH the values are in a.u.. The position of the first excitation energies which corresponds to the poles is indicated by vertical bars.

Lyden et al. [92] used in situ electrical impedance measurements to investigate the role of disorder in polysulfide PEC with electrodeposited, polycrystalline CdSe photoanodes. Their results were consistent with disorder-dominated percolation conduction and independent of any CdS formed on the anode surface (as verified by measurements in sulfide-free electrolyte). The source of the observed frequency dispersion was located at the polycrystalline electrode/electrolyte interface. 

Fig. 14. Factor analysis loadings (first and second spectral components) for thermal unfolding of RNase A as monitored with amide F FTIR and far-UV ECD. In each case a pretransition is evident in the curves before the main transition at 55°C. This full band shape analysis can sense smaller variations and can be partitioned to give added insight. Since the main ECD change could be shown to be loss of intensity, the major structural change was unfolding of a helix. The frequency dispersion of the FTIR change showed that some /3-sheet loss accompanied this pretransitional helix unfolding, but that most sheet loss was in the main transition.

The sequential order of the ZXX, XZX and XXZ (laboratory reference frame) polarization labels is important only to the extent that frequency dispersion affects the magnitude of the elements of... 

Further work on long polyenes, including vibrational distortion, frequency dispersion effects and electron correlation, would be important for evaluating more accurate asymptotic longitudinal polarizabilities and hyperpolarizabilities. 

For spin-f nuclei, dipolar interactions may be modulated by intramolecular (DF, reorientation etc.) and/or intermolecular (TD) processes. In general, the intra- and inter-molecular processes can produce quite different Tj frequency dispersion curves. In practice, NMR field cycling experiments are often needed to extend the frequency domain from those employed in conventional spectrometers to a lower frequency range (i.e., the kHz regime) for unambiguous separation (and identification) of different relaxation mechanisms. The proton spin relaxation by anisotropic TD in various mesophases has been considered by Zumer and Vilfan.131 133,159 In the nematic phase, Zumer and Vilfan found the following expression for T ... 

Au(lll) and Au(210) electrodes have been investigated [20] using electrochemical immitance spectroscopy in aqueous solutions of HGIO4 and KF in the doublelayer potential region, in order to identify and explain frequency dispersion of interfacial capacitance. At negative potentials, the behavior closest to the ideal dispersionless behavior has always been observed. In KF solutions, at positive potentials, dispersion on both electrodes may be attributed... 

If these statements were correct, we would then be in trouble. When the frequency dispersion Avo is large, no problem is to be expected. But what happens if the pump laser exhibits a high stability with a very short Avo In this situation, and for certain geometries of light condensers, it would also be possible to have At short, since they are independent quantities. Therefore, it looks as if it were possible, in such situation, to have AvA t — A Vo A t [Pg.544]

The effects of coupling of the DTO and RB units in not only one- but also three-dimensional arrays are discussed below and molecular weight trends illustrated. A fundamental connection between relaxation times and normal mode frequencies, shown to hold in all dimensions, allows the rapid derivation of the common viscoelastic and dielectric response functions from a knowledge of the appropriate lattice vibration spectra. It is found that the time and frequency dispersion behavior is much sharper when the oscillator elements are established in three-dimensional quasi-lattices as in the case of organic glasses. 

Here we suggest that in dilute polymer solutions there very probably exists a high frequency dispersion region corresponding to the DTO model, and examine one possible case, the secondary loss observed in poly (propylene) oxide. 

The interesting question is whether in dilute polymer solutions there exists a low frequency dispersion region described by the RB theory, so that just as in the bulk polymer we have to contend with two dispersion regions. The existence of a RB dispersion region in polymer solutions may be associated with entanglement and hence a very sensitive function of polymer concentration and molecular weight. 

Chien (C7) has proposed an energy mechanism for explaining the initial decrease in film thickness and subsequent formation of waves. Mayer (M7) has dealt with the manner in which the waves, which are initially fairly regular near the inception line, later develop into roll waves, etc., downstream, and Lighthill (L10) has also considered the manner in which waveforms may change by amplitude and frequency dispersion. 

Fig. 2.54 presents a two-dimensional carbon-proton shift correlation of D-lactose after mutarotational equilibration (40% a-, 60% / -D-lactose in deuterium oxide), demonstrating the good resolution of overlapping proton resonances between 3.6 and 4 ppm by means of the larger frequency dispersion of carbon-13 shifts in the second dimension. The assignment known for one nucleus - carbon-13 in this case - can be used to analyze the crowded resonances of the other nucleus. This is the significance of the two-dimensional CH shift correlation, in addition to the identification of CH bonds. For practical evaluation, the contour plot shown in Fig. 2.54(b) proves to be more useful than the stacked representation (Fig. 2.54(a)). In the case of D-lactose, selective proton decoupling between 3.6 and 4 ppm would not afford results of similiar quality. 

In the field of optics, dispersion denotes the retardation of a light ray. usually resulting in a change of direction as it passes into or out of a substance, (o an extenl depending on the frequency. Dispersion is a critically imponant property of optical glass. 

Various DMEs have been developed [7] and they are useful in various experiments. Blunt-ended DMEs are, for example, not useful in experiments carried out at higher frequencies. The shielding effect mentioned earlier creates a non-uniform distribution of current along the surface of the drop, and spurious frequency dispersion effects appear. 

Anomalous effects are often observed due to solution entering the capillary at the instant the mercury drop falls. In ac measurements, this phenomenon leads to anomalous frequency dispersion [12], In addition, the drop time becomes irreproducible. These effects may be diminished to a large extent by coating the internal wall of the capillary with a film of silicone [13]. A tip made of hydro-phobic (solvophobic) material may also be attached to the glass capillary. For example, a polyethylene tip was used [14] to discriminate against the attack of fluorides on glass in the study of double-layer structure in the presence of fluorides. In another study, capillary tips were modified with commercial narrow-bore PTFE tubes to determine arsenic in basic solution [15]. This procedure is also used for the hanging mercury drop electrode discussed in Section III. 

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