Shift of the frequencies

Usually, the most general nonspecific effects of dipole-orientational and electronic polarization of the medium are discussed, and the results of the theory of relaxational shifts developed under the approximation of a continuous dielectric medium may be used.(86 88) The shift of the frequency of the emitted light with time is a function of the dielectric constant e0, the refractive index n, and the relaxation time xR ... 

The results of a study of the laser-Raman spectra of sucrose are summarized in Table IX. The most important features observed187 when the concentration was varied consisted in shifts of the frequencies of the CH2OH group, which are sensitive to intra- and inter-molecular hydrogen-bonding. In addition, the association of D-glucose with D-fructose that leads to the... 

A method has been described108 for the vanadium(V) complexes with MeOH, utilizing the shift of the frequencies for the sym and asym vibrations of Me from 2835 and 2950 cm-1 in free MeOH to 2810 and 2910cm 1, respectively, in VO(OMe)L2 complexes, where HL = cupferron, 8-quinoli-nol, etc. The IR spectra of VO(OH)L2 complexes of the above two ligands have been recorded in this publication. 

The frequency analysis of this peak has been performed [18] and is shown in Fig. 27 in the temperature range - 112 to - 38 °C. In addition to the expected shift of the frequency at the peak maximum with increasing temperature, there was a large increase of ax, as we as a narrowing of the peak. Such a behaviour indicates that the dielectric / relaxation does not correspond to a unique process, but contains different processes with various activation energies, which gradually merge when the frequency is increased. 

In the expression (53), i/r coul>s the eigen function of Hamiltonian Coui(fi) and zn (q, — 8qs) is the wave function of, sth mode of the system without electron. Note that the potential of the electron interaction with the vibrations E/,-(r, q ) does not include in Hamiltonian H( p ), therefore the equilibrium position of the vibration mode is shifted to the value Sqs with respect to one in the system with electron (48). It is supposed that the vibrations are the phonons of the media, and the shift of the equilibrium positions are only taken into consideration. The possible shift of the frequencies may be easily taken into account by the corresponding changes in the phonon energy (see Chapter 2, formulas (20b), (27) and (27a)). The set of quantum numbers in (51) is v = (p, ns ), and the corresponding energies are... 

The isotopic shifts of the frequencies of straight vibrations of hydroxyls (cm-1)... 

When measurements such as those in Figure 2 are performed at various frequencies, the peak shifts to higher temperature at higher frequency, as shown in Figure 4 for an epoxy polymer (11). Here the measurements were made of Young s modulus at frequencies from 0.33 to 30 Hz as a function of temperature. As a rule of thumb, the peak shifts by about V C for every decade increase in frequency (12). Specifically, it is commonly assumed that the shift of the frequency, f, at which damping has a peak varies with absolute temperature, T, according to the Arrhenius rate equation... 

Fig. 65. Spectrum of water (bending mode) at various sili-con/electrolyte interfaces (a) nitromethane (b) acetonitrile (c) dimethyl sulphoxide. Note the progressive shift of the frequency upon increasing basicity of the solvent. (After [180]). Reprinted by permission of Elsevier Science.

In the monosubsti-tuted ethylenes (Table XLV), there is very little change in the frequency as the size of the substituent group is increased and it would appear that with propylene the maximum shift of the frequency had been attained. However, there are a number of substituent groups which lower the value of the frequency by an appreciable amount Table XLVI) and it would appear from the nature of such substituents that this change is associated with the contribution of valence bond structures to the resonance of the molecule in which the ethylenic bond has single bond, rather than double bond character. In the lowering of the frequency, the mass of the substituent... 

Another probe of the local environment around the azulene solute molecule was the shift of the frequency of the S3 Sq absorption band, as a function of density. This solvachromic shift, or stabilization of the electronic states of the solute in the presence of the solute, was accurately described using the same radial distribution function used to reproduce the collisional deactivation rates. The applicability of the same radial distribution function to treat collisional deactivation and solvachromic frequency shifts suggests that both have a similar dependence on local density. 

The enthalpy of hydrogen bond in cyclic dimers (Fig. 20a) in the ABA and AOBA is equal to —35.3 0.8 kJ/mol per hydrogen bond at T 300 K. For the quantitative estimation of the enthalpy the Iogansen method [296] has been applied, which is based on the analysis of the shift of the frequency of twisting vibration pOH and that of the gravity center of the Voh band of associates with relation to the corresponding shifts for monomers. The determination of frequencies pQ on and of ABA and AOBA monomers, which are needed... 

That means that, beside a time-independent phase shift, there exists a phase shift of the frequency 2co j, where co j is the circular frequency of the electric field. The Kerr cell is a set of two parallel electrodes placed between crossed polarizers. Thus the optical signal s behind the crossed polarizers is given by... 

The shifts of the frequency mode of vibration for phosphates are correlated with the amount of water displaced by each of these compoimds from the lipid membrane and with the dipole potential (Table 34.2). 

These considerations, however, cannot exclude the possibility that a vibration of a pyridine-halide-metal (atom or surface) complex is responsible for the debated Raman feature. This would explain the shift of the frequency from that of a metal-halide frequency, the stability to cathodic potentials" (and, perhaps, the relative insensitivity to the metal itself). One should mention in this context that Krasser et reported a band at 240 cm in the Raman spectrum of pyridine-silver cluster complexes, which they associate with a pyridine-Ag mode. 

Figure 8 shows the frequency functions for single cell protein content obtained by the same cultivation methods as just outlined. Considering the set of steady-state results obtained by the same start-up procedure (the top four frames In Figure 8), It Is apparent that there Is a significant shift of the frequency function towards higher protein contents and also Increased skewing to the right as the overall population specific growth rate Increases.

The IT Scale. Proposed in 1977 by the present authors (33h) this scale is based on the solvent-induced shifts of the frequency maxima of the x - ir transitions of seven indicators 4-nitroanisole (VII), N,N-diethyl-3-nitro-aniline (VIII), 4-methoxy-/S-nitrostyrene (IX), l-ethyl-4-nitrobenzene (X), N-methyI-2-nitro-p-toluidine (XI), N,N-diethyl-4-nitroaniline (XII) and 4-di-methylaminobenzophenone (XIII). 

The use of calcimn probes as lifdime-based sensors requires an undtfstanding of how the decay times change in response to Ca. One example is shown in Figure 5.29 for Quin-2. The mean decay time of Quin-2 increases horn 1.3 ns in the absence of Ca to 11.5 ns in the presence of Ca. Other laboratories have observed similar lifetime changes for Quin-2. This increase in lifetime results in a dramatic shift of the frequency response to lower frequencies. At intermediate Ca concentrations, where C in-2 is partially saturated with Ca , one can visually see that the frequency response is heterogeneous, and one can discern the contributions of the short and long decay times of Quin-2. 

---