High frequency permittivity

Tredgold et at. [397] adopted a rather different approach to self-assembly. In Equation (1.11) in Section 1.3 it was shown that, when London forces predominate, materials having different high frequency permittivities, and hence different refractive indices, will tend to separate. 

FTIR spectroscopy of electrolyte solutions has been employed to distinguish among free solvent molecules, solvent molecules bound to ions, and ion aggregates themselves. Furthermore, solvation numbers and association constants have been calculated from quantitative absorption measurements. Microwave spectra confirm the information from FTIR investigations. High frequency permittivity data deduced from MW and IR measurements yield information on the dynamic processes in electrolyte solutions. 

IIL High frequency permittivity measurements on electrolyte solutions and their solvents... 

V. Information on ion cluster formation from high frequency permittivity spectra... 

Ion-pair formation data from high frequency permittivity m for aqueous solutions of 1.1, 2.1 and 2.2 electrolytes 30,31 ... 

E,o and are the low- and high-frequency values of the permittivity for the relaxation process with relaxation time t,. The static permittivity is equal to the low- frequency permittivity for the first relaxation process Sjo. In addition, the high-frequency permittivity for the th relaxation is equal to the low-frequency permittivity for the (i + l)th relaxation Ep+po- Thus, for a liquid having n relaxation processes, there are n values of e,o which must be specified together with n different relaxation times, t, and finally the high-frequency permittivity for the last relaxation process, e oq. 

According to the Debye model there are three parameters associated with dielectric relaxation in a simple solvent, namely, the static permittivity s, the Debye relaxation time td, and the high-frequency permittivity Eoq. The static permittivity has already been discussed in detail in sections 4.3 and 4.4. In this section attention is especially focused on the Debye relaxation time td and the related quantity, the longitudinal relaxation time Tl. The significance of these parameters for solvents with multiple relaxation processes is considered. The high-frequency permittivity and its relationship to the optical permittivity Eop is also discussed. 

The static permittivity, ss, (frequency close to zero) and very high-frequency permittivity co could be defined in term of total polarization and distortion polarization as described by Eqs (14) and (15) ... 

A dipolar process is described in terms of three quantities the orientation polarization, the vibrational polarization, and the relaxation time. The first of the three is expressed as A =85-8oc, where is as defined earlier, and is the limiting high-frequency permittivity. The vibrational polarization is expressed as A8vib=eoo- op. where op is the refractive index of the material, usually at the... 

Note Ss is the equilibrium permittivity is the high-frequency permittivity r is the dielectric relaxation time AEji, is the activation energy and Ho is the dipole moment of the guest molecule in the vapor phase. 

The static permittivity (e and high-frequency permittivity (e) show the same behavior with regard to hydrate formation (Fig. 3a). When hydrate formation is taking place, free water is converted into hydrate water, and the volume fraction of free water in the emulsion falls. As a consequence, the low-frequeney permittivity de-ereases, and the level of this permittivity may thus be taken as a direct measure of the amount of water converted into hydrate. 

In another set of experiments (7) the influence on hydrate formation of various surface-active compounds extracted from crude oils was investigated. Tetrahydrofuran was used as the hydrate forming compound. In Fig. 5 flie high-frequency permittivity of emulsions stabilized by asphaltenes from crude A (see Table 2) is displayed as a function of time. The oil-phase solvent was a mixture of toluene and decane (1 4 or 3 2 in volumetric ratio, respectively). The aqueous phase constituted 40 v/v% of the emulsion. The asphaltene contents were 2 or 5 w/w%, respectively (w/w with regard to the oil phase). The water bath temperature was kept constant at -1.3°C through the course of the experiment... 

Initially, the high-frequency permittivity is steadily reduced from an initial value of 8 down to values in the range 3-5, reflecting the formation of hydrates. After 0.5 h flic permittivity has attained a fairly constant level, indicating that no more hydrates are formed. The final permittivity levels for the samples containing 5% asphaltenes seem to be somewhat higher than for the samples with 2% asphaltenes. However, the eomposition of the oil phase (i.e., the ratio between toluene and decane) also seems to have some influence on the final permittivity levels, and thus the amount of hydrates formed. 

Figure 6 High-frequency permittivity vs. time during hydrate formation Influence of waxes. (Adapted from Ref. 7.)...

PBNT. Lead Barium Neodymium Titanate has very low dielectric loss and its high frequency permittivity is stable over a wide temperature range, and so it is used in microwave resonators and filters. 

Barthel, J. and Buchner, R. (1991). High-frequency permittivity and its use in the investigation of solution properties. Pure Appl. Chem., 63,1473-1482. 

At lower temperatures the j8 process can be observed in the glass phase. The high-frequency permittivity above the jS relaxation is estimated to be 3.48 that distinctly exceeds n, indicating probably the y process. The activation enthalpy for the jS relaxation is 38kJ/mol for nonaligned sample, compared with 54kJ/mol for the homopolymer. The planar aligned sample yields 71 kJ/mol. 

Coq and are the limiting low and high frequency permittivities respectively, co is the angular frequency, cu = 2 tt/. If the relaxation function is given by the empirical relation of Williams and Watts 1970 Williams et al., 1971)... 

For the analysis of dielectric spectra, various strategies are available, which yield quantitative parameters like the electrical conductivity relaxation time T of possible relaxation processes, the high frequency permittivity e, etc. 

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