High-frequency dielectric data

These results allow a test of the Onsager cavity model for a uniform dielectric continuum solvent with a dielectric response that is well modeled by Eq. (24). Our group recently tested this model for methanol. In this case, both high frequency (co) data (see Barthel et al. [Ill]) and short time resolution C(t) data [32] exist. 

An innovative approach due to Haider et al. [113] may help to sidestep the challenges involved in explicit molecular dynamics simulation and obtain information on these slow dynamics. The authors use the results of dielectric reflectance spectroscopy to model the IL as a dielectric continuum, and study the solvation response of the IL in this framework. The calculated response is not a good description of the subpicosecond dynamics, a problem the authors ascribe to limited data on the high frequency dielectric response, but may be qualitatively correct at longer times. We have already expressed concern regarding the use of the dielectric continuum model for ILs in Section IV. A, but believe that if the wavelength dependence of the dielectric constant can be adequately modeled, this approach may be the most productive theoretical analysis of these slow dynamics. 

The static dielectric constants eo, can be determined from the analysis of IR spectra with sufficient spectral data coverage below and above the reststrahlen regions. For photon energies far above the phonon resonances but still sufficiently below the electronic band-to-band transitions, the DFs converge to the high-frequency dielectric constants OCjwhich is related to 0, by the Lyddane-Sachs-Teller relation (3.5). measure the sum of... 

The CD function indicates that the dielectric loss (e") of glycerol follows the power law e" /Pcd at high frequencies (f fmx), where/max is the frequency corresponding to the dielectric loss peak. However, the high-frequency experimental data in Fig. 24 demonstrate a significant deviation from the expected asymptotic behavior both for CD and KWW functions, e" values... 

Table 5.5 shows experimental values of E, E and the cohesive energies (from Table 5.3) for a number of AB compounds. The average energy gap results are those calculated from experimental data on high-frequency dielectric constants for the crystals. Later we will compare these values of E with those calculated from our earlier bonding models. 

Fig. 4.1-49 Ge. Temperature dependence of the high-frequency dielectric constant [1.48]. Experimental data points [ 1.49] and ah initio calculations (solid line)-, the dotted line is the theoretical result without the effect of thermal expansion, and the dashed line is the solid line shifted to match the experimental data...

One of the reports of dielectric functions of ZnO is that by Ashkenov et al. [135] who characterized thin films grown by pulsed laser deposition on c-plane sapphire and a single-crystalline sample grown by seeded chemical vapor transport method. The static dielectric constant was obtained from infrared spectroscopic ellipsometry measurements. The high-frequency dielectric constant was calculated through the Lyddane-Sachs-Teller (LST) relation, (Equation 1.31), using the static constant and the TO- and LO-phonon mode frequencies. The results are compared with the data from some of the previous studies in Table 3.8. 

For the data presented in Figure 1-4, it can be noted that measured permittivity is low at high frequencies and often becomes very high at low frequencies (due to interfacial polarization). The modulus representation shows very small absolute modulus values at low frequencies (and the low frequency semicircle is invisible in Figure 2-6B) where the impedance notation is particularly powerful but will resolve high-frequency dielectric responses well. Figure 2-6 illustrates this example for the - R,ntI dl circuit. 

A novel optimization approach based on the Newton-Kantorovich iterative scheme applied to the Riccati equation describing the reflection from the inhomogeneous half-space was proposed recently [7]. The method works well with complicated highly contrasted dielectric profiles and retains stability with respect to the noise in the input data. However, this algorithm like others needs the measurement data to be given in a broad frequency band. In this work, the method is improved to be valid for the input data obtained in an essentially restricted frequency band, i.e. when both low and high frequency data are not available. This... 

Paddison et al. performed high frequency (4 dielectric relaxation studies, in the Gig ertz range, of hydrated Nafion 117 for the purpose of understanding fundamental mechanisms, for example, water molecule rotation and other possible processes that are involved in charge transport. Pure, bulk, liquid water is known to exhibit a distinct dielectric relaxation in the range 10—100 GHz in the form of an e" versus /peak and a sharp drop in the real part of the dielectric permittivity at high / A network analyzer was used for data acquisition, and measurements were taken in reflection mode. 

We assume that if many of the liquids of interest, such as propylene carbonate, were studied by higher frequency (measurement techniques, new, high frequency components would be discovered which would account at least partially for the short time scale dynamics we see in the solvation C(f) data. Indeed, the apparent observation of a single Debye time is inconsistent with theories of liquids that take into account dipole-dipole interactions (see Kivelson [109]). Furthermore, some of the liquids studied have extraordinarily large apparent infinite frequency dielectric constants (e.g., = 10... 

Experimental methods are applicable for a wide range of frequencies. High-frequency measurements employ commercially available dielectric constant meters, Q-meters, and so on the impedance bridge method is widely employed at low frequencies. The levels of the frequencies applied experimentally are very important for data interpretation and comparison. 

The high frequency limit of for this second process is therefore n. The result of the fit is shown in Table III where the mean values of the various parameters and their associated 95% confidence intervals are given. Considering the small amplitude of the second dispersion both in absolute t rms and in relation to the main dispersion the parameters 6m, n and Y are quite well defined, and therefore it may be concluded that the double Debye representation is an acceptable description of the dielectric behaviour of water up to around 2THz. Other alternative interpretations are clearly possible but no attempt has been made here to follow these up at this stage. What is clear is that a small subsidiary dispersion region in the far infrared is necessary to account for all the presently available permittivity data, and that such a dispersion is centred around 650GHz and has an amplitude of about 2.4 in comparison with that of the principal dispersion which is approximately 75. 

Because of measurements of dielectric relaxation made at frequencies that were too low, and a long extrapolation to high frequencies, this parameter is frequently not determined precisely, and in the literature there are discrepancies between data reported for a given solvent. For instance, for DMF one may find the following values 2.51 [195], 3 [196], 4.5 [197] and 5.0 [198] op for DMF is 2.040. For other solvents also, the reported data of vary considerably. 

The high-frequency precision of t.d.s. methods has been tested by making measurements on water itself. The data for water at 278 K are shown on Figure 12, together with a r resentative sample of frequency domain measurements. On the basis of most of the previous dielectric S. K. Garg and C. P. Smyth, J. Phys. Chem., 1965,69, 1254. 

Impedance data are presented in different formats to emphasize specific classes of behavior. The impedance format emphasizes the values at low frequency, which t5rpically are of greatest importance for electrochemical systems that are influenced by mass transfer and reaction kinetics. The admittance format, which emphasizes the capacitive behavior at high frequencies, is often employed for solid-state systems. The complex capacity format is used for dielectric systems in which the capacity is often the feature of greatest interest. 

As far as comparison with experimental data is concerned, the fractional Klein-Kramers model under discussion may be suitable for the explanation of dielectric relaxation of dilute solution of polar molecules (such as CHCI3, CH3CI, etc.) in nonpolar glassy solvents (such as decalin at low temperatures see, e.g., Ref. 93). Here, in contrast to the normal diffusion, the model can explain qualitatively the inertia-corrected anomalous (Cole-Cole-like) dielectric relaxation behavior of such solutions at low frequencies. However, one would expect that the model is not applicable at high frequencies (in the far-infrared region), where the librational character of the rotational motion must be taken... 

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