High-frequency permittivity, measuring

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

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. 

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. 

Changes in the concentration of dispersed conducting particles also result in apparent changes in measured total high-frequency permittivity e p and low-frequency conductivity cr p of composite media. The Maxwell-Wagner equation for dilute monodispersed emulsion, where and = real permittivities ("dielectric constants") of the dispersion "insulating" media and the disperse conducting particles phase, and Op = conductivities of the dispersion media and the disperse phase, respectively, and O = volume fraction of the disperse phase, yields total measured system permittivity as [1, p. 91] ... 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

In the equation s is the measured dielectric constant and e0 the permittivity of the vacuum, M is the molar mass and p the molecular density, while Aa and A (po2) are the isotope effects on the polarizability and the square of the permanent dipole moment respectively. Unfortunately, because the isotope effects under discussion are small, and high precision in measurements of bulk phase polarization is difficult to achieve, this approach has fallen into disfavor and now is only rarely used. Polarizability isotope effects, Aa, are better determined by measuring the frequency dependence of the refractive index (see below), and isotope effects on permanent dipole moments with spectroscopic experiments. 

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. 

Dielectric relaxation — Dielectric materials have the ability to store energy when an external electric field is applied (see -> dielectric constant, dielectric - permittivity). Dielectric relaxation is the delayed response of a dielectric medium to an external field, e.g., AC sinusoidal voltage, usually at high frequencies. The resulting current is made up of a charging current and a loss current. The relaxation can be described as a frequency-dependent permittivity. The real part of the complex permittivity (e1) is a measure of how much energy from an external electric field is stored in a material, the imaginary part (e") is called the loss factor. The latter is the measure of how dissipative a material is to an exter-... 

Several comprehensive reviews on the BDS measurement technique and its application have been published recently [3,4,95,98], and the details of experimental tools, sample holders for solids, powders, thin films, and liquids were described there. Note that in the frequency range 10 6-3 x 1010 Hz the complex dielectric permittivity e (co) can be also evaluated from time-domain measurements of the dielectric relaxation function (t) which is related to ( ) by (14). In the frequency range 10-6-105 Hz the experimental approach is simple and less time-consuming than measurement in the frequency domain [3,99-102], However, the evaluation of complex dielectric permittivity in the frequency domain requires the Fourier transform. The details of this technique and different approaches including electrical modulus M oo) = 1/ ( ) measurements in the low-frequency range were presented recently in a very detailed review [3]. Here we will concentrate more on the time-domain measurements in the high-frequency range 105—3 x 1010, usually called time-domain reflectometry (TDR) methods. These will still be called TDS methods. 

Usually, the exponents a and (3 are referred to as measures of symmetrical and unsymmetrical relaxation peak broadening. This terminology is a consequence of the fact that the imaginary part of the complex susceptibility for the HN dielectric permittivity exhibits power-law asymptotic forms Im e (( ) coa and Im s (co) co aP in the low- and high-frequency limits, respectively. 

Microwave measurements have established with some high degree of probability that a small spread of relaxation times is exhibited by pure water. According to the Cole-Cole equation, the region between the static permittivity and the infinite frequency permittivity is spanned by the complex permittivity e, as defined in equation (13), where t is the principal relaxation time and a the spread parameter w = 2itv is the radial e = (Co - c )/tl + (j OT) -"] (13)... 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

From Maxwell s theory of electromagnetic waves it follows that the relative permittivity of a material is equal to the square of its refractive index measured at the same frequency. Refractive index given by Table 1.2 is measured at the frequency of the D line of sodium. Thus it gives the proportion of (electronic) polarizability still effective at very high frequencies (optical frequencies) compared with polarizability at very low frequencies given by the dielectric constant. It can be seen from Table 1.2 that the dielectric constant is equal to the square of the refractive index for apolar molecules whereas for polar molecules the difference is mainly because of the permanent dipole. In the following discussion the Clausius-Mossoti equation will be used to define supplementary terms justifying the difference between the dielectric constant and the square of the refractive index (Eq. (29) The Debye model). 

In general, polarizability, a, is difficult to determine experimentally. However, the ratio of the capacity of a condenser in a vacuum to that in the medium under consideration, i.e., the relative permittivity (earlier, dielectric constant), of the medium, can be measured. At low frequencies, the relative permittivity of electrical nonconductors is almost independent of the frequency. At high frequencies, the relative permittivity depends on the frequency, since the permanent dipoles are no longer able to establish a preferred orientation, because of rapid alteration of the field. 

---