Water spectra permittivity

In this section we calculate the water spectrum in the range 0-1000 cm-1. This calculation is based on an analytical theory elaborated in 2005-2006 with the addition of a new criterion (38), related to the 50-cm 1 band in the low-frequency Raman spectrum. The calculation scheme was briefly described in Section II. One of our goals is to compare the spectra of liquid H20 and D20 and the relevant parameters of the model. Particularly, we consider the isotopic shift of the complex permittivity/absorption spectra and the terahertz (THz) spectra of both fluids. Additionally, in Appendix II we take into account the coupling of two modes, pertinent to elastically vibrating HB molecules. 

The first term, which contains the the static dielectric permittivities of the three media , 2, and 3, represents the Keesom plus the Debye energy. It plays an important role for forces in water since water molecules have a strong dipole moment. Usually, however, the second term dominates in Eq. (6.23). The dielectric permittivity is not a constant but it depends on the frequency of the electric field. The static dielectric permittivities are the values of this dielectric function at zero frequency. 1 iv), 2 iv), and 3(iv) are the dielectric permittivities at imaginary frequencies iv, and v = 2 KksT/h = 3.9 x 1013 Hz at 25°C. This corresponds to a wavelength of 760 nm, which is the optical regime of the spectrum. The energy is in the order of electronic states of the outer electrons. 

Figure 4.100 shows the Argand diagram of water (curve 1) and the permittivity for 0.8 M KCl (curve 2) in water. The stractural part of the spectrum is represented by curve 3. The difference of curves 2 and 3 is the result of electrolytic conductance. 

Our consideration concerns the wideband spectrum of liquid water (H20 and D20) in the range 0-1000 cm-1 and the spectrum of ice H20 in the far-infrared range 10—1000 cm-1. We apply the two-fraction (mixed) model, shortly described in Section A. In this model, one fraction refers to the librational (LIB) and the other refer to the vibrational (VIB) modes of molecular motion. In Sections B, C, and D we illustrate the loss spectra relevant to each of the four specific mechanisms (we reserve the term loss for the imaginary part of s). In Section E we write down the formulas for the total permittivity/absorption spectra by taking into account all the above-mentioned mechanisms. 

Namely, the LDL is in some respect similar to our LIB fraction regarding its connection with the HB network and dominance in contribution to the low-frequency spectrum (described by the first term in (39)), in particular, to the static permittivity 8S. However, in contrast to RAK, it is hardly reasonable to bring this fraction into correlation with the HB network itself due to the almost free libration of the dipoles in an intermolecular (hat) potential. On the other hand, it is reasonable to assign the VIB fraction to the HB network, which in our simplified calculation scheme is modeled by a dimer of oppositely charged water molecules connected by a hydrogen bond. Thus, in our opinion... 

The model described in this chapter can be applied to the calculation of the permittivity spectra in water in the broad frequency range 0-1000 cm-1 and to calculation of the ice far-IR spectra in the resonance region 50-1000 cm-1. As seen in Fig. 26 (curves I), in a nonresonance ice spectrum only the transverse-vibration mechanism (d) works. Indeed, we see from Fig. 24b that at v < 50 cm-1, namely in the submillimeter wavelength region and at lower frequencies, mechanisms a-c practically vanish. 

The Hamaker constant can be evaluated accmately using the continuum theory, developed by Lifshitz and coworkers [40]. A key property in this theory is the frequency dependence of the dielectric permittivity, e( ). If this spectrum were the same for particles and solvent, then A=0. Since the refractive index n is also related to t ( ), the van der Waals forces tend to be very weak when the particles and solvent have similar refractive indices. A few examples of values for for interactions across vacuum and across water, obtained using the continuum theory, are given in table C2.6.3. 

In microwave dielectric measurements (> 30 GHz) the dieleclric permittivity and dielectric losses for bound and free water show significantly different magnitudes. Thus, in measurements at high microwave frequencies the contribution from bound water in the dieleclric losses will be negligibly small, and the contribution from the free water fraction can be found. In contrast to the above-mentioned procedures used for calculation of bound water from the relaxation spectrum analysis, this approach will not involve analyses of overlapping relaxation processes and can thus easily be applied to microemulsions having a complex relaxation spectrum. 

Since the volume fractions of free, cpf, and bound, cp, water are both unknown, it is convenient to measure the dielectric permittivity in a frequency range where the dielectric loss of bound water may be safely neglected. The relaxation spectrum of free and bound water for our systems will safely satisfy this requirement at the measurement frequency of 75 GHz. In this case, die complex permittivity of the bound water is equal to its real part, i.e., = s -i-... 

The dynamics of lubricant interaction with added water is even more complicated. In addition to high-frequency permittivity changes described by Eq. 7-7, the entire impedance spectrum undergoes a complicated pattern of time-dependent changes. The low-frequency impedance changes caused by water will be discussed in a later section of this chapter. In the bulk solution a complex kinetics of water-oil interactions occurs, combining several mutually dependent processes of emulsification of free nonbound water, formation of inverse micelles, and evaporation of free and micellated water [21]. 

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