Librational band fractions libration

In water/ice the LIB fraction describes the librational band, centered at 700—800 cm-1 and located near the border with the IR range. In the case of water the LIB fraction explains also the nonresonance low-frequency relaxation range. 

This drawback is avoided in the variant 2a + 2b, which concerns the second stage of our modeling. An explicit but very simplified consideration of the HB-related effects is now given in terms of a two-fraction model. Here the LIB fraction is involved similarly with the variant la. In the case of water, the variant 2a explains the low-frequency relaxation (Debye) and the libration bands. In the case of ice only the latter band is considered. 

It is important that the total complex permittivity (28) comprises also the term or(v), originated in the LIB fraction from motion of a permanent dipole in the hat well. Hence, the total loss (35) of water comprises an additional term e"r(v), while in the RS, given by Eqs. (38), the corresponding term is lacking. This situation has a place, since we assume that rotation/libration of a polar molecule as a whole, which generates the librational band, does not contribute to the RS (in RS the latter band is very weak). Owing to this (viz., to absence of the term (v) in the formula for RS), the Raman spectra differ principally from the dielectric spectra. Another reason for such a difference arises due to the terms ( q)2, and... 

The model comprises the librational (LIB) and vibrational (VIB) fractions. A rigid permanent dipole, constituting the first (LIB) fraction, performs nonharmonic reorientation in the part of the structure formed by weak or torn hydrogen bonds (HB). This fraction stipulates the librational band of ice located at 800 cm-1. The second (VIB) fraction, constituted by two elastically vibrating oppositely charged HB molecules, describes T- and V-bands, located in... 

Molecules, reorienting in the hat well, belong to the main fraction of the fluids under consideration. This fraction comprises, in both water and ice, about 70% of all molecules. An underlying molecular mechanism, which governs the librational band, can be interpreted as follows. During the mean lifetime Tor, a dipole performs in the hat well on average about two (in water) and a half (in ice) libration cycles. In the case of water this motion is rather free, since a large part of the hat well constitutes a flat bottom (see Fig. 21b). In the case of ice, librations are more restricted. Indeed, as seen in Fig. 21a, the potential bottom is rather narrow. 

The LIB fraction (the fraction of monomers) containing about 55-70% of all water molecules comprises a permanent dipole, namely, a neutral molecule librating in a tight surrounding of other molecules in a condensed medium. This motion, governed by mechanism a, is responsible for the librational band, placed near the boundary of the IR region, and for the low-frequency Debye relaxation band, placed at microwaves. The Debye spectrum is not considered in this work. 

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