Wideband spectra model

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. 

The depth of any reasonable potential well should of course be finite. Moreover, the recorded spectrum of such an important liquid as water comprises two absorption bands One, rather narrow, is placed near the frequency 200 cm, and another, wide and intense band, is situated around the frequency 500 or 700 cm-1, for heavy or ordinary water, respectively. In view of the rules (56) and (57), such an effect can arise due to dipoles reorientation of two types, each being characterized by its maximum angular deflection from the equilibrium orientation of a dipole moment.20 The simplest geometrically model potential satisfying this condition is the rectangular potential with finite well depth, entitled hat-flat (HF), since its form resembles a hat. We shall demonstrate in Section VII that the HF model could be used for a qualitative description of wideband spectra recorded in water21 and in a nonassociated liquid. 

The hat-curved model also gives a satisfactory description of the wideband dielectric/FIR spectra of a nonassociated polar fluid (CH3F) (Fig. 25). It is worthwhile mentioning that only a poor description of the low-frequency (Debye) spectrum could be accomplished, if the rectangular potential were used for such a calculation [32] see also Section IV.G.3. Unlike Fig. 25b, the estimated peak-loss frequency does not coincide38 in this case with the experimental frequency vD. 

In Fig. 2a we depict the wideband loss spectrum of water calculated in terms of the hat model for room temperature (27°C). For ice at —7°C a similar calculation (but in a much narrower band) is presented in Fig. 2b. The fitted molecular parameters are presented in Table I (some of these parameters will be determined below). During the lifetime Tor a dipole performs in water and ice about two librations and about six librations in supercooled water (mor = 5.6). 

Choosing room temperature as 20.2°C, we depict in Fig. 5a the wideband absorption frequency dependence a(v) of water H20 and in Fig. 6a we depict that of water D20. The fitted parameters of the model are presented in Table II. The total loss spectrum e"(v) is shown in Figs. 5b and 6b, respectively, for OW and HW. The solid lines in Figs. 5a,b and 6a,b mark the results of our calculations. 

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