Wideband spectra

The liquid-state theory—in particular, that capable of describing the wideband spectra s = s — if of the complex permittivity and of absorption... 

First, we emphasize importance of studies of the effect of temperature T on the wideband spectra of water. A new step could be made in terms of the composite model described in Section VII. We may try to employ the following property discovered in this section. The parameters of the model, pertinent to intermolecular-potential geometry and to cooperative motions of the H-bonded molecules, exhibit only a small dependence on T. Hopefully, this result may facilitate describing or, better, predicting by means of analytical formulas the dependence on T of the wideband spectra of water and of aqueous solutions. 

It would be important to find analogous mechanism also for description of the main (librational) absorption band in water. After that it would be interesting to calculate for such molecular structures the spectral junction complex dielectric permittivity in terms of the ACF method. If this attempt will be successful, a new level of a nonheuristic molecular modeling of water and, generally, of aqueous media could be accomplished. We hope to convincingly demonstrate in the future that even a drastically simplified local-order structure of water could constitute a basis for a satisfactory description of the wideband spectra of water in terms of an analytical theory. 

This relation will be used further for calculation of the wideband spectra. Note again, that it is equally applicable for a rigid reorienting dipole and also for a nonrigid one formed by two oscillating charges. 

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. 

Although it is crude, our simplified approach permits us to investigate the main effect, namely, influence on wideband spectra of steric restrictions to reorientations of a strongly polar molecule. 

R-band characteristic for H20. Thus, it was suggested [47] that the confined rotator-extended diffusion model is capable of qualitatively describing the wideband spectra of water. 

Models 1-4 have a fundamental drawback The librational absorption band calculated for water appears to be too wide. This drawback at first glance could be overcome, if one employs the so-called field models, in which the static potential presents a smooth well (where a notion of a collision of a dipole with a wall actually has no physical sense). However, from the discussion given just below we shall see that this reasonable idea does not work properly with respect to calculating the wideband spectra in water. 

A general approach (VIG, GT) to a linear-response analytical theory, which is used in our work, is viewed briefly in Section V.B. In Section V.C we consider the main features of the hat-curved model and present the formulae for its dipolar autocorrelator—that is, for the spectral function (SF) L(z). (Until Section V.E we avoid details of the derivation of this spectral function L). Being combined with the formulas, given in Section V.B, this correlator enables us to calculate the wideband spectra in liquids of interest. In Section V.D our theory is applied to polar fluids and the results obtained will be summarized and discussed. 

A theory, accounting for an internal field correction [40, 41], gives the relationship % ( ), Eq. (139), between the complex susceptibility and permittivity. For calculation of the wideband spectra it is more convenient to employ the reverse dependence (% ), Eq. (141). 

Evident progress in studies of liquids has been achieved up to now with the use of computer simulations and of the models based on analytical theory. These methods provide different information and are mutually complementary. The first method employs rather rigorous potential functions and yields usually a chaotic picture of the multiple-particle trajectories but has not been able to give, as far as we know, a satisfactory description of the wideband spectra. The analytical theory is based on a phenomenological consideration (which possibly gives more regular trajectories of the particles than arise in reality ) in terms of a potential well. It can be tractable only if the profile of such a well is rather... 

Both HC-HO and HC-CS models yield very good description of the wideband spectra in ordinary and heavy water, but interpretation of these compsite model differs. 

Both hat-curved-harmonic oscillator and hat-curved-cosine-squared potential composite models considered in this section give excellent description of wideband spectra of water H20 and D20 in the range from 0 to 1000 cm-1. However, it appears that the physical picture of fast vibrations of the H-bonded molecules differ for these two approaches. In the first one, where... 

If the electrolyte concentration Cm varies, the wideband spectra are controlled only by one parameter (x) of the hybrid model. Other parameters of this model—the normalized well depth u, the libration amplitude ft, and the p-correcting coefficient —can be set independent of Cm and therefore could be fit by comparison of the calculated and recorded [70, 71] spectra of water (see Table XVI). 

Above (in Sections V—VII) the effect of the temperature Ton wideband spectra of water was briefly studied (only for two temperatures). The following important properties of our models were then found ... 

It should be noted that a number of the experimental data [93-98] is available concerning the wideband spectra of ice, which are sufficient at least for the start of above mentioned theoretical research. Useful empiric formulas were also suggested [99]. The hypothesis that a substantial contribution to the R-band is given in ice by stretching vibrations of the H-bonded molecules appears to be still more plausible than in the case of water, for which the experimental data [62, 63] confirm this viewpoint (see also Section VII). 

---