Water, librational modes

A noteworthy feature of the photoacoustic spectra shown in Figure 2 Is the presence of water librations. These are frustrated rotations and have been observed for ice (24) by infrared spectroscopy, as well as for water adsorbed on Ft and Ag surfaces by electron energy loss spectroscopy (25-27). The three libration modes have been associated with the bands at 600, 538 and 468 cm" > this set of peaks occurs for water adsorbed on both the hydroxylated and methoxylated silica. 

This band is a combination of deformation and librational modes, and is a very broad band. The band appears in a region typically free of interference in many agri-food samples. In some cases, the band can be used to monitor water content. 

Work by Nandi et al. [50] and by Hsu et al. [48] illustrated the importance of including high-frequency data into the expression for or the representation of s(cu) that is used as input into the continuum theory for S(t). They investigated SD in water and found that very good agreement with experimental SD data could be obtained using a representation of (o>) that includes the librational modes of the hydrogen bond network in addition to the exponential decay of the collective dipole time correlation. 

Finally, it was shown in various ways that it is the water librational motions that are important in the VET and that these involve coupled water molecular motions, since there is a significant contribution from non-IBI terms here. In view of the remarks above about the shape of the force spectrum itself differing in the absence and presence of the solute charges, and the validity of the IBI perspective in the absence of charges, the implication is that for the hypothetical no charge CC1 vibration at the same frequency, the librations would still be important for the VET, but they would involve only pair effects for the VET and would perforce interact significantly more feebly with the mode. 

Before returning to the main Coulomb force theme, it is important to stress that in LT formula simulations focused on the force on the solute vibrational mode, any energy transfer to implicated solvent modes, e.g., the water librations above, is actually inferred, rather than directly demonstrated. That is to say, such transfer — which is of course just vibration-vibration (VV) transfer — is not directly probed. We return to this issue at the conclusion of this chapter. 

Intermolecular effects in ionic solutions can also be studied in the Raman region between 200 and 1000 cm . Librational modes of water show up here. The intensity of such peaks changes linearly with the ionic concentration. The Vj bending mode in the Raman spectra of alkali halides in water was studied by Weston. They may also be interpreted in terms of models of primary hydration (water staying with the ion in motion) and a secondary disturbed region. 

Another quantity that can be obtained is the density of states of mobile protons, in particular the translational and librational modes for water of hydration as compared to those of bulk water. This method has been used with success for studying the self-dynamics of bulk water as a function of the temperature [62] as previously reported. 

Figure 2(a) shows Raman spectra in a wide frequency range in proton disordered Ih (thin spectra) and ordered XI phase (thick spectra). In spite of the low resolution (Av 15cm ), changes of spectra by the transition can be seen clearly in the lattice (translational, librational) modes and also in the stretching bands of water molecules. Particularly, peaks... 

Hindered rotations (librational modes) of a rigid water molecule in ice are observed in the frequency range of 600-900cm In Ih phase, as shown in the top of Fig. 5, weak and broad peaks are observed at about 770cm and 910cm" (shown by arrows) and the spectra show almost no polarization dependence. In addition to these peaks, a step-wise jump is seen at 1080cm and it becomes more clear in c(a,a)b spectrum in XI phase, the origin of which has not been known yet. 

As shown in Fig. 6(a), for an isolated water molecule there are three types of librational modes, twist(T), wag(W) and rock(R). Using the factor group analysis for the four molecules in a primitive cell, 12 librational modes in XI phase are divided into... 

Figure 6 (a) three types of librational mode of a single water molecule, (b) Typical... 

Molybdenum trioxide supported on alumina is the precursor of molybdenum disulfide based hydrodesulflirisation catalysts. Sulfiding of supported M0O3 is facilitated by bound water. INS spectroscopy was used to determine the nature of the water in hydrated M0O3/AI2O3 [92, 93]. The librational modes of co-ordinated water (Fig. 7.22) are observed in INS spectra when the water molecule is bound through the oxygen atom ( 9.2). 

Fig. 7.22 Librational modes of coordinated water molecules. Dotted lines are axes, 0 and 0 refer to forward and reverse motions of hydrogen atoms normal to the plane of the paper arrows are motions in the plane of the paper.

Potassium oxalate monohydrate [58] forms chains of alternating oxalate and water moieties. INS of single crystals has been used to assign the water translational and librational modes. Fig. 9.5. 

A small amount of carbonate is shown between 1415 and 1470 cm-1. The bands at 3400 and 1600 cm-1 belong to adsorbed water. The subscripts s, b and I refer to stretching, bending and librational modes, respectively (see Table 7.1). ( Licensed under a Creative Commons Attributions License.)... 

First let us compare the librational mode found for ice by Marchi [8] using lattice mode spectroscopy (see Fig. 18) with our smooth water-like absorption dependence illustrated by the right-hand part of Fig. 20a. This spectrum evidently agree much better with the experimental data than the noise-like pattern calculated by the MD method and depicted in the lower part of Fig. 18. It is important that in the work by Marchi [8] the dipole-induced-dipole terms provide the dominant contribution to the total intensities. However, in view of a recently MD modeling of water spectra by Sharma et al. [29], the polarization effects depend on the environment in a strong intermolecular way, which possibly was not taken into account in the cited treatment by Marchi. 

Another significant application of the centroid-based PI-QTST has been in the area of heterogeneous electron transfer (ET) across the electrodeelectrolyte interface [50]. In the latter research, a computer simulation method was developed for the study of such reactions in the adiabatic limit while allowing for the full quantization of all water solvent modes (i.e., collective dipole librations, molecular bends and stretches, etc.). 

Vibrational modes of water. Shown are the internal modes (a) symmetric stretch, (b) bending, (c) asymmetric stretch, and the librational modes (d) wag, (e) twist, and (f) rock. Not shown are the three hindered translational modes. 

In liquid water there are a number of eoUeetive inter-molecular vibrational modes, such as the HB excitation around 200 cm, which is like a breathing mode involving displacement of many molecules. Another example is the libration mode at around 600 cm, which is a restricted rotation, due to hydrogen-bonding. These low-frequency modes contribute to the entropy and specific heat of liquid water. But these modes are highly anharmonic, with a short lifetime, so the above description based on a harmonic oscillator cannot be used to describe them. 

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