Molecular inertial effects in liquids: Poley absorption, collision-induced absorption, low-frequency Raman spectrum and Boson peaks
Introduction
Poley [1] had found that the difference between the high-frequency permittivity and the square of the infrared refractive index, (ε∞−nir2), of several dipolar liquids at ambient temperature was proportional to the square of their molecule's dipole moment. This led him to predict that there is a significant power absorption in these liquids in the 1.2–70 cm−1 region. Interest in further investigating its features helped develop new techniques for accurate measurements of the permittivity and absorption coefficient in the far-infrared region of the spectra, and the new results obtained on a variety of liquids enabled modeling of its features in terms of inertial effects of a molecule undergoing rotational oscillations with its dipole vector slowly changing direction, like that of movements of a gyroscope. Davies [2] named the broad peak in the far-infrared spectra of low-viscosity liquids `Poley absorption'. This far-infrared absorption has since been found in a variety of supercooled viscous liquids and glasses [3], [4], [5], [6], [7], [8].
In the crystalline structures of ice clathrates, dipolar (and non-dipolar) molecules are trapped in the small-size symmetrical and rigid cages formed by tetrahedrally hydrogen-bonded water molecules. Crystal structure of one such ice clathrate of type II in space group Fd3m has been shown in Fig. 1(A), where tetrahedrally H-bonded water molecules shown by circles form the cage-like structures. The encaged molecules undergo both rotational oscillations and orientational diffusion [9], [10]. From detailed studies of rotational motions of the encaged molecules in the relatively low-frequency dielectric spectra of ice clathrates, Davidson [9] had inferred that there should be a contribution from the far-infrared polarization to their low frequency refractive index, which would not be due to water molecules. Instead it would be due to the rotational oscillations of the molecules inside the cages. An approximate treatment of the data led him to deduce that the frequency for rotation of the tetrahydrofuran molecule inside the cage of structure II is ∼20 cm−1. Similar rotational oscillations have been observed also for other clathrate structures [11], [12], [13], [14].
A subsequent study of the far-infrared absorption spectra [15] showed that there are two peaks in the spectra of the tetrahydrofuran-ice clathrate, one at 25 cm−1 and the second at 38 cm−1. These were attributed to the rotational oscillation of the tetrahydrofuran molecule about its two axes, while confined to the cages of the ice clathrate crystal. The absorption peaks in the far-infrared spectra resemble the Poley absorption, and have the same temperature dependence of their frequency. Contribution to the dielectric properties from orientational motions of the encaged molecules is observed at lower frequencies in the MHz range [9], [10], depending upon the temperature, and those from the orientational motions of the water molecules confined to the lattice sites of the clathrate structure appears at still lower frequencies. Thus, like liquids and glasses, the spectra of ice clathrates shows, (i) a peak in the far-infrared frequencies, (ii) a broad relaxation spectra due to the motion of the encaged molecules at intermediate frequencies, and (iii) a relaxation equivalent to the α-process at lowest frequencies. This is illustrated in Fig. 1(B). The motion of the guest molecules as studied by dielectric methods, is found to have a low activation and its relaxation rate to follow the Arrhenius equation. Similarity of the infrared and dielectric relaxation features of the reorientation of guest molecules in clathrates with the infrared and β-relaxation features observed in liquids and glasses was discussed earlier [16], where it was concluded that the two processes observed in clathrates and in viscous liquids are mechanistically analogous.
Low-frequency Raman spectra of liquids and glasses also show features, which have been of much interest since the 1970s, when the name Boson peak was given to a low frequency peak observed in the Raman spectrum. In 1971, before it was called the Boson-peak, Wang and Wright [17], [18] had reported a detailed study of the low-frequency Raman spectrum of the liquid and glassy states of glycerol. They had found that a peak in the measured Raman scattering intensity, IRaman, appears in the vicinity of 27 cm−1 in the supercooled liquid state of glycerol at 213 K. More recently, similar peaks have been reported in the 1.2–2.4 THz (i.e., 40–80 cm−1 range) of the spectra of dielectric loss of several viscous liquids and glasses [19], [20]. This peak also has been identified as the Boson peak, because the scattering function for the light is approximately proportional to the magnitude of ε′′. Features observed in inelastic neutron scattering experiments have since been referred to as the Boson peak, and low temperature heat capacity data have been attributed to the same phenomenon as that which gives rise to the Boson peak [21], [22]. For further details, papers in these proceedings and the proceedings of the third IDMRCS [23] may be consulted. Most recently, Kirillov et al. [24] and Kirillov [25] have provided brief reviews of the theoretical studies of the Boson peak, and Angell et al. [26] have summarized some of the earlier findings.
The low-frequency Raman scattering and the far-infrared absorption spectra of molecular liquids [27], [28], [29], [30], [31], [32], [33] and aqueous solutions [34], have also shown the above noted features. It is noteworthy that in 1975, Evans [35] had written a comprehensive review of the far-infrared absorption and the low-frequency Raman and neutron scattering studies on liquids. He had critically examined the application of various theories, in particular Mori's and subsequent mathematical formalisms, compared the respective observations on liquids from the Raman and far-infrared techniques and had critically appraised their merits [35].
Perova and Vij [36] and Perova et al. [37] were the first to have directly compared the features of the low-frequency Raman spectrum against those of the far-infrared absorption spectrum of several liquids over the 10–250 cm−1 range. They examined the features of the infrared absorption coefficient against an apparently comparable quantity R, which was determined from the magnitude of the measured Raman scattering intensity IRaman and the frequency. They found that the infrared absorption spectra and the R spectra in the 10–250 cm−1 are in general agreement with each other, but differ in detail. Therefore they concluded that collective rotational oscillations of molecular dipoles [36] in liquids may be treated in terms of the lattice vibrations in Szigetti's model for crystalline solids. Because the former was a property of a rigid glass and the latter a property of a low-viscosity liquid, they maintained that the Boson peak may be distinct from the Poley absorption. (This is reminiscent of the β-relaxation process which until 1970 was seen to be a property of a glass and not of a liquid [38], [39].) Perova [40] has reviewed earlier studies on the low-frequency Raman and far-infrared absorption in liquids.
Here we examine the similarities between the low-frequency Raman scattering features which includes the Boson peak in the Raman spectra, and the Poley absorption features in the far-infrared spectra and propose that the underlying molecular process of the features in the two spectra are similar. These features also seem analogous to the infrared absorption features attributed to rotational oscillations of molecules confined to the cage-like structures of an ice clathrate, in which geometrical symmetry of the cages makes mathematical treatment less complicated. Theoretical implications of this similarity are excluded from the discussion here, and it is pointed out that there is an additional feature in the THz frequency range, which arises from collision-induced absorption of non-dipolar molecules.
Section snippets
Poley absorption and the dipole inertial effects in liquids
Since the observation of a broad peak in the far-infrared absorption spectra of liquids is not widely known, it is appropriate to provide briefly its history. It had been recognized since the 1930s that the limiting high-frequency permittivity of orientation polarization, ε∞, of a liquid exceeds the square of its optical refractive index, nD2 After accurate measurements of the far infrared absorption became possible in the 1950s, and the refractive index in the far infrared frequency range, nir
Collision-induced absorption in the far-infrared region
Poley's finding [1] and Hill's formalism [50], [51] led to a broader search for an absorption peak in the far-infrared spectra of chlorobenzene, methylchloroform and other dipolar liquids. Chlorobenzene showed a peak at 48 cm−1 (1.44 THz), with a height of 12.6 Neper cm−1 and half width of 73 cm−1 after correction for the inertial effects according to Powles' modification [78] of Rocard's extension [79] of the Debye theory for dielectric absorption. But the need for more accurate observations
Far-infrared absorption in structures with permanent cages
It is clear that the far-infrared absorption observed in the ice clathrates [9], [10], [15] and in other type of clathrates [11], [12], [13], [14] would not have contributions from the collision-induced absorption, because the molecules are confined either to the lattice sites or within the cages. Since the cages formed by the molecules of the crystal lattice have a geometrical symmetry and calculations of the electrical field inside these cages has been possible (see citations in Refs. [9],
Low-frequency Raman scattering and the Boson peak
As mentioned earlier here, in their detailed study of the Raman scattering spectra of glycerol in both liquid and glassy states in the 5–100 cm−1 range, Wang and Wright [17], [18] had observed that the measured Raman scattering intensity, IRaman, shows a peak at ∼27 cm−1 at 213 K. After a comprehensive discussion of the subject, they explained this peak and the remaining features of the spectra in terms of a model for damped harmonic oscillator representing the vibrational modes.
Almost
Comparison of the low-frequency Raman spectra with the Poley absorption
Most studies have regarded the peak observed in the vicinity of ∼20–30 cm−1 in the spectrum of [IRaman(ν)/ν(1+n(ν))] of glasses and liquids as Boson peak, and its original interpretation, which was in terms of acoustic phonons, seems to have changed to an interpretation in terms of `strongly damped vibrational excitations', as in the original interpretation by Wang and Wright [17], [18], and in the interpretation of the Poley absorption, where the scaling by the factor ν−1[1−exp(−hcν/kBT)]−1
Comparison of the Boson peak and Poley absorption in liquids.
In order to directly compare the frequency range of a liquid's Poley absorption and Boson peak at ambient or high temperatures it is necessary to briefly describe how such peaks have been observed. In the literature, the Raman scattering intensity has been plotted by transforming into three terms, (i) IRaman(ν)/[ν(n(ν)+1)], (ii) IRaman(ν)ν/(n(ν)+1), and (iii) IRaman(ν)/(n(ν)+1). These three plots emphasize different parts of the spectral feature. Moreover, in the usual plots against ν, the wave
The collision-induced absorption in liquids
The faster process of collision-induced absorption in the far-infrared spectra, which involves translational motions, remains unresolved from the Poley absorption in some dipolar liquids. But since Hill [90] had later resolved the true contributions from Poley absorption in the measured αir(ν), it is possible to determine the far-infrared spectral profile arising from the collision-induced absorption alone by using her procedure. Another manner of observing this fast process may be by
Conclusions
A comparison of the far-infrared absorption and the low-frequency Raman scattering peaks for several molecular liquids and glasses shows that the two are similar within the uncertainty caused by molecule-specific effects that obscure the far-infrared absorption and not the Raman scattering. There are of course difficulties in assigning a particular feature in the light scattering spectra to Boson peaks, which have been seen at different places in the frequency spectrum of the Raman
Acknowledgements
I am grateful to Professors J.K. Vij and W.T. Coffey and to Dr T.S. Perova of Trinity College, Dublin, Ireland, for clarifying discussion. This study was supported by a grant from Natural Sciences and Engineering Research Council of Canada for my general research.
References (133)
- et al.
Chem. Phys. Lett.
(1982) - et al.
J. Molec. Struct.
(1999) J. Molec. Struct.
(1999)- et al.
Chem. Phys. Lett.
(1981) - et al.
Phys. Lett. A.
(1987) - et al.
Vibrat. Spectrosc.
(1997) - et al.
J. Molec. Liq.
(1996) - et al.
J. Mol. Struct.
(1999) - et al.
J. Molec. Liquid.
(1984) - et al.
Chem. Phys. Lett.
(1989)
Adv. Molec. Relax. Processes
Chem. Phys. Lett.
Chem. Phys. Lett.
Spectrochim. Acta
J. Non-Cryst. Solids
J. Appl. Sci. B
Accounts Chem. Res.
J. Chem. Phys.
J. Chem. Soc. Faraday Trans. II
J. Chem. Phys.
Mol. Phys.
J. Chem. Phys.
J. Chem. Phys.
J. Phys. Soc. Jap.
Discuss. Faraday Soc.
Can. J. Chem.
Ann. N.Y. Acad. Sci.
J. Chem. Phys.
J. Chem. Phys.
Phys. Rev. E
Contemp. Phys.
J. Chem Phys.
J. Chem. Phys.
Proceedings of Third IDMRS
J. Non-Cryst. Solids
Appl. Phys. Rev.
Russ. J. Phys. Chem.
J. Chem. Phys.
J. Chem. Phys.
Pis'ma Zh. Eksp. Teor. Fiz.
JETP Lett.
J. Chem. Phys.
J. Chem. Phys.
Adv. Chem. Phys.
Nature
Compt. Rend. Acad. Sci. Paris
Trans. Faraday Soc.
Cited by (46)
New understanding of TeO<inf>2</inf>–ZnO–Na<inf>2</inf>O ternary glass system
2021, Journal of Alloys and CompoundsCitation Excerpt :Those low energy excitations are used in different cases and among them it is used for explaining the presence of dispersed intensities, which are not present inside parent crystals on Raman spectra and incoherent neutron diffusion (INS) [33–35]. This point has been researched for many years theoretically or experimentally [36–50]. For more than four decades of research, the origin of this peak named as ‘Boson peak’, where the vibrational population of the energetic levels of this peak was dependent on the temperature following the Bose-Einstein statistical prediction, is intensively studied and however is still not satisfactorily explained.
Direct measurement of molecular mobility and crystallisation of amorphous pharmaceuticals using terahertz spectroscopy
2016, Advanced Drug Delivery ReviewsManifestation of thermodynamic glass transition by structure and picosecond dynamics in alkali tellurite glasses
2012, Journal of Non-Crystalline SolidsRattling the cage: Micro- to mesoscopic structure in liquids as simple as argon and as complicated as water
2011, Journal of Molecular LiquidsCitation Excerpt :Thus the spectra have two contributions: from (essentially single-molecule) rotations and librations, and from collision-induced effects [49]. Collision-induced effects were first introduced to explain light scattering from atomic liquids but play a major role in the spectra of all molecular liquids [46,75–77]. The spectra can in principle be simplified if either the permanent dipole moment or the anisotropic part of the polarizability tensor vanishes.
Terahertz vibrational modes induced by heterogeneous nucleation in n-alkanes
2010, Chemical Physics Letters