Absorption, collision-induced

L. Frommhold, Collision Induced Absorption in Gases, 1st edition, Cambridge Monographs on Atomic, Molecular, and Chemical Physics, Vol. 2 Cambridge University Press, England, 1993. 

FIGURE 4-6 Absorption bands of (a) 02 and (b) collision-induced absorptions of 02 with 02 and for the f.26-/am band with N2, respectively (adapted from Solomon et al., f998). 

Mlawer, E. J S. A. Clough, P. D. Brown, T. M. Stephen, J. C. Landry, A. Goldman, and F. J. Murcray, Observed Atmospheric Collision-Induced Absorption in Near-Infrared Oxygen Bands, J. Geophys. Res., 103, 3859-3863 (1998). 

Spectroscopy is concerned with the interaction of light with matter. This monograph deals with collision-induced absorption of radiation in gases, especially in the infrared region of the spectrum. Contrary to the more familiar molecular spectroscopy which has been treated in a number of well-known volumes, this monograph focuses on the supermolecular spectra observable in dense gases it is the first monograph on the subject. 

A search and a find. Rotovibrational collision-induced absorption was discovered incidentally in a search for the elusive spectra of van der Waals molecules ( dimers ). In his famous dissertation of 1873, J. D. van der... 

Hence, the process was named collision-induced absorption. Whereas the term interaction-induced absorption used by some early on seems to cautiously leave the question open whether free or bound complexes generate the absorption, Welsh and associates bravely state their conclusion as collisional interactions. Since then, other names have also been used, such as pressure-induced and supermolecular absorption. 

Figure 1.2 illustrates the difference between the transitions involved in van der Waals dimer bands which Welsh and associates hoped to find, and the collision-induced absorption spectra that were discovered instead. Intermolecular interaction is known to be repulsive at near range and attractive at more distant range. As a consequence, a potential well exists which for most molecular pairs is substantial enough to support bound states. Such a bound state is indicated in Fig. 1.2 (solid curve b). When infrared radiation of a suitable frequency is present, the dimer may undergo various transitions from the initial state (solid curve) to a final state which may have a rather similar interaction potential (dashed curve b ) and dimer level spacings. Such transitions (marked bound-bound) often involve a change of the rotovibrational state(s) EVj of one or both molecule(s),... 

Subsequent work has revealed that collision-induced absorption is observable even in mixtures of monatomic gases, albeit not in unmixed monatomic gases. In rare gas mixtures, the translational absorption profile occurs in the microwave and far infrared regions. In mixtures of molecular gases, such translational absorption profiles are sometimes discernible but they are generally masked by the induced rotational bands mentioned. 

Beyond the binary systems. Spectroscopic signatures arising from more than just two interacting atoms or molecules were also discovered in the pioneering days of the collision-induced absorption studies. These involve a variation with pressure of the normalized profiles, a(a>)/n2, which are pressure invariant only in the low-pressure limit. For example, a splitting of induced Q branches was observed that increases with pressure the intercollisional dip. It was explained by van Kranendonk as a correlation of the dipoles induced in subsequent collisions [404]. An interference effect at very low (microwave) frequencies was similarly explained [318]. At densities near the onset of these interference effects, one may try to model these as a three-body, spectral signature , but we will refer to these processes as many-body intercollisional interference effects which they certainly are at low frequencies and also at condensed matter densities. 

Of a special astronomical interest is the absorption due to pairs of H2 molecules which is an important opacity source in the atmospheres of various types of cool stars, such as late stars, low-mass stars, brown dwarfs, certain white dwarfs, population III stars, etc., and in the atmospheres of the outer planets. In short absorption of infrared or visible radiation by molecular complexes is important in dense, essentially neutral atmospheres composed of non-polar gases such as hydrogen. For a treatment of such atmospheres, the absorption of pairs like H-He, H2-He, H2-H2, etc., must be known. Furthermore, it has been pointed out that for technical applications, for example in gas-core nuclear rockets, a knowledge of induced spectra is required for estimates of heat transfer [307, 308]. The transport properties of gases at high temperatures depend on collisional induction. Collision-induced absorption may be an important loss mechanism in gas lasers. Non-linear interactions of a supermolecular nature become important at high laser powers, especially at high gas densities. 

Content. After a brief overview of molecular collisions and interactions, dipole radiation, and instrumentation (Chapter 2), we consider examples of measured collision-induced spectra, from the simplest systems (rare gas mixtures at low density) to the more complex molecular systems. Chapter 3 reviews the measurements. It is divided into three parts translational, rototranslational and rotovibrational induced spectra. Each of these considers the binary and ternary spectra, and van der Waals molecules we also take a brief look at the spectra of dense systems (liquids and solids). Once the experimental evidence is collected and understood in terms of simple models, a more theoretical approach is chosen for the discussion of induced dipole moments (Chapter 4) and the spectra (Chapters 5 and 6). Chapters 3 through 6 are the backbone of the book. Related topics, such as redistribution of radiation, electronic collision-induced absorption and emission, etc., and applications are considered in Chapter 7. 

For some of the more common molecules, the low-order molecular multipole moments are known [166, 378] (Landolt-Bornstein 1974). Collision-induced absorption of molecular gases arises mainly from multipolar induction. Studies of collision-induced absorption in the molecular gases provides, therefore, useful information on multipole moments [38]. 

These line shapes are generally not very useful for collision-induced absorption work, because pressure broadening, Doppler effect and instrumental resolution are here of no great concern. In Chapters 5 and 6 we will consider a number of other ad hoc model functions that have acquired a certain significance in collision-induced absorption. 

The frequencies of interest for studies of collision-induced absorption range from microwave frequencies to the ultraviolet, depending on the systems and specific transitions considered. Light sources, monochromators, detectors and pressure cells are needed for such studies, which are more or less the same as in the conventional spectroscopies. 

Sample cells. Variable temperature. Temperature control has been essential in much of the collision-induced absorption studies. Temperature variation accesses different parts of the intermolecular interaction potential and redistributes the relative importance of overlap and multipolar induction. Furthermore, at low temperatures, collision-induced line shapes are relatively sharp induced lines may be resolved at low temperatures whose structures may be masked at higher temperatures. 

I. R. Dagg, Collision-induced Absorption in the Microwave Region, in Phenomena Induced by Intermolecular Interactions. G. Birnbaum, ed., Plenum Press, New York, 1985. 

The induced spectra of rare gases in the far infrared are particularly simple but show characteristic features common to all collision-induced absorption. These will be considered first. 

Figure 3.3 shows the microwave collision-induced absorption coefficient of a neon-xenon gas mixture as function of the product of the Ne and Xe densities the ratios of Ne to Xe densities are k = 1.95, 1.53 and 0.59... 

At gas densities where three-body spectral components are just discernible, one might expect that induced spectra consist of a superposition of two- and three-body components whose intensities vary proportionally to density squared and cubed, respectively. At still higher densities, components might appear whose N-body nature would be revealed by their intensity variations proportional to gN (N > 3). At elevated densities, analyses of collision-induced absorption spectra have indeed revealed the presence of spectral components of an intensity that varies according to qn, with N = 3 and, in a few cases using higher densities, with N > 3. 

The question arises whether collision-induced absorption spectra observed at elevated density can be cast in a form that separates the various many-body components into meaningful two-, three-, etc., body virial coefficients. 

Returning to our topic of collision-induced absorption, the interesting... 

Measurements such as these can be conducted to determine the three-body virial coefficients, M 12) and M 21) of collision-induced absorption. To that end, it is useful to measure the variation of yi (and also of yo> Eq. 3.6, where possible) with small amounts of gas 1 mixed with large amounts of the other gas 2, and with small amounts of 2 mixed with 1, to determine the ternary spectral moments M 12 and M 21 separately, with a minumum of interference from the weaker terms. In a mixture of helium and argon, for example, two different three-body coefficients can be determined, those of the He-Ar-Ar and the He-He-Ar complexes. 

Measurements of enhancement spectra exist for several gases and mixtures. Figure 3.14 shows the collision-induced absorption spectra of H2-X pairs, with X = He, Ne, Ar, Kr, Xe [213]. The translational lines were omitted for technical reasons. Because the spectra are recorded at room temperature, the So(J) lines of H2 are quite diffuse. Most prominent is the So(l) line at 587 cm-1, but lines at other rotational transition frequencies of H2 are also discernible, for example So(0) at 354 cm-1, So(2) at 815 cm-1, and So(3) at 1035 cm-1, especially for the massive pairs. 

According to theory, most collision-induced absorption spectra should not only consist of contributions of the free-state to free-state transitions typical of collisional pairs, but also of contributions arising from bound-to-free and bound-to-bound transitions involving van der Waals molecules. In the rotovibrational spectra such dimer bands have been known for some time, but in CIA studies of the rototranslational band, where path lengths have generally been limited to a few meters, dimer features have been seen only recently [268], The dimer spectra are an integral part of the interaction-induced absorption. 

Above we have stated that over a substantial range of gas densities, essential parts of the profiles of collision-induced absorption spectra are invariant if normalized by density squared, a/q2, in pure gases, or by the product of densities, cl/q Q2, in mixed gases. Induced spectra that show this density-squared dependence may be considered to be of a binary origin. Above, we have seen examples that at very low frequencies many-body effects may cause deviations from the density-squared behavior at any pressure, over a limited frequency band near zero frequency (intercol-lisional effect). Furthermore, with increasing densities, a diffuse N-body effect with N > 2 more or less affects most parts of the observable spectra. It is interesting to study in some detail how the three-body (and perhaps higher-order) interactions modify the binary profiles. 

It has been known since the early days of collision-induced absorption that spectral moments may be represented in the form of a virial expansion, with the coefficients of the Nth power of density, qn, representing the N-body contributions [402, 400], The coefficients of qn for N = 2 and 3 have been expressed in terms of the induced dipole and interaction potential surfaces. The measurement of the variation of spectral moments with density is, therefore, of interest for the two-body, three-body, etc., induced dipole components. 

Carbon dioxide. Collision-induced absorption in carbon dioxide shows a discernible density dependence beyond density squared, even at densities as low as 20 amagats [34]. Over a range of densities up to 85 amagats the variation of the absorption with density may be closely represented by a (truncated) virial series (as in Eq. 1.2, with I(v) replaced by a(v)) of just two terms, one quadratic and the other cubic in density. The coefficient of g3 is negative. Relative to the leading quadratic coefficient, it is,... 

Historically, collision-induced absorption was discovered in the fundamental band of oxygen and nitrogen [128], Fig. 1.1. Literally, any molecular complex may be expected to have more or less prominent induced bands in the fundamental band and overtone regions of the molecules involved-besides the rototranslational bands considered above. Induced vibrational spectra are indeed known for many molecular systems and selected examples will be discussed below. Since in virtually all of these spectra rotation and vibration are coupled, we will generally refer to these as rotovibrational induced spectra. 

Interestingly, at the higher temperatures and if low densities are employed, the Q branch has a minumum near the Q ) transition frequency at 4155 cm-1, and there are two maxima (in the early days of collision-induced absorption, these were called the Qr and Qp lines ) these and the resulting dip between the maxima are clearly visible in the high-temperature spectra, Fig. 3.31. These maxima have a frequency separation... 

Furthermore, sometimes a much less pronounced absorption dip is seen at the rotovibrational transition frequencies. Knowledge of the dip is nearly as old as collision-induced absorption itself the earliest report [129] mentions an unexplained component X at about 4100 cm-1, observed in hydrogen-rare gas mixtures. Subsequent studies [120, 121, 175] pointed out the main features of the new phenomenon. Specifically, it was noted that... 

From the beginnings, attempts to model the line shapes of collision-induced absorption spectra were based on the assumption that the various rotational lines of induced spectra, Figs. 3.10 through 3.14, are superpositions of scaled and shifted line profiles, g(C)(v), °f a small number of different, e.g., overlap- and quadrupole-induced, types [313, 404],... 

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