Q-branch spectra

Derivation of the isotropic Q-branch spectra for the case of linear molecules is analogous to the case for spherical molecules. The integral part of the kinetic equation determines the set of eigenfunctions of the collisional operator... 

Rosasco J. L., Lempert W., Hurst W. S., Fein A. Line interference effects in the vibrational Q-branch spectra of N2 and CO, Chem. Phys. Lett. 97, 435-40 (1983). 

D Robert, Collisional effects on Raman Q-branch spectra at high temperature. In HD Bist, JR Durig, JF Sullivan, eds. Raman Spectroscopy Sixty Years On. Vibrational Spectra and Structure Vol 17B. Amsterdam Elsevier, 1989, pp 57-82. 

For the case that there are not too many constituents in the gas under investigation, the use of the pure rotational CARS technique may be superior to vibrational CARS thermometry since the spectra are easily resolvable (for N2 the adjacent rotational peaks have a spacing of approximately 8 cm i) compared with the congestion of the rotational lines in the vibrational bands of the Q-branch spectra (see Figure 11). An experimental comparison of rotational and vibrational CARS techniques, under similar conditions has been made that demonstrates that rotational CARS may be viable for flame-temperature measurements up to 2000 K. Of course, the pure rotational approach cannot be applied for spherical molecules which have no pure rotational CARS spectrum. An elegant method, using Fourier analysis based on the periodicity of pure rotational CARS spectra has been introduced recently. 

The separation of individual lines within the Q branch is small, causing the branch to stand out as more intense than the rest of the band. This appearance is typical of all Q branches in infrared spectra because of the similarity of the rotational constants in the upper and lower states of the transition. 

Fig. 3.2. Q-branch transformation with increase of density in strong collision (a) and weak collision (b) approximation at T = 0.1 (I) T = 0.3 (II) T = 10 (III). All spectra are normalized to 1 at their maxima.

With formulae (3.58), (3.59) and (3.66) Q-branch contours are calculated for CARS spectra of spherical rotators at various pressures and for various magnitudes of parameter y (Fig. 3.14). For comparison with experimental data, obtained in [162], the characteristic parameters of the spectra were extracted from these contours half-widths and shifts of the maximum subject to the density. They are plotted in Fig. 3.15 and Fig. 3.16. The corresponding experimental dependences for methane were plotted by one-parameter fitting. As a result, the cross-section for rotational energy relaxation oe is found ... 

Since good resolution of the Q-branch is hardly achievable by means of the usual Raman spectroscopy the first verification of this formula was carried out on side branches of anisotropic spectra which are easier to resolve (see Fig. 0.2 and Fig. 3.1). Generally speaking the right formula for component widths of these branches must be separately derived [212] but approximate estimation for the S-branch may be done as proposed in [213] ... 

The best resolution of Q-branch rotational structure in a N2-Ar mixture was achieved by means of coherent anti-Stokes/Stokes Raman spectroscopy (CARS/CSRS) at very low pressures and temperatures (Fig. 0.4). A few components of such spectra obtained in [227] are shown in Fig. 5.9. A composition of well-resolved Lorentzian lines was compared in [227] with theoretical description of the spectrum based on the secular simplification. The line widths (5.55) are presented as... 

Fig. 5.12. Q-branch narrowing in classical. /-diffusion theory in strong collision (1) and weak collision (2) models [215], The widths are taken from experimental spectra shown in Fig. 5.11 for systems CO-He ( ) and N2-Ar (o).

Fig. 5.20. Full width of nitrogen Q-branch CARS spectra measured at 295 K versus densities (squares) and calculated width using the MEG law (circles) [14]. Shown also are the error bar and the width measured in liquid nitrogen (triangle), (a) Density range up to 700 amagat. (b) Density range up to 100 amagat showing part of Fig. 5.20(a) in more detail...

The IR spectra of linear molecules at low pressure do not contain a Q-branch at all. The intensity increases with 1/tj in the central part of this spectrum exclusively due to the exchange between P- and R-branches (Fig. 6.4). The secular simplification is inapplicable in this case. In order to describe the rise of intensity in a gap of the IR spectrum with increase of density, one has to know the exact solution of the problem, e.g. (6.45H6.47). Using it, one can calculate... 

One possibility for this was demonstrated in Chapter 3. If impact theory is still valid in a moderately dense fluid where non-model stochastic perturbation theory has been already found applicable, then evidently the continuation of the theory to liquid densities is justified. This simplest opportunity of unified description of nitrogen isotropic Q-branch from rarefied gas to liquid is validated due to the small enough frequency scale of rotation-vibration interaction. The frequency scales corresponding to IR and anisotropic Raman spectra are much larger. So the common applicability region for perturbation and impact theories hardly exists. The analysis of numerous experimental data proves that in simple (non-associated) systems there are three different scenarios of linear rotator spectral transformation. The IR spectrum in rarefied gas is a P-R doublet with either resolved or unresolved rotational structure. In the process of condensation the following may happen. 

The liquid phase cage model accounts for appearance in the spectrum of resolved rotational components by effective isotropization of the rapidly fluctuating interaction. This interpretation of the gas-like spectral manifestations seems to be more adequate to the nature of the liquid phase, than the impact description or the hypothesis of over-barrier rotation. Whether it is possible to obtain in the liquid cage model triplet IR spectra of linear rotators with sufficiently intense Q-branch and gas-like smoothed P-R structure has not yet been investigated. This investigation requires numerical calculations for spectra at an arbitrary value of parameter Vtv. 

Temkin S. I., Burshtein A. I. On the shape of the Q-branch of Raman scattering spectra in dense media. Theory, Chem. Phys. Lett. 66, 52-6 (1978). 

Kozlov D. N., Pykhov R. L., Smirnov V. V., Vereschagin K. A., Burshtein A. I., Storozhev A. V. Rotational relaxation of nitrogen in argon collisional broadening of Q-branch components in coherent Raman spectra of cooled gas, J. Raman Spectr. 22, 403-7 (1991). 

Sala J. P., Bonamy J., Robert D., Lavorel B., Millot G., Berger H. A rotational thermalization model for the calculation of collisionally narrowed isotropic Raman scattering spectra - application to the SRS N2 Q-branch, Chem. Phys. 106, 427-39 (1986). 

Rahn L. A., Palmer R. E., Koszykowski M. L., Greenhalgh D. A. Comparison of rotationally inelastic collision models for Q-branch Raman spectra of N2, Chem. Phys. Lett. 133, 513-6 (1987). 

Q-branch rotational structure 179-82 spectra of nitrogen in argon 180 spectral collapse theory 150 spectral width 107 strong collision model 188 cumulant expansions 85-91... 

Q branch spect A series of lines in molecular spectra that correspond to changes in the vibrational quantum numberwith no change in the rotational quantum number. kyir. branch ... 

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... 

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