Line Mixing Effects Research Articles

Branch dependence of halfwidths: Theoretical analysis of N2-broadened halfwidths of CH3Br in the v6 band

The N2-broadened halfwidths of CH3Br in the ν6 band have been calculated, along with the relaxation matrices W. These calculations employ our modified and refined versions of the Robert-Bonamy formalism. Extensive comparisons between the predicted halfwidths from the models and experimental measurements at T = 296 K are presented. Our latest model very closely matches the measurements. Meanwhile, we considered line mixing effects in the spectral profile of the RQ(j,0) sub-branch. Our method probably yields too large values of the off-diagonal elements of W. Finally, by comparing our calculated halfwidths with the data in HITRAN, we have observed generally good agreement, especially for lines with high values of j. However, the agreement becomes poor for lines with low values of j, deteriorating as j decreases. We identified a factor contributing to this poor agreement: the neglect of branch dependence in the development of HITRAN data. We believe that for lines with low values of j, this oversight undermines the reliability of the halfwidth values of CH3Br in HITRAN.

Evaluation of spectral line mixing models and the effects on high pressure radiative heat transfer calculations

At higher pressures, the spectral lines in a gas spectrum can become more broadened and shifted due to collisional effects, leading to increased spectral line mixing. In the present study, we have reviewed different line mixing models for modeling the absorption spectra for three gases of CO2, CO, and H2O and applied these models to simulate radiative spectra for pressures within approximately 5–100 bar. The simulated data were compared with the yet-published high-pressure spectral experimental data as well as experimental data published in the literature. It has been found that the empirical “pseudo-Lorentz” line shape model considering the line mixing effects shows the best performance for modeling high-pressure gas spectra for the tested conditions, which is easy to be implemented and relatively accurate, thus is recommended for high-pressure radiative heat transfer calculations in engineering applications. Based on the selected “pseudo-Lorentz” line mixing model, we have constructed a high-pressure absorption coefficients database for CO2, CO, and H2O for pressure ranging from 1 bar to 80 bar. The newly generated database considering the spectral line mixing effects was tested for radiative heat transfer calculations, and the results were compared with the ones without considering the line mixing effects. The significance of ignoring the line mixing effects on radiative heat transfer calculations under different pressures was evaluated with one-dimensional radiative heat transfer benchmark cases. The high-pressure absorption coefficients database is available from the corresponding author upon request.

The j and k dependencies of the line coupling and line mixing effects: Theoretical studies of the relaxation matrices of N2-broadened CH3D

Line coupling and line mixing effects in parallel and perpendicular bands of CH3D perturbed by N2 have been studied. The work focuses on exhibiting the j and k dependencies of these two processes. The calculations were based on a previously reported anisotropic intermolecular potential including both the long-range multipole, induction, and dispersion forces and a short-range atom-atom model. It is shown that components with L1 = 3 of the atom-atom model are dominant contributions to the diffusion operator. As a consequence, in comparison with other molecular systems such as the CH3Cl-N2 and CH3I-N2, theoretically predicted line coupling and line mixing effects exhibit completely new j and k dependencies. In general, the theoretically calculated halfwidths and intra-doublets’ off-diagonal elements of the relaxation matrix are in reasonable agreement with measurements.

Line shape parameters of air-broadened 12CO2 transitions in the 2.0 µm region, with their temperature dependence

The 20013–00001 and 20012–00001 bands of 12C16O2 in the 2 µm region are used by many instruments on-board satellites and in ground-based networks to monitor the CO2 column-averaged dry air mole fraction in the Earth's atmosphere. An accurate knowledge of the corresponding spectroscopic parameters and their temperature dependence is thus needed to map sources and sinks of carbon dioxide. In this work, we retrieve the line-shape parameters and their temperature dependence exponents/coefficients for the P(16) and P(28) transitions of the 20012–00001 band, and the R(24) and R(30) transitions of the 20013–00001 band. These parameters are obtained from a multi-spectrum fit procedure using a speed-dependent Nelkin-Ghatak profile including the line-mixing effect in its first-order approximation. High signal-to-noise spectra (quality factor between typically 3000 and 6000) are recorded at different conditions of pressure (from 50 to 750 Torr) and temperature (from 245 to 330 K) for mixtures of CO2 in air using a comb-assisted cavity ring down spectrometer with a temperature stabilized high finesse cavity. Air-broadening coefficients are measured with an estimated uncertainty better than 0.1% and absolute frequencies of the transitions are obtained with uncertainty better than 100 kHz. The determined line-shape parameters are consistent with previous values derived in the 1.6 µm region confirming the absence of significant vibrational dependence (except for the air-pressure shift coefficient). The retrieved parameters agree well with literature values by Fourier transform spectroscopy and classical molecular dynamic simulations. The parameters of the speed-dependent Voigt profiles provided by the HITRAN2020 database are mostly validated. The comparison to the CO2 line parameters adopted for the OCO missions is discussed.

Quantitative volumetric laser absorption imaging of methane and temperature in flames utilizing line-mixing effects

A mid-infrared volumetric laser absorption imaging technique was developed for quantitative three-dimensional measurements of methane concentration and temperature in combustion flows. The spectroscopic method utilizes temperature-dependent collisional line mixing amongst a cluster of rovibrational transitions of the R(15) maniold of the v3 asymmetric stretch band of methane. Notably, line mixing effects are shown to increase sensitivity of the ratiometric thermometry, and a first-order model enables quantitative inference of species. 3D volumetric imaging is demonstrated experimentally on a methane-oxygen laminar flame doublet (<cm) backlit with tunable radiation from an interband cascade laser near 3.16 μm. 2D images were collected at six different projection angles on a high-speed mid-infrared camera, yielding an aggregate of 27,648 unique lines of sight capturing the scene with a pixel resolution of ∼70 μm. A linear tomographic reconstruction of spectrally-resolved absorbance with a 3D masked Tikhonov regularization method was performed to obtain methane spectra at every grid point, which enables subsequent interpretation of local gas properties. Importantly, this method enables quantitative temperature and species imaging in the fuel decomposition regions of flames.

Line coupling and line mixing effects on calculated widths of symmetric-top molecules with the k-degeneracy: A theoretical study of N2-, O2-, and air-broadened lines of CH3I

Calculations of the N2-, O2-, and air-broadened widths, together with their temperature dependence exponents have been made for transitions of CH3I in the ν5 and ν6 bands. The calculations are based on a semi-classical line shape formalism developed by the current authors through modifying and refining the Robert-Bonamy formalism. In recent years, we have applied this formalism for linear molecules, symmetric-top molecules with inversion symmetry, and asymmetric-top molecules. For symmetric-top molecules with the k degeneracy such as CH3I, the formalism has a new feature. In this case, one should consider each of the CH3I transitions labeled by ki or f ≠ 0 as a doublet. Then, one needs to consider the effects of the line mixing process between these two components. Comparisons of our theoretical predictions with some data available demonstrate a very reasonable agreement. Finally we propose new experiments at higher perturber pressures that would enable one to check the theoretically calculated relaxation matrices and to extend the analysis to the inter-doublet mixing effects.

CRDS measurements of air-broadened lines in the 1.6 µm band of 12CO2: Line shape parameters with their temperature dependence

The 12CO2 band at 1.6 µm is used for carbon dioxide monitoring in the Earth atmosphere. The targeted accuracy of these measurements motivates important efforts to improve the quality of the spectroscopic parameters in atmospheric conditions. In the present work, the line shapes of the R(6), R(12), R(16), R(18) and R(20) transitions of the 30013-00001 band of 12CO2 in air are studied with a cavity ring down spectrometer (CRDS). For each transition, high signal-to-noise ratio spectra (between 2000 and 20000) are recorded at different temperatures (250, 274, 285, 295 and 320 K) and total pressures (50, 100, 250, 500 and 750 Torr). To this end, a spectrally narrowed and stable (sub-kHz) laser source is coupled into a temperature regulated high-finesse optical cavity. The frequency scale of each spectrum is accurately determined from measurements of the frequency of the beat note between a part of the laser light and the closest tooth of a frequency comb referenced to a rubidium clock. A multi-spectrum fit procedure with quadratic speed dependent Nelkin-Ghatak profiles, including line-mixing effects, has been used to derive for each transition, the different spectroscopic parameters and their temperature dependence. Results are discussed in comparison with previous experimental data, HITRAN2020 database and values obtained from requantized classical molecular dynamics simulations (rCMDS).

Line mixing study on the fundamental rovibrational band of nitric oxide near 5.3 [formula omitted

In this work, we report quantitative absorbance measurements of nitric oxide (NO) diluted in nitrogen between 1700 to 2000 cm−1 and present three line mixing modeling approaches for the measured spectra. Static cell measurements were taken using a narrow-linewidth, external-cavity quantum-cascade laser at temperatures of 293 K and 802 K and pressures of 20–34 atm. The measured results exhibit considerable deviations from the spectra simulated by a superposition of Lorentzian line profiles due to significant line mixing coupling effects at high-number-density conditions. Our previous work demonstrated a line mixing model based on relaxation matrix theory and the Modified Exponential Gap (MEG) law for the NO R-branch. With expanded access to the P- and Q-branches, the measured data indicated significant line mixing effects between lines of different branches in addition to those within the same branch. An empirical two-scaling-factor inter-branch MEG model is presented that delivers strong agreement across the measured spectra, with residuals less than 2% for the spectrum at 293 K and 34 atm. In addition, the Energy Corrected Sudden (ECS) scaling law is shown to produce reasonable agreement across the measured spectra, excluding the Q-branch. In the Q-branch peak, the ECS model overpredicts the measured data by about 7%. The different line mixing models presented and discussed in this work will improve NO absorption predictions vital for laser absorption applications in high-number-density gas conditions. Future studies may seek to account for inter-spin-split coupling to further improve the ECS application to NO absorption.

Theoretical study of CH3Cl-N2 line shapes in the ν1 band. Line mixing effects in QR doublets and QQk sub-branches

Line coupling and line mixing effects of CH3Cl lines in the ν1 band perturbed by N2 have been investigated. We have taken into account the non-diagonality of the exp(−S2) operator within specified line spaces as well as the k-degeneracy of the transitions (due to the double degeneracy of the j,k levels with k ≠ 0). These transitions should be considered as doublets coupled by the line mixing process. A new problem appears in the calculation when the atom-atom potential model is introduced. In order to overcome this difficulty, a pragmatic approach is proposed. Comparisons of theoretically calculated matrix elements of W with measurements of QR(j,k) doublets as well as some QQk sub-branches, which are strongly affected by line mixing, have been made. The results show that the formalism improved in this way leads to rather accurate predictions.

CO-Ar collisions: ab initio model matches experimental spectra at a sub percent level over a wide pressure range

We use three independent spectroscopic techniques, operating in the millimeter-wavelength range, to study molecule-atom collisions, and validate our quantum-scattering calculations on two recent potential energy surfaces. We study the first pure rotational transition in a CO molecule perturbed by Ar. This molecular system is a good prototype of atmospherically relevant cases. It is, on the one hand, affordable for calculation of the line shape parameters by modern ab initio methods, and on the other hand, is very convenient for experimental studies because of its regular, well spaced rotational spectrum having a moderate intensity. We show that the simulated collision-perturbed spectra, which are based on our fully ab initio calculations, agree with the experimental line profiles at sub-percent level over a wide range (more than four orders of magnitude) of pressures. We demonstrate that the agreement between theory and experiment can be further improved if the model accounts for the collisional transfer of an optical coherence between different rotational transitions (the line-mixing effect). We show that the two surfaces tested in this work lead to a very similar agreement with the experiment. Capability of calculating line shape parameters in a broad range of temperatures is demonstrated.

Characterization of line mixing effects in the 11101←00001 band of carbon dioxide for pressures up to 19 atm

Fourier-transform spectra of room-temperature carbon dioxide compressed to pressures up to 19 atm reported previously are re-analyzed to obtain weak line-mixing parameters and a representation of full line mixing for transitions observed in the P- and Q-branches of the 11101 ← 00001 (Π ← Σ) band centered at 2076.86 cm−1. Similar analyses for the R-branch transitions are prevented by strong Coriolis resonances that nearly completely transfer the intensities of R-branch transitions to the P-branch. The weak line mixing coefficients are retrieved experimentally and are modeled using the Exponential Power Gap scaling law. Another modeling is performed with an Energy-Corrected-Sudden type approach making use of a symmetric relaxation matrix satisfying all basic relations. Comparisons of experimental and calculated parameters with results available in the literature are presented and discussed.

Measurements of pressure broadening of N2 in the anisotropic tensor component of spontaneous Raman spectra

Spontaneous Raman scattering from nitrogen is well-suited for temperature measurements in combustion experiments, especially at high pressure which increases the Raman signal because of the higher density in the measurement volume. In this work we investigate high density effects on the anisotropic tensor component of ro-vibrational spontaneous Raman scattering, which must be understood to obtain accurate thermometry in high pressure gases using high-fidelity Raman simulations. We measure the collision broadening for the anisotropic component of spontaneous Raman scattering from room temperature nitrogen over the pressure range 10–70 atm for three gas compositions: pure nitrogen, air, and nitrogen in argon. Line broadening coefficients inferred from these measurements were found to be 14 ± 5% larger than the corresponding broadening coefficients of the isotropic Q branch. Air broadening coefficients were found to be very similar and about 2.5% smaller than nitrogen self-broadening coefficients. Argon broadening coefficients were 25% smaller at rotational quantum number 7 and about 50% smaller at rotational quantum number 21. Additionally, we found that our unmixed line model for the O and S branches gave good fits for all pressures, which indicates that line mixing effects are not significant in the O and S branches over this range of pressures. Using indirect experimental evidence we infer that line mixing effects in the anisotropic component of the Q branch were below the threshold set by our experimental spectral resolution at pressures up to 70 atm at room temperature. Assuming that the anisotropic Q branch lines mix like the isotropic lines results in a small systematic error in the inferred temperature at flame temperatures, with the error increasing slowly with pressure. The bias can be easily removed by modeling the anisotropic spectrum separately from the isotropic spectrum. Line mixing effects should be included in the model of the isotropic part of the Raman spectrum, but can probably be neglected in the anisotropic part of the spontaneous Raman spectrum of N 2 for pressures below 400 atm at flame temperatures.

Exploiting line-mixing effects for laser absorption spectroscopy at extreme combustion pressures

A unique spectroscopic strategy has been developed for laser absorption sensing of carbon monoxide (CO) and carbon dioxide (CO2) at extreme pressures (P > 50 atm) relevant to modern combustion devices. The strategy exploits the band narrowing effects of line mixing, which acutely impact spectrally dense regions, such as bandheads, where line spacing is small. Line mixing is shown to counter collisional line-broadening effects that reduce differential absorption at elevated pressures and often limit the pressure range of laser absorption methods. In this work, the R-branch bandheads of CO and CO2, which are only observed at high temperatures relevant to combustion, are targeted near 2.3 µm and 4.2 µm, respectively. Spectral line-mixing models were developed for each bandhead region to account for the collision-induced population transfer rates between rotational energy states over a wide range of elevated temperatures and pressures. Modified-exponential-gap models using the relaxation matrix formalism were shown to capture the thermodynamic dependence of the population transfer rates and enabled scaling. Differential absorption at the bandheads was observed to increase by up to a factor of ten at high gas densities, due to line-mixing effects, enabling detection with relatively narrow-band tunable semi-conductor lasers. With refined spectroscopic models, laser absorption measurements of temperature, CO, and CO2 were demonstrated over a range of high pressures (up to 104 atm) in a sub-scale rocket combustor operated with kerosene and supercritical methane.

Temperature-dependent line mixing in the R-branch of the v3 band of methane

High-temperature line mixing behavior was studied for 15 R-branch line manifolds in the v3 band of methane from 3.14 µm to 3.28 µm. The temperature-dependence of the line mixing parameters for the R(4) to R(18) manifolds perturbed by nitrogen were empirically-determined over a range of temperatures from 300–1000 K using Fourier transform infrared spectroscopy in a heated gas cell. A more extensive line mixing investigation of the rovibrational transitions comprising the R(15) manifold was performed at lower pressures (0.3–2 atm) using laser absorption spectroscopy from 300–1600 K in both the heated cell and a high-enthalpy shock tube. Measured spectra were modeled and fit using both a modified exponential gap model and a perturbation theory-based first-order model to capture the pressure- and temperature-dependence of the line mixing effects. The modified exponential gap model was found to sufficiently capture the line mixing behavior at pressures greater than 20 atm, while perturbation theory enables more accurate characterization of the behavior at the lower pressures. The applicability of both the modified exponential gap model and perturbation theory is also discussed with analyses of the fitting residuals and the parameter uncertainties to provide reference for the use of the two empirical models in simulating the R-branch of the v3 band of 12CH4 over a wide range of thermodynamic conditions.

Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures

Temperature-dependent line mixing and line broadening parameters were empirically-determined for rovibrational transitions (J = 99–145) in the (0000 → 0001) and (0110 → 0111) bandheads of carbon dioxide near 4.2 µm. Collisional effects by argon on the high rotational energy lines (E″ = 3920–8090 cm−1) in the R-branch were studied over a range of temperatures from 1200–3000 K in a shock tube. Measured absorption spectra comprising the target lines in an argon bath gas at near-atmospheric pressures were fit with Voigt profiles to determine line-broadening coefficients, with temperature dependence accounted by a power law. With line broadening established, line-mixing effects were examined at elevated pressures up to 58 atm and similar temperatures, reflecting conditions in high-pressure combustion environments. A modified exponential gap model for line mixing was developed to capture the pressure and temperature dependence of collisional transfer rates for the bandhead region using the relaxation matrix formalism.

Line shape parameters of PH3 transitions: Theoretical studies of self-broadened widths and line mixing effects.

Line mixing effects have been calculated in various parallel and perpendicular bands of self-broadened PH3 lines and compared with recent experimental data. The theoretical approach is an extension to symmetric tops with high inversion barrier of the formalism previously developed for NH3 [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. The model takes into account the non-diagonality of the scattering operator within the line space as well as, in a correct way, the double degeneracy of the j, k levels when k ≠ 0. Transitions between such levels should be considered as doublets whose components may be coupled by the line mixing process. It has been shown that, at low pressure, the inversion of the experimental data will strongly depend on the splitting between the two components of a doublet. When it is significant, one can measure independently both the width of one component and the intra-doublet coupling matrix element. Otherwise, one can only measure the sum of these two elements. Comparisons with measurements show that the present formalism leads to accurate predictions of the experimental line shapes.

Line mixing and broadening in the v(1→3) first overtone bandhead of carbon monoxide at high temperatures and high pressures

Temperature-dependent line mixing and line broadening parameters were empirically-determined for 17 rovibrational transitions in the v(1→3) bandhead of carbon monoxide near 2.3 µm. Collisional effects on the high rotational energy lines (E″ = 5500–8600 cm−1) in the R-branch were studied over a range of temperatures from 1200–3750 K in a shock tube and heated gas cell. Measured spectra comprising the target lines in Ar and CO bath gases were fit with Voigt profiles at near-atmospheric pressures to determine line-broadening coefficients, with temperature dependence accounted by a power law. With line broadening established, line-mixing effects were examined at elevated pressures up to 60 atm at similar temperatures, reflecting conditions in high-pressure combustion environments. A modified exponential gap model for line mixing was developed to capture the pressure and temperature dependence of collisional transfer rates for the bandhead region using the relaxation matrix formalism.

FTS measurements of O2 collision-induced absorption in the 565–700 nm region using a high pressure gas absorption cell

The collision-induced absorption (CIA) spectra of oxygen and dry air have been measured in the near-infrared and visible regions, covering the O2(B) band at 687 nm and double transitions in the 630 nm and 577 nm regions. A custom-design 1 m path length high-pressure cell was developed and configured to a Bruker 125HR Fourier transform spectrometer at the Jet Propulsion Laboratory. A super-luminous Laser Driven Light Source (LDLS) was also used to improve the photon flux incident upon the spectrometer. A series of spectra of pure O2 and dry air were obtained at various high pressures up to 131 bars at room temperature. For the measurement of O2–O2 CIA in the B band region, the monomer resonance absorption contribution has been subtracted from the observed spectra by simulating the O2(B) band absorption with a speed-dependent Voigt line shape profile with line mixing effects taken into account. The remaining absorption component was regarded as the CIA in the region. The integrated absorption coefficient was measured to be 3.2(6) × 10−6 cm−2/Amagat2 for the O2(B) band region, which is significantly lower than literature values. For the two double transition bands in the 630 and 577 nm regions, the integrated CIA bands from the present work were measured to be 2.50(14) and 3.26(18) × 10−4 cm−2/Amagat2, respectively. The present measurements are significantly higher than prior measurements for the 630 nm band region, while they are slightly lower than prior measurements for the 577 nm band region. For dry air, the integrated CIA bands were measured to be 0.10(2) and 0.15(2) × 10−4 cm−2/Amagat2, respectively, for the 630 and 577 nm regions, no appreciable contribution from O2–N2 pairs was observed. The results are compiled in electronic supplements.

Pure rotational coherent anti-Stokes Raman spectroscopy of ethylene, experiments and modelling

Rotational coherent anti-Stokes Raman spectroscopy (CARS) is an established diagnostic technique for temperature and concentration measurements in combustion-related experiments. CARS has mainly been applied on di- and tri-atomics with linear molecular symmetry, for which good agreement is achieved between experimental and theoretical spectra. Hydrocarbons have so far been less attractive for rotational CARS studies, partly because of their complex molecular symmetries making it challenging to obtain molecular parameters necessary for a successful modeling. Nevertheless, in this work we have studied the asymmetric top molecule ethylene (C2H4) using rotational CARS through experiments and theoretical modelling. Experimental spectra have been recorded at temperatures between 293 K and 804 K, and theoretical spectra have been calculated with a novel method for which the crucial temperature-dependent linewidth parameters were determined by comparison of experimental and theoretically calculated spectra. Line-mixing effects and temperature dependence of the isolated linewidths were studied using a semi-classical approach considering an exponential gap law and a scaling law. Subsequently, theoretically calculated spectra were used to evaluate the temperatures of the experimental spectra for validation of the method. The evaluated temperatures were in good agreement with thermocouple temperatures with differences up to ±7 K. Hence, this work not only investigates the potential of using rotational CARS on ethylene for diagnostic purposes, but also expands the applicability of the technique to a whole new class of molecules with asymmetric-top molecular symmetry.

Self and N2 collisional broadening of rovibrational lines in the ν6 band of methyl iodide (12CH3I) at room temperature: The J and K dependence

Following our recent study devoted to measurements of intensities of rovibrational lines in the ν6 band of methyl iodide (12CH3I) centered at 892.918 cm−1, room temperature infrared spectra of methyl iodide diluted in nitrogen at fourteen total pressures between 20 and 300 hPa have been recorded using the Fourier transform spectrometer Bruker IF125HR located at the LISA facility in Créteil. Three hundred and forty six N2-broadening coefficients of methyl iodide rovibrational lines have been measured in the 824–951 cm−1 spectral range using mono-spectrum non-linear least squares fitting of Voigt profiles. Pressure-induced line shifts were not needed to fit the spectra to the noise level and line mixing effects could be neglected. Six hundred and eight self-broadening coefficients have also been measured in the same spectral range using the pure methyl iodide spectra recorded in our previous work. The measured self-broadening coefficients range from 0.1460 to 0.3786 cm−1 atm−1 and the N2-broadening coefficients range from 0.0723 to 0.1481 cm−1 atm−1 at 295 K. The average accuracy on the measured self- and N2-broadening coefficients was estimated to 3%. Comparisons with measurements reported in the literature for the ν5 band of CH3I shows a satisfactory agreement with average differences of 7% and 4% for the self- and N2-broadening coefficients, respectively. The J and K rotational dependences of these coefficients have been observed and the latter modeled using an empirical polynomial expansion. On average, the empirical expression reproduces the measured self- and N2-broadening coefficients to within 3% and 4%, respectively. The data obtained in the present work represent a significant contribution to the determination of broadening coefficients of CH3I and complement the list of line positions and intensities generated in our previous work, thus providing useful spectroscopic information for atmospheric remote sensing and industrial detection of CH3I.