Rare Gas Pressure Broadening of the NO Fundamental Vibrational Band

Journal of Molecular Spectroscopy 208, 153–160 (2001) doi:10.1006/jmsp.2001.8401, available online at http://www.idealibrary.com on

Rare Gas Pressure Broadening of the NO Fundamental Vibrational Band Robert S. Pope and Paul J. Wolf Department of Engineering Physics, Air Force Institute of Technology, Wright–Patterson AFB, Ohio 45433-7765 Received July 11, 2000; in revised form May 8, 2001

Pressure broadening of rotational transitions in the nitric oxide fundamental band was studied using Fourier transform spectroscopy. Rotational level dependent broadening coefficients were determined for both the 2 51/2 and 2 53/2 substates at 300 K using the five noble gases as the broadening species. Pressure broadening coefficients were also determined for Q-branch transitions using Ar as the collision partner. This information was subsequently used to study the broadening of the Q-branch absorption lines at 900 Torr total pressure. The high-pressure spectra showed significant deviations from a simple fit using a sum C 2001 Academic Press of Lorentzians that indicated the possible effects of line coupling. ° Key Words: pressure broadening; line broadening; nitric oxide; NO; Fourier transform spectroscopy; infrared spectroscopy. INTRODUCTION

An accurate understanding of the chemical situation in the atmosphere requires the combined efforts of detailed modeling and concerted measurements involving many compounds. Although only a minor atmospheric constituent, nitric oxide plays a major role in the chemistry of the troposphere and the stratosphere. Consequently, the remote sensing of NO provides one of many means to probe the health of the earth’s atmosphere. The fundamental band (v = 0 → v = 1) of NO has strong absorption near 5.3 µm, making infrared absorption a favorable choice for detecting this species. The collision broadening of rotational transition line shapes in the NO vibrational fundamental band has received much attention primarily due to the importance in remotely monitoring this species using satellite, air, and ground-based instruments. Several papers have appeared in the literature detailing precise line positions, intensities, and pressure broadening coefficients of the NO fundamental vibrational band (1, 2) as a result of this application of atmospheric spectroscopy. The majority of these studies have naturally concentrated on self-broadening and broadening by atmospheric gases such as N2 . More recently reported studies detail the results of precise temperature dependent broadening by N2 (3, 4), broadening by O2 (5, 6), and the development of new cw tunable diode laser spectroscopic techniques to measure broadening coefficients (7). Fundamentally, the pressure broadening of spectral lines is intimately connected to collision theory (8, 9). The collision interaction between a particle and an oscillator undergoing a transition produces a time dependent perturbation of an oscillator’s energy levels and, as a result, the oscillation frequency varies in the time over the occurrence of the interaction. This interaction leads to both a displacement of the center oscillation frequency and a broadening of the spectral line. Semiclassical treatments

of pressure broadening of rotational spectral lines suggest that both elastic and inelastic (energy transfer) collisions contribute to modified line shape (10). Pressure broadening experiments, therefore, provide a potential means to determine inelastic collision rate coefficients (i.e., state-to-state rotational energy transfer rate coefficients) without resort to the detailed experiments required to obtain such data directly (11). The conversion of pressure broadening to inelastic collision rate coefficients usually assumes elastic collisions are unimportant in broadening these lines, a supposition that is not always justified. Our motivation in this work is primarily driven by the need to provide data for quantitative discussion of the importance of inelastic collisions in the broadening of spectral lines where elastic collisions cannot be justifiability ignored. The NO–rare gas system presents a prototype for collision interactions between a molecule with a permanent dipole moment and a structureless particle (i.e., dipole–induced dipole interactions), which should be amenable to theoretical analysis. As a consequence, the data reported here should be valuable in determining state-to-state R–T rate coefficients and may ultimately provide useful information concerning interaction potentials. In addition to reporting pressure broadening cross sections for the P- and R-branches in the NO fundamental band, we also present evidence for Qbranch line mixing in collisions with argon. EXPERIMENT

Nitric oxide absorption spectra were recorded with a Bomem DA8.002 Fourier transform spectrometer (FTS). The 200– 10 000 cm−1 spectral range of a Globar light source was limited by a 2.54-cm diameter bandpass filter with a center frequency, ν0 , of 1886 cm−1 . This filter restricted the NO absorption frequencies to ±116.3 cm−1 (full width at half-maximum, FWHM) around ν0 . We used a KBr beam-splitter with a range of

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450–4000 cm−1 to divide the beam in the interferometer and an LN2 cooled MCT detector to record the interferogram. The sample cell was a single-pass cylindrical quartz tube, 10 cm long and 2.54 cm in diameter, with CaF2 windows at either end. A source aperture, 0.5 mm in diameter, provided reasonable illumination of the sample, which permitted using the FTS with a spectral resolution of 0.005 cm−1 . In the absence of a buffer gas, the NO fundamental band absorption signal saturated at about 1 Torr of NO over this 10-cm path length. Thus, the cell typically contained a base pressure of 0.5 Torr of NO to which research grade noble gases (He, Ne, Ar, Kr, and Xe) were incrementally added. The NO absorption signal intensity degraded at high foreign gas pressures. Therefore, up to an additional 10 Torr of NO was introduced into the cell to improve the signal-to-noise ratio (S/N) ratio, thereby compensating for the reduced intensity. The gas pressures in the cell were monitored with calibrated MKS Baratron capacitance manometers and the absorption spectra were recorded at ambient room temperature (300 K). Additional details were described by Pope (12). Figure 1 shows a typical absorption spectrum of the NO fundamental band, corrected for the bandpass filter response. Each rotational transition in the P- and R-branch has two components due to transitions in the 2 51/2 and 2 53/2 magnetic electronic substates. These electronic levels result from the strong coupling of the electronic motion to the internuclear axis that made the total angular momentum Ä a “good” quantum number as described by Hund’s case (a) (13). In most cases, the P-branch S/N ratio significantly diminished beyond about J 00 = 5.5. The cause was attributed to a combination of a lower peak intensity for a substantially broadened line with the spectral response of the bandpass filter, with the latter being the more important factor. To compensate for this, we made some measurements with a different filter centered at 1840 cm−1 with a 160 cm−1 bandwidth

(FWHM). This filter extended our data collection to J 00 = 14.5 in the P-branch. (Data were collected only for Ar bath gas using the second filter.) All absorption spectra were transformed unapodized to minimize instrumental broadening of the spectral lines. The response time of the MCT detector typically required a mirror scan speed of 0.5 cm/s, so a 100-scan run at 0.005 cm−1 resolution took about 7 h. In addition to studying pressure broadening of the P- and R-branches of the NO fundamental band, we also studied the broadening of the Q-branch in collisions with argon. There was a two-fold purpose to this part of the experiment. First, quantitative pressure broadening coefficients were determined for several lines in the Q-branch at pressures low enough to produce spectral lines with minimal overlap. In this study, the Ar broadened NO spectra were recorded for pressures ranging between 10 Torr and 100 Torr. Second, we increased the Ar pressure to 860 Torr with 40 Torr of NO in the cell in order to search for line coupling effects. The analysis was semiquantitative in that we looked for whether or not the Q-branch exhibited deviations from purely Lorentzian behavior. In a minor modification to the experiment, we replaced the quartz absorption cell with a 10 cm long, stainless steel absorption cell with 4-mm-thick ZnSe windows at each end to accommodate these high pressures. The remainder of the spectrometer arrangement was identical to the other experiments. DATA ANALYSIS

Figure 2 shows a representative spectral line profile for the R(6.5) line. Both collision and Doppler broadening were considered in our analyses by fitting each rotational line to a Voigt line profile using a nonlinear least squares fitting routine. Specifically, the Voigt profile for a single spectral line is a0

P(ν − ν0 ) = √ 2πa1

Z+∞ −∞

1ν L2 2a12

exp(−t 2 ) h i2 dt. √ 0 ) −t + (ν−ν 2a

[1]

1

The terms in Eq. (1) are defined below: a0 = a1 =

α0 1ν L √ , Where α0 in the area under the Voigt profile. 2πa1 1ν D √ , Where 1ν D is the Gaussian (Doppler) half width 2ln2

at half maximum (HWHM). 1ν L is the Lorentzian HWHM. ν0 is the transition frequency at line center.

FIG. 1. Absorbance spectrum of the nitric oxide fundamental band obtained with 0.5 Torr of NO and 10 Torr of argon at 0.005 cm−1 resolution.

The Doppler widths were constrained to calculated values to reduce the number of free parameters in the fit. However, instead of using a single value for the Doppler width for each line in the spectrum, a frequency-dependent Doppler width was calculated for each line at a fixed temperature of 300 ◦ K. The spectra of the NO fundamental band was not only complicated by the simultaneous presence of the two magnetic

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e–f pair with equal widths and intensities. Thus, for the 3/2 subband, only one set of unique line parameters was obtained for each 3-doublet pair. In contrast, the doublets in the 1/2 subband were usually resolvable for pressures below 150 Torr as illustrated in Fig. 2b. In this case, the fits were performed by independently varying both the line centers and widths for each e and f 3-doubled component with the constraint that the intensities remained equal (14). Thus, the analysis of a pair of resolved lines in the 1/2 subband produced unique positions and widths for each 3-doubled component, but each line shared a common strength parameter. For cases in which the 1/2 substate spectral lines were not resolved, the pair of lines were analyzed using the method outlined above for the unresolved 3/2 subband. Finally, at low J and high bath gas pressures, the spacing between rotational lines from the 1/2 and 3/2 substates was sufficiently small so that both doublets were fit simultaneously. Instrumental effects due to the spectrometer were also considered in the analyses of the spectral lineshapes (12). Of the three major instrumental effects, namely, finite resolution, aperture effect, and asymmetry due to phase errors, the last of the three proved to be most significant. Therefore, the analyses included a correction to the lineshapes using Bell’s asymmetry correction (15). See Pope (12) for more complete details. Fits to typical peaks in the 1/2 and 3/2 subbands with the fit residuals are also shown in Fig. 2. After the widths of all the peaks in each spectrum were obtained, the broadening coefficients were determined from a linear least squares fit to a plot of the Lorentzian HWHM vs bath gas pressure. The self-broadening contribution was subtracted using the values determined by Ballard et al. (16), which forced the intercept to pass through zero. An example of this analysis is shown in Fig. 3. The error bars for these data were obtained from FIG. 2. A lineshape fitted to the R(6.5) line of NO. The spectrum is obtained with 2.0 Torr of NO broadened by 50 Torr of Ne. The residuals are shown at the bottom of each figure and they are offset by −0.1 for easy display. The data in (a) are characteristic of the 2 53/2 subband, and the spectral features appear as a single line because the 3-doublet splitting falls below the resolution of the FTS instrument. The spectral line depicted in (b) belongs to the 2 51/2 subband. Here, 3-doubling is clearly observed.

electronic subbands, but 3-doubling, a process that removed the two-fold degeneracy of each magnetic substate, further added to the numbers of transitions. For transitions involving the 3/2 substate, the 3-doubled splitting was approximately 0.001 cm−1 , a value that was well below the resolution of the FTS. Consequently, the 3-doubled spectral features in this substate were not resolved at any pressure under our experimental conditions. An example of a 3/2 sub-state spectral line is depicted in Fig. 2a. These blended spectral features were fit with a sum of two Voigt profiles by adjusting the intensity, width, and line positions under the following constraints. First, the separation between the line centers for each e and f component was fixed to a value obtained from the literature (3). Second, we constrained each

FIG. 3. An example of a linear least squares fit to the Lorentzian HWHM as a function of bath gas pressure. The data belong to the R(6.5) lines of NO broadened by Ar. The slopes of these lines provide the broadening coefficients.

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the fits of the Voigt profile to the individual lineshapes, and they were typically less than 1% of the Lorentzian linewidth (1-σ ). Therefore, they were not displayed in the plot. In addition, the intercepts passed through zero to within error, indicating that our results were consistent with Ballard’s self-broadening values. Broadening coefficients were determined separately in all cases for rotational absorption lines in both the 1/2 and 3/2 magnetic substates, and the results are provided in Tables 1 and 2. Although the broadening coefficients were determined individually for the e and f doublet peaks of the 1/2 substate, we found that these 3-doubled components had identical broadening coefficients to within experimental uncertainties. That is, we could not statistically distinguish differential broadening between the 3-doubled components, and, therefore, we reported broadening coefficients that were weighted averages of the e and f components. Broadening coefficients for the R1/2 (1.5) and R3/2 (1.5) lines were not determined in this study because

TABLE 2 NO+Noble Gas Broadening Coefficients for the Ω = 3/2 Substate of the NO Fundamental Band

TABLE 1 NO + Noble Gas Broadening Coefficients for the Ω = 1/2 Substate of the NO Fundamental Band

Note. The errors (1σ in the mean) are provided in parentheses and all coefficients have units of 10−5 cm−1 Torr−1 .

Note. These coefficients represent weighted averages for both the e and f 3-doublet components. The errors (1σ in the mean) are provided in parentheses and all coefficients have units of 10−5 cm−1 Torr−1 .

they were strongly overlapped and no self-broadening data was available (due again to the strong overlap). For all the lines analyzed, we never observed the characteristic residuals of Dicke narrowing. Analyses of the Q-branch lines presented more difficulty because the spectral features were very close together. We used an algorithm called DUDV to simultaneously fit 30 spectral features in the Q-branch with a Voigt profile that included J 00 = 1.5 to 8.5 in the 3/2 subband and J 00 = 0.5 to 6.5 in the 1/2 subband. The utility of this algorithm has been discussed in Refs. (12, 17). With three parameters for each line plus three parameters for the instrument effects and three more for the baseline, there were potentially 96 free parameters in the fit. Therefore, the following approximations were made to simplify the analysis: each 3-doublet pair was constrained to possess equal strengths and widths and we fixed the separation between each e–f pair; all intensities were ratioed to the intensity of the Q 1/2 (1.5) line, which reduced the linestrength parameter to a single free parameter; the location of each f -parity line was fixed relative to the Q 3/2 (1.5) line, which set the location of one peak of each 3-doublet relative to the most intense, easily identifiable peak in the measured spectrum, thereby reducing the line position variables to a single free parameter; and the widths of

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of self-broadening were subtracted from the measured widths using the self-broadening coefficients of Lempert et al. (19). A linear least squares fit with a zero intercept was then performed to the width vs pressure data as for all previous pressure broadening determinations. The Q-branch broadening coefficients are summarized in Table 3. RESULTS AND DISCUSSION

FIG. 4. The spectrum of the Q-branch of NO is illustrated here along with a fit to 30 rotational lines. The NO pressure is 2.5 Torr and the Ar pressure is 75 Torr.

the Q 1/2 (4.5), Q 1/2 (5.5), and Q 1/2 (6.5) lines were ratioed to the width of the Q 1/2 (3.5) line. The last approximation helped to account for the three weak nonresolvable lines in the spectrum and minimized errors in the more intense Q 3/2 lines with which they overlapped. The information utilized to enforce the first set of constraints was obtained from the HITRAN database (18) and the work of Spencer (3). These assumptions significantly reduced the number of free line parameters from 90 to 14 (12 independently determined linewidths, one line position, and one intensity). For the instrument parameters, the maximum optical path difference and the aperture effect were fixed at calculated values, as has been done for all other DUDV fits in this research (12), and the asymmetry effect was set to zero because it was not observed in these spectra. Finally, a two-parameter baseline increased the total parameter space to 16. A typical low-pressure fit to the NO + Ar Q-branch is shown in Fig. 4. After each spectrum was fit using DUDV, the effects

Figure 5 illustrates the behavior of the broadening coefficients for the P- and R-branches as a function of rotational level with Ar as the bath gas. Here, the broadening coefficients were plotted vs m, where m = −J 00 for the P-branch and m = J 00 +1 for the R-branch. Clearly, the broadening coefficients showed a strong dependence on rotational quantum number, which indicated angular momentum dependence to the inelastic collision mechanism. In addition, the broadening in the 2 53/2 substate transitions was larger than those in the 2 51/2 substate. Similar plots were obtained for the remaining noble gases. Converting the pressure broadening coefficients into cross sections by factoring out the dependence of the collision reduced mass, µ, permits a direct comparison of the results for the different broadening gases. The broadening coefficients were converted into cross sections using the relation σ =

γ cπ k B T , hvi

[2]

where γ is the pressure broadening coefficient, c the speed of light, and hvi the average speed of the two collision partners (i.e.,hvi = (8kB T /π µ)1/2 ). The results for all of the noble gas collision partners are summarized in Fig. 6, where we now plot

TABLE 3 Broadening Coefficients for the Q-Branch of the NO Fundamental Band for Collisions with Argon

Note. The errors (1σ in the mean) are provided in parentheses and all coefficients have units of 10−5 cm−1 Torr−1 .

FIG. 5. This plot shows a summary of the NO pressure broadening coefficients with Ar as a function of m. The quoted errors are 1-σ uncertainties in the mean value of the coefficients.

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FIG. 6. A graphical summary of the NO pressure broadening cross sections vs |m| for each noble gas. Data for the Ä = 1/2 substate is displayed in (a) and the Ä = 3/2 substate in (b). An example of a polynomial fit to the data is presented in (a) for NO broadened by Ar.

the data against |m|. Thus, two values, one from each branch, were averaged for each |m|. The cross sections for He and Ne show a relatively weak dependence on the rotational quantum number in contrast to the heavier noble gases. This behavior revealed the inability of the lighter gases to efficiently change the angular momentum of the NO molecule since the angular momentum in the collision depends on the reduced mass of the collision pair. We assumed that the elastic collision contribution to the line width is constant for all the noble gases in making this comment. For convenience, we fit the data in Fig. 6 with polynomials to provide a quantitative, systematic means to summarize the data and the trends in the data. An example is shown for Ar + NO and the results are tabulated in Table 4. Systematic studies of NO broadening in the fundamental band by the noble gases have not appeared in the literature. The data

we present for Xe and Ne are new, while the only previous result for NO broadened by Kr is that of Hanson et al. (20), who measured the broadening coefficient of the R1/2 (18.5) line and reported a value 26% smaller than the value determined here. Likewise, only a very limited set of data exists for He (21–24) and Ar (20, 22, 24–26). Of the four reported studies using He as the collision partner, the broadening of four spectral lines [R1/2 (0.5), R1/2 (1.5), R1/2 (4.5), and R3/2 (4.5)] reported by Rohrbeck et al. (24) matches our results to within experimental error. The other references report results from single rotational states that are in excess of 22% larger than the values we report. Finally, a comparison of our results with those of two previous J -dependent studies in the fundamental band (25, 26) shows our data to be systematically higher. The discrepancies are not large, but they fall outside the uncertainties presented here. Referring to Table 3, the broadening coefficients in the Qbranch show a decrease with increasing J , just as for the P and R branches, and there is no discernible differential broadening between the magnetic substates. As stated previously, the widths of the J = 4.5, 5.5, and 6.5 lines in the 1/2 subband were fixed relative to the width of the J = 3.5 line, with the ratios between the widths set according to the ratios between the self-broadened widths reported by Lempert et al. (19). Thus the broadening coefficients for the J = 3.5 to 6.5 lines in the 1/2 subband have not been independently determined in the current study but are fixed to ratios determined by previous researchers. These broadening coefficients provide the basis for a search for line coupling in the Q-branch. Line coupling or line mixing occurs when interference effects between strongly overlapping lines cause deviations from directly additive Lorentzian line profiles. Of course, this assumes that the particular rotational levels involved in the transition are coupled by collisions. The spectrum acquired for the line coupling study was obtained with a gas mixture composed of 40 Torr of NO with 860 Torr of Ar. The run included 100 co-adds at 0.005 cm−1 TABLE 4 Polynomial Coefficients Representing the Best Fits to the Broadening Cross Sections: σ = A + B1|m| + B2|m|2 + B3|m|3

Note. The broadening cross sections are in units of cm2 and the correlation coefficients, r , are obtained from the fit to data.

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CONCLUSIONS

FIG. 7. A DUDV fit to the Q-branch NO fundamental band a˙ t 900 Torr total pressure. The fit of a sum of Lorentzians shows a significant deviation from a Lorentzian behavior, which is characteristic of line coupling. The residuals are indicated at the bottom of the figure.

resolution using the bandpass filter centered at 1840 cm−1 . The spectra obtained at these high pressures were fit using the DUDV program. Here, the linewidths were locked to values calculated using the broadening coefficients obtained at low pressures. Both Voigt and Lorentzian fits to the lineshapes produced no difference in the results, which suggested that Doppler broadening was negligible at these pressures. The fit to the Q-branch at 900 Torr total pressure is shown in Fig. 7. Figure 7 contains two features that are characteristic of line coupling in a Q-branch. The first is the narrowing of the Qbranch at the bandhead, shown at the right of the figure where the data return to 100% transmittance faster than the sum-ofLorentzians fit. The second indicative feature is the deviation between the 1/2 and 3/2 subbands near 1876 cm−1 . There is less absorption in the data than modeled by the sum-of-Lorentzians fit, indicating that the Q 1/2 lines are collapsing into a single feature near 1876.1 cm−1 , while the Q 3/2 lines are collapsing into a feature near 1875.75 cm−1 , leaving a gap in between. There are several other minor deviations from Lorentzian behavior toward higher J , which are best indicated in the residuals. The quality of the fit deteriorates at lower wave numbers because the contributions from higher-J lines that are not included in the fit start to become significant. Previous evidence of line coupling in the Q-branch of the NO fundamental has been reported by Lempert (et al. 19) only for self-broadening measured by Raman spectroscopy. The results of the current study, therefore, represent the first semiquantitative indication of line coupling in the NO Q-branch by a noble gas using the FTS technique. Obviously, further study and modeling is required to firmly cement these observations.

The first systematic study of collision broadening of rotational transitions in the fundamental band of NO by the five noble gases is reported. Broadening coefficients and cross sections are determined for both the Ä = 1/2 and Ä = 3/2 substates of NO 2 5 state. The data show a clear dependence on the rotational quantum number that is indicative of trends observed in the energy transfer rate coefficients from rotationally inelastic collision experiments. We make no attempt here to determine total rotational energy transfer rate coefficients via scaling law modeling of the data because the effects of elastic collisions must be included in such an analyses. The data, however, are available for use in such studies. We also have report broadening coefficients in the Q-branch of NO with Ar as the broadening gas. These coefficients are utilized in the analysis data obtained at high pressures, where we indicate that line coupling in the Q-branch of the NO fundamental band may exist in collisions with argon. Detailed modeling is required to clarify this effect. ACKNOWLEDGMENTS We gratefully acknowledge the financial support of the Air Force Research Laboratory, Directed Energy Directorate, Kirtland AFB, New Mexico and the Air Force Office of Scientific Research. The authors are also indebted to Dr. Michael Hoke and Dr. Robert Hawkins, Air Force Research Laboratory (Space Vehicles Directorate), Hanscom AFB, Massachusetts for providing valuable assistance in fitting the lineshapes with the DUDV program. We also thank Professor Glen P. Perram for insightful discussions and Capt. John Cornicelli for his help in obtaining preliminary line broadening data.

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