International Journal of SpectroscopyVolume 2011 (2011), Article ID 816548, 7 pagesdoi:10.1155/2011/816548

Research Article

On the Pressure and Temperature Dependence of the Absorption Coefficient of NH₃

F. Aousgi, S. Hadded, and H. Aroui

Laboratoire de Physique Moléculaire, Ecole Supérieure des Sciences et Techniques de Tunis, 5 Avenue Taha Hussein, Tunis 1008, Tunisia

Received 27 June 2011; Accepted 24 August 2011

Academic Editor: Jean-Valère Naubron

Copyright © 2011 F. Aousgi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The effects of pressure and temperature on the absorption coefficient of ammonia (NH₃) gas self-perturbed and perturbed by nitrogen (N₂) gas have been measured. We varied the gas pressure from 10 to 160 Torr and the temperature from 235 to 296 K in order to study the absorption coefficient at the center and the wings of lines in the band of NH₃. These measurements were made using a high resolution (0.0038 cm⁻¹) Bruker Fourier-transform spectrometer. These spectra have been analyzed using the method of multipressure technique permitting to succeed to an evolution of the absorption coefficient with the pressure and the quantum numbers and of the NH₃ molecule. The results show that the absorption coefficient varies as a quadratic function of the pressure at the center of a given line. However, it has a linear evolution in the wings of the line. Moreover, the absorption coefficients are inversely proportional to temperature in the wings when NH₃ lines are broadened by N₂. The retrieved values of these coefficients were used to derive the temperature dependence of N₂ broadening NH₃ lines. The absorption coefficients were shown to fit closely the well-known exponential law.

1. Introduction

The infrared spectroscopic investigations of the atmospheres of stars, planets, and their satellites, using infrared spectroscopy, not only provide valuable information about the chemical elements that they consist of, but also about the horizontal and the vertical distribution of their minor constituents. Due to the complexity of the line profiles used to model the spectral shapes (absorption, broadening, intensity), it is necessary to determine experimentally the line parameters of the spectra in order to test the models being used.

Several studies in the literature have investigated the spectral properties of NH₃ in several infrared bands. Aroui et al. [1] have studied the self-broadening and line intensities, Nouri et al. [2] have studied the temperature dependence of pressure broadening, and other authors [3, 4] were interested in the absorption coefficient at the line centers of NH₃. Experimentally absorption coefficients for broadband ArF excimer radiation laser were determined for NH₃ at temperatures up to 3500 K [5]. Measurements of the NH₃ absorption coefficients at CO₂ laser wavelengths have been done by Zelinger et al. [5] using photoacoustic spectroscopy. NH₃ absorption coefficients were also measured by Allario and Seals [6] using several transitions of a CO₂ laser for small concentrations of NH₃ perturbed by N₂. The influence of CO₂ Laser line width on the measured absorption coefficients of atmospheric ammonia has been studied by Voitsekhovskaya et al. [7].

The focus of the present study is to present absorption line profile measurements of NH₃ in the 6 μm region ( branch of the band). In this range, we resolved the spectra for different and quantum numbers. We have determined the absorption coefficients in the centers and in the wings of NH₃ lines self-perturbed and perturbed by N₂ at various pressures (10–160 Torr). The measurements were made for different gas temperatures 235, 245, 268, and 296 K. The analysis was made as a function of and quantum numbers, and the results were compared to the previous investigations.

2. Experimental

The measurements were made using a high-resolution Bruker Fourier transform spectrometer (Bruker IFS 120 HR) [8, 9]. This spectrometer is equipped with different components: a Globar source, a KBr beam splitter, a filter eliminating infrared radiation above 2500 cm⁻¹, and a photovoltaic HgCdTe detector cooled at 77 K by liquid nitrogen.

The spectral resolution was about 0.0038 cm⁻¹ after apodization with a triangular function. This value is equal to the half-width at half maximum of the apparatus function approximated in the calculations by a Gaussian shape. This approximation has a negligible contribution to systematic errors since the pressure-broadened lines were much larger [2, 10]. Ammonia gas in natural abundances was provided by Air Liquid France with stated purity of 98.5%. The spectra were measured at different pressures covering the lines of the branch of the band of ammonia. NH3 and N₂ gases were contained in a metallic cell with a 2.5 cm path length for NH₃ self-perturbed, and in a Pyrex glass cell with a 15 cm path length for NH₃ perturbed by N₂. Both of the absorption cells are sealed by CaF₂ windows.

The pressures of the gases were measured accurately using three calibrated capacitive MKS Baratron transducers with full-scale readings of 10, 100, and 1000 mbar. The accuracy of these manometers is 0.5% of the readout. Ammonia sample pressures were allowed to stabilize for sufficient time before the spectrum of the sample was finally recorded.

For NH₃ self-perturbed, the pressure was varied from 5 to 120 mbar, whereas for NH₃ perturbed by N₂ we varied the gas pressure from 10 to 160 Torr. For the present experiments, the temperatures varies from 235 to 296 K. Each temperature was monitored by three calibrated thermocouples (Pt-100).

The measured intensity of the incident light () and the transmitted light () at wave-number were converted to transmission spectra using Lambert-Beer’s law

Table 1 summarizes the experimental parameters. The spectral region for this study is between 1470 and 1600 cm⁻¹. Figure 1 shows short transmittance spectra of NH₃ around 1550 cm⁻¹ exhibiting some prominent lines of the branch. These spectra were recorded at  K. At low pressure, the lines are separated, but when the pressure increases the lines widen and begin to overlap.

Table 1: Experimental parameters.

Studied gas
Temperature
Pressure of the perturbed gas (mbar)
Cell length (cm)

NH₃–NH₃
296
10~141
2.5

NH₃–N₂
235, 245, 268, 296
10~141
15

Figure 1: Transmittance spectrum of NH₃ around 1550 cm⁻¹ showing some lines of the branch of the band. The pressures of NH₃ are 15 and 31 mb.

3. Fitting Procedures

The absorption coefficient of an isolated line of the band is obtained by comparing the recorded line with a synthetic line. The adjustment is performed using the Rosenkranz profile given [11, 12] by where is the NH₃ pressure, is the partial pressure of the perturbing gas, represents the line , its intensity, its wave number including the collisional shift ,   the unperturbed or zero pressure wave number), its broadening coefficient, and its mixing parameter.

The modelled transmission is the result of a convolution of with a Doppler profile () and the apparatus function of the spectrometer () [10]. where represents the length of the absorption cell.

The differences between the experimental and calculated spectra were minimized by adjusting the parameters , , , and using a nonlinear least-squares multipressure fitting technique where all spectra at various pressures are successively adjusted using (3). An example of multipressure fit in the case of line for four NH₃ pressures (30, 60, 91, and 120 mbar) is shown in Figure 2. Residual (measured minus calculated) spectra are shown in the lower part of graphs.

Figure 2: Results of multipressure fits for the line in the band of NH₃ self-perturbed at 296 K. (—) and (•) are the measured and calculated values, respectively. Residual (measured minus calculated) spectra are shown in the lower part of the graphs.

As illustrated by this figure, the theoretical model given by (3) proves sufficiently accurate to fit very well the observed spectral lines without accounting for Dicke narrowing and/or speed dependence and demonstrates at the same time that the line coupling cannot be neglected.

4. Results Analysis

4.1. Line Center Absorption Coefficients

We have made measurements of the absorption coefficients for 60 isolated lines of NH₃ in the spectral region between 1470 and 1600 cm⁻¹. For illustration, the evolution of the absorption coefficient à  K for the line at various pressures of NH₃ is shown in Figure 3(a).

Figure 3: Variation of the absorption coefficient and its inverse in the center of the line versus and , respectively, at  K.

In the low-pressure regime, we notice that the absorption coefficient of a given line varies as a quadratic function of pressure as given by the following equation: where is a constant value depending on the individual line.

This figure shows that at high-pressure region, the absorption coefficient tends towards a constant value and hence becomes independent of pressure.

These results are in agreement with those published in [4], where the author studied some lines of the band of NH₃.

The inverse of the absorption coefficient as a function of the square of the NH₃ pressure is plotted in Figure 3(b) for the line. Indeed, one can see that these two parameters vary linearly. The slope of the obtained straight line is related to the line intensity and self-broadening coefficient of the considered line [4].

Results obtained for NH₃ perturbed by N₂, show that the peak absorption coefficient, for the 60 lines studied in this work, is decreasing with the N₂ pressure. Figure 4 illustrates the variation of the line center absorption coefficients versus the N₂ pressure for the lines at  K. This figure also shows that the absorption coefficient decreases with the pressure of the perturbing gas. Moreover, it illustrates that decreases with quantum number for a given . For example, the of line is greater than that of line.

Figure 4: Variation of the absorption coefficient in the line center versus the N₂ pressure () for the lines.

Figure 5 represents the evolution of the absorption coefficient with the quantum number in the case of NH₃–NH₃ gas mixture at  K and  Torr. The coefficient has a maximum at for the lines and decreases monotonically for with increasing .

Figure 5: Variation of the absorption coefficient of and lines with the quantum numbers and . Case of NH₃–NH₃ gas mixture at  Torr for  K.

According to the literature [10, 13], the line intensity depends on the statistical weight factor , which is related to the quantum numbers and . The intensities of the transition having a statistical weight (i.e., for , ) are generally higher than of those lines having a statistical weight for . As illustrated by Table 4, one can conclude that the absorption coefficients and the line intensities vary in the same way as a function of the quantum numbers.

4.2. Line Wing Absorption Coefficients

According to our analysis, we observe a quadratic dependence of the absorption coefficient as a function of pressure of the NH₃ gas that can be modeled as follows [14]: is the normalized absorption coefficient depending on the temperature and the wave number of the line; is the NH₃ pressure. Table 2 gives the self-absorption coefficient of the two wings of and lines as a function of the square of NH₃ pressure () at  K. Figure 6 shows the variation of self-absorption coefficient of the right wings of and lines as a function of the square of NH₃ pressure (). One can see that the wing absorption coefficients increase linearly with pressure.

Table 2: Self-absorption coefficient of the two wings of and lines as a function of the square of NH₃ pressure () at  K.

(atm²)
(cm⁻¹)

2.28
14.9
14.4
—
1.64

18
61
—
48.5
—

37
123.8
125.9
80.5
81.5

63
191.5
191.5
122.1
121.5

140
384.4
382.3
256.5
256.3

Figure 6: Variation of self-absorption coefficient in the right wings of and lines as a function of the square of NH₃ pressure (): Case of NH₃–NH₃ gas mixture at  K.

All the self-absorption coefficients measured for the pressure and temperature ranges considered in this study validate the above quadratic pressure dependence given by (5).

For NH₃–N₂ gas mixtures, a sample of the absorption coefficient for the two wings of the line as a function of N₂ pressure () at  K is given by Table 3. This table reveals an increasing of with . So the coefficient can be described by the following equation [15]: where is the normalized absorption coefficient.

Table 3: Absorption coefficient of two wings of the for NH₃-N₂ mixtures as a function of N₂ pressure () at  K.

(atm)
(cm⁻¹ atm⁻¹)

29.6
15.1
13.8

59.2
19.4
18.4

89.6
24.1
23.9

121.9
27.7
26.7

138.9
30.8
30.1

Table 4: Values of the normalized absorption coefficients and for NH₃ broadened by N₂ at  K.

Transition
(cm⁻¹)
NH₃–NH₃
NH₃–N₂

(cm⁻¹ atm⁻²) ()
(cm⁻¹ atm⁻²) ()
(cm⁻¹ atm⁻²) ()
(cm⁻¹ atm⁻²) ()

1591.1050
1.467 (0.098)
1.493 (0.063)
2.731 (0.437)
2.448 (0.245)

1595.0801
6.759 (0.348)
1.045 (0.069)
3.228 (0.233)
2.799 (0.303)

1572.4882
3.282 (0.139)
3.435(0.065)
2.807 (0.100)
2.956 (0.542)

1579.6363
16.39 (0.431)
2.216 (0.047)
3.859 (0.274)
4.176 (0.183)

1554.7340
2.065 (0.047)
2.009 (0.050)
3.490 (0.329)
3.006 (0.207)

1558.2494
1.344 (0.046)
1.370 (0.011)
2.815 (0.269)
2.923 (0.218)

1561.3835
4.217 (0.086)
4.1741 (0.150)
9.782 (0.707)
9.632 (0.462)

1564.0825
10.40 (0.186)
0.566 (0.042)
2.338 (0.203)
5.111 (0.511)

1538.0102
0.860 (0.083)
0.838 (0.058)
3.693 (0.372)
3.343 (0.171)

1541.0041
2.520 (0.075)
2.272 (0.021)
2.883 (0.540)
2.893 (0.534)

1543.8550
2.468 (0.07)
2.990 (0.029)
5.638 (0.248)
5.391 (0.583)

1546.3315
5.805 (0.194)
4.610 (0.270)
4.829 (0.028)
4.013 (0.539)

1548.4290
13.527 (0.381)
2.471 (0.142)
2.920 (0.220)
3.510 (0.208)

1522.3847
1.370 (0.033)
1.518 (0.024)
2.020 (0.384)
1.021 (0.134)

1522.7763
—
—
2.006 (0.399)
1.894 (0.064)

1527.0615
2.822 (0.093)
2.583 (0.053)
4.232 (0.364)
4.313 (0.372)

1529.2897
1.524 (0.015)
1.553 (0.058)
2.424 (0.146)
2.172 (0.221)

1531.1590
1.571 (0.07)
1.4164 (0.056)
3.784 (0.522)
3.003 (0.625)

1532.6831
20.697 (0.570)
2.250 (0.118)
4.430 (0.076)
9.116 (0.919)

1509.4479
1.818 (0.053)
1.863 (0.108)
1.415 (0.044)
1.445 (0.055)

1511.3125
1.169 (0.064)
1.510 (0.047)
1.183 (0.195)
1.312 (0.247)

1513.0439
1.823 (0.094)
1.888 (0.074)
1.657 (0.131)
1.431 (0.442)

1514.6055
2.319 (0.176)
2.145 (0.141)
1.810 (0.157)
1.500 (0.104)

1515.8819
3.013 (0.035)
3.074 (0.162)
2.200 (0.179)
1.946 (0.226)

1516.8521
8.994 (0.217)
1.248 (0.070)
2.080 (0.120)
2.632 (0.091)

1494.2421
0.375 (0.038)
0.334 (0.009)
1.116 (0.113)
1.180 (0.101)

1493.5269
—
—
1.145 (0.142)
1.328 (0.215)

1496.1740
0.546 (0.105)
0.597 (0.072)
2.357 (0.153)
2.785 (0.261)

1497.6750
1.982 (0.104)
2.123 (0.071)
4.054 (0.261)
4.521 (0.276)

1499.8028
2.199 (0.022)
2.877 (0.264)
2.710 (0.236)
2.499 (0.917)

1500.5103
11.869 (1.307)
10.742 (1.414)
—
—

1500.9439
7.227 (0.231)
2.221 (0.335)
1.423 (0.349)
1.799 (0.368)

The and parameters were determined using (6) and the absorption coefficient values for the right and left wings of the each line considered in this work. The results at  K are given in Table 4 for 32 ro-vibrational antisymmetric lines in the branch of the band along with the estimated errors given in parentheses. These errors correspond to the statistical errors expressed as one-time standard deviation for all spectroscopic parameters determined in this work. As expected, the errors vary widely with the lines. The stronger and less blended ones are better determined. For the lines which are too weak or too strongly blended, no reliable fit could be obtained. For this reason, some lines have been disregarded. The assignments of the lines considered in this table are taken from [16]. Within the experimental errors, as seen by Table 4, the values of and are practically identical for the two wings.

Figure 7 shows the variation of the absorption coefficient with the N₂ pressure for the two wings of the line for NH₃–N₂ mixtures at  K. As shown by this figure, the variation of the absorption coefficient divided by the NH₃ pressure () with the N₂ pressure is linear. Also, we observe that the values of and parameters are practically the same for the left and right wings of the lines.

Figure 7: Variation of versus the N₂ pressure () for the two wings of the line perturbed by N₂ at  K.

4.3. Temperature Dependence

Spectra of the band of NH₃ perturbed by N₂ were recorded at four temperatures 235, 245, 268, and 296 K for different pressures of nitrogen (). For these spectra, the pressure of NH₃ was fixed. Variation of the absorption coefficient at the line center as a function of for the line for and 265 K is shown by Figure 8 which illustrates a decreasing of the absorption coefficient with temperature.

Figure 8: Variation of the absorption coefficient as a function of the N₂ pressure () for the line for the temperatures and 265 K.

According to Shi and Zhang and Bauer et al. [17, 18], the temperature dependence of absorption coefficient could be presented by the simple power law: where is the temperature exponent and is the reference temperature. In our case  K.

From the measured values of the absorption coefficients for the considered temperatures, one can determine the values of the exponent A as the slope of least square fits from the graphs of as a function of . The straight lines obtained for all the transitions considered in this work validate (7) within the indicated temperature range. Figure 9 illustrates the variation of as a function of for the line. The variation is linear; the slope of the line obtained from a linear regression gives a temperature exponent .

Figure 9: Variation of as a function of for the left wing of line. The slope of the line obtained from a linear regression represents the temperature exponent .

This dependence is in agreement with the work performed by Bauer et al. [18] in their study of the temperature dependence of the absorption coefficient of H₂O transitions.

5. Conclusion

Using spectra recorded using a Fourier transform spectrometer and a multispectrum fitting technique, we have determined the absorption coefficients at the center and in the wings of 60 lines pertaining to the branch of the band of NH₃ as a function of NH₃ and N₂ pressures for different temperatures. The present results are in agreement with other recent measurements. In the low-pressure region, the self-absorption coefficient at the center of a given line varies with pressure as a quadratic function. At higher pressures, this coefficient tends to become constant. For NH₃–N₂ mixture, the values of the absorption coefficients exhibit a decreasing with N₂ pressure.

In the wings of the lines, these coefficients show an increasing with the square of NH₃ pressure, while for NH₃-N₂ gas mixtures they increase with N₂ pressure.

For this gas mixture, we have studied the temperature dependence of absorption coefficient which fits closely an exponential low. The temperature exponents of this law were derived for the line.

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