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Diode-laser spectroscopy: Pressure dependence of N2-broadening coefficients of lines in the ν4+ν5 band of C2H2
Journal of Molecular Spectroscopy 254 (2009) 10–15
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Diode-laser spectroscopy: Pressure dependence of N2-broadening coefficients of lines in the m4 þ m5 band of C2H2 Laurent Fissiaux, Miguël Dhyne, Muriel Lepère *,1 Laboratoire Lasers et Spectroscopies, Research center in Physics of Matter and Radiation (PMR), University of Namur (FUNDP), 61, rue de Bruxelles, B-5000 Namur, Belgium
a r t i c l e
i n f o
Article history: Received 29 October 2008 In revised form 1 December 2008 Available online 13 December 2008 Keywords: Collisional broadening Acetylene Pressure dependence Diode-laser
a b s t r a c t In this work, we have measured the N2-broadening coefficients of 12 absorption lines in the m4 þ m5 band of acetylene at room temperature, using a tunable diode-laser spectrometer. For each line under study, we have recorded spectra at 4–16 pressures of nitrogen ranging from 4.03 to 179.5 mbar. The line profiles were individually fitted, at each pressure, with different line shape models including fine effects as Dicke narrowing or/and speed dependence effect. From these fits, we have obtained the collisional half-widths at each pressure and then determined accurately the N2-broadening coefficients of 12 lines. After that, we have studied the pressure dependence of the collisional broadening and narrowing coefficients following the considered line profile model. Finally, our results are compared with the previous studies realized in various absorption bands. Ó 2008 Elsevier Inc. All rights reserved.
1. Introduction Acetylene is a minor constituent of our atmosphere [1] as well as in the atmospheres of Saturn, Jupiter [2] and Titan [3]. The measurements of self and foreign-gas broadening coefficients provide important information for the analysis of atmospheric spectra and on intermolecular potentials via theoretical calculations. To obtain such line parameters as precise as possible, it is essential to fit the experimental profile with a theoretical line shape taking into account the different physical effects affecting the broadening of line. In this work, we have measured N2-broadening coefficients of 12 C2 H2 at room temperature for 12 lines belonging to the R-branch of the m4 þ m5 band in the spectral range 1275–1394 cm1 at a high-resolution using a diode-laser spectrometer. For each line under study, we have recorded spectra at 4–16 pressures of nitrogen ranging between 4.03 and 179.5 mbar. We retrieved the collisional line widths fitting the experimental profiles by the Voigt, Rautian, Galatry lineshape models and for the high pressures (>100 mbar) by a model taking into account simultaneously the Dicke narrowing and the speed dependence effect. The large range of pressures allowed an accurate collisional broadening coefficient determination. We also studied the dependence of collisional broadening as a function of pressure to determine the best experimental conditions and the most suited theoretical line shape model. The colli-
* Corresponding author. Fax: +32 81 72 45 85. E-mail address: [email protected] (M. Lepère). 1 Research Associate with F.R.S.-FNRS, Belgium 0022-2852/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2008.12.003
sional broadening coefficients derived from our measurements are compared with values available in the literature [4–8]. Podolske et al. [4] have reported a line strength study in the m4 þ m5 band and, they have measured collisional broadenings for 3 lines of C2H2 perturbed by N2 and H2 for m4 þ m5 band. Devi et al. [5] have measured the N2- and air-broadening coefficients for 29 lines in the same band. Later, Bouanich et al. [6] and Lambot et al. [7] have realized respectively theoretical and experimental studies, for several lines in the m5 band of C2H2 perturbed by N2 and O2. The more recent study, reported by Pine [8] in 1993, was devoted to the measurement of the line mixing and the self, N2-, Ar-broadenings and line mixing were measured in the m1 þ m5 band. In this work, we have also studied the pressure dependence of the collisional narrowing coefficients following each theoretical line shape model. These experimental results have been compared with the calculated values using the theory of diffusion. 2. Experimental details The spectra of C2H2–N2 mixtures were recorded with an improved Laser Analytics (LS3 model) tunable diode-laser spectrometer previously detailed in Ref. [9]. The spectra resulted from an average of 100 scans in order to increase the signal-to-noise ratio. The relative calibration was obtained by introducing in the laser beam a confocal étalon with a free spectral range of 0.007958 cm1. Nitrogen was supplied by Air Liquide company with a purity of 99.9%, while acetylene was provided by Air Liquide company with a purity of 99.6%. The gas mixtures were contained in a White-type cell with one meter-distance between mirrors and
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L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
with KBr windows. The pressures of C2H2 in the absorption cell were always chosen to be small (ranging from 0.0067 to 0.4463 mbar). Nevertheless, the C2H2 pressure was considered for all lines, and corrections were made to take into account the small contributions due to self-broadening were determined from the measurements of Lepère et al. [10]. The pressures of pure C2H2 and C2H2 + N2 mixture were measured using three MKS Baratron gauges with full scale readings of 1.2, 120 and 1200 mbar. All data were recorded at the room temperature (i.e., 24.5 ± 1.5 °C). To obtain a good homogeneity in the mixtures, we waited 15 min before each spectrum record. An example of the spectra obtained for the R(11) line of C2H2 at 1356.8555 cm1 [11] is shown in Fig. 1. For each line under study, we have recorded the following consecutive spectra: (1) laser emission profile through the empty cell, (2) the record of the line at very low gas pressure of pure C2H2 and very small absorption, allowing the determination of the instrumental function, (3–6) the N2-broadened spectra at four different nitrogen pressures, (7) the record of the étalon fringe pattern allowing relative calibration in wavenumber, (8) the pure C2H2 saturated line which represents the 0% transmission level. 3. Data reduction The experimental absorbance aðmÞ can be deduced for each perturber pressure using the Beer–Lambert’s law as
aðmÞ ¼ ln
It ðmÞ ; I0 ðmÞ
ð1Þ
where It ðmÞ and I0 ðmÞ are respectively the transmitted through the gas sample and incident intensities at wavenumber m (cm1). The line parameters were obtained by fitting a theoretical lineshape to the measured absorbance. First, we used the Voigt profile [12] which has three adjustable parameters. This profile is simply the convolution between a Gauss function (Doppler effect) and a Lorentz function (collisional effect), assuming that both effects are independent. It can be defined as [13]
aV ðA; x; yÞ ¼ A
y
p
Z
þ1
1
expðt 2 Þ y2
þ ðx tÞ
2
dt ¼ A Re½W ðx; yÞ;
ð2Þ
with
2
1
W ðx; yÞ ¼
i
p
Z
þ1
1
expðt 2 Þ dt; x þ iy t
and
A¼
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi m m0 pffiffiffiffiffiffiffiffi c S ln 2 pffiffiffiffi ; y ¼ ln 2 c ; x ¼ ln 2 :
cD
cD p
cD
ð4Þ
Here S = S0 p1, with S0 (in cm2 atm1) the line intensity and p1 (in atm) the absorber pressure; m0 (in cm1) is the position of the line center (the eventual pressure shifts are very weak at such pressure and are not considered in this study); cD (in cm1) is the theoretical Doppler half-width that we calculate; cc (in cm1) is the collisional half-width and is equal to c0 p2 þ cself p1 where c0 (in cm1 atm1) is the collisional broadening coefficient of C2H2 diluted in N2 ; cself (in cm1 atm1) is the self-broadening coefficient, p1 and p2 (in atm) are the partial pressures of the absorbing molecule and the perturber, respectively. In reality, Doppler and collisional effects are not independent and intermolecular collisions perturb Doppler effect. The mean translation motion of the active molecules is reduced and the free streaming motion of the molecules becomes diffuse. This is well known as the Dicke effect [14]. We also fit the experimental profiles the Rautian and Sobel’man [15] and Galatry [16] models taking into account the Dicke effect and provide an additional parameter bc which represents the collisional narrowing effect due to the molecular confinement. The Rautian and Sobel’man model is also called hard collision model because it assumes that the velocity of the active molecule after the collision is independent of its velocity before the collision. This model is best suited when the perturber mass is larger than the mass of the active molecule. This profile may be described as [15]:
aR ðA; x; y; zÞ ¼ A Re
Wðx; y þ zÞ pffiffiffiffi 1 pzWðx; y þ zÞ
ð5Þ
where the parameters A, x and y are the same as defined in Eq. (4) and
z¼
pffiffiffiffiffiffiffiffi bc ln 2
ð6Þ
cD
with bc (in cm1) representing the average effect of collisions on Doppler broadening. Here, bc ¼ b0 p2 where b0 (in cm1 atm1) is the collisional narrowing coefficient. The Galatry model is also called soft collision model because it assumes that the duration of each collision is short and does not modify significantly the velocity of the active molecule. This second model is best suited when the active molecule mass is larger than the perturber one. It can be defined by [16]:
A
Z
aG ðA; x; y; zÞ ¼ pffiffiffiffi Re p
7
ð3Þ
þ1
1
zt 1 þ ezt dt exp ixt yt 2 2z ð7Þ
6 0.007958 cm
-1
5 4 3 8
N2-pressures (mbar) : 3 : 30.57 4 : 40.82 5 : 54.90 6 : 65.50
Fig. 1. Example of spectra recorded for the R(11) line at 1356.8555 cm1 in the m4 þ m5 band of C2H2 perturbed by N2. (1) The diode-laser emission profile, (2) the spectrum of the line at very low pressure of pure C2H2 and very small absorption, (3–6) the broadened line recorded at different pressures of N2, (7) the confocal étalon fringe pattern used for the relation calibration in wavenumber, (8) the saturated line giving the 0% transmission level.
with the same definition of the parameters. The collisional narrowing coefficient b0 may be compared to the dynamical friction parameter b0diff (in cm1 atm1) of the Brownian motion, expressed as [17]:
b0diff ¼
kB T ; 2pcmD
ð8Þ
where kB is the Boltzmann constant, T (in K) is the temperature, c (in m/s) is the light velocity, m (in a.m.u.) is the absorber molecular mass and D (in cm2 s1) is the mass diffusion coefficient for the C2H2 + N2 system, calculated following [17]. At low pressures (below 100 mbar), the collisional widths were several times smaller than the Doppler widths and we have considered the Voigt profile as well as the Rautian and the Galatry models.
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L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
For pressures above 100 mbar, we have used a model taking account simultaneously the Dicke narrowing and speed dependence effect. In this model, the collisional profile may no longer be represented by a simple Lorentz function, but should be described by a weighted sum of Lorentz profiles (WSL) for each velocity of the absorber [18]. In this work, we used a speed-dependent hard collision model developed by Lance et al. [19] and adapted by Lerot et al. [20]. In order to take into account the instrumental distortions, the effective Doppler half-width was fixed in the fitting procedure to the cD value given by [21]
cD ¼ ðc2DT þ c2App Þ1=2 ;
ð9Þ
where cDT and cApp are the theoretical Doppler and contribution due to instrument distortion [22]. The theoretical Doppler was calcuqffiffiffi lated as cDT ¼ 3:581 107 m0 MT with m0 (in cm1) the wavenumber of the measured transition, T (in K) the temperature, M (in a.m.u) the molecular mass. The apparatus half-width was determined by fitting to the absorbance line, recorded at very small pressure and absorption, a function expressed as
aðm m0 Þ ¼ ln
Z
þ1
fApp ðmi Þ expðkDop ðm m0 mi ÞLÞdmi ;
ð10Þ
1
with L the absorption length, fApp ðmi Þ the Gaussian instrumental profile with an adjustable half-width cApp and kDop ðm m0 Þ the theoretical Gaussian Doppler profile. Fig. 2 illustrates an example of Voigt fit obtained for the R(9) transition in the m4 þ m5 band of C2H2 (p = 0.0340 mbar) diluted in
1.6 1.4
P(N2) = 122.20 mbar
Exp Voigt
P(C2H2) = 0.0340 mbar
1.2
α(ν)
1.0 0.8 0.6 0.4 0.2 0.0 0.1
Voigt
0.0 -0.1 0.1
Rautian
(O-C)*10
0.0 -0.1 0.1
Galatry
0.0 -0.1 0.1
SDHC
0.0 -0.1 1351.99
1352.00
1352.01
1352.02
-1
ν (cm ) Fig. 2. The measured absorbance for the R(9) line in the m4 þ m5 band of C2H2 (p = 0.0340 mbar) perturbed by 122.20 mbar of N2. This experimental line shape is fitted using a Voigt profile (). The residuals, difference between observed and calculated values multiplied by 10, are represented at the bottom of the figure for the fitted Voigt, Rautian, Galatry and SDHC models.
122.20 mbar of nitrogen at room temperature. The Voigt, Rautian, Galatry and the Speed Dependence Hard Collision (SDHC) models are used to fit the experimental line shape. The residuals (observed minus calculated, 10(o–c)) are shown at the bottom of Fig. 2. The Rautian and the Galatry profiles fit the observed line shape better than the Voigt line shape because they also include the effect due to the Dicke narrowing. In the case of C2H2 broadened with N2, the mass ratio (ratio of mass of target gas that of the broadening gas) is close to 1 and hence the differences between Rautian and Galatry line shapes are not significant. The SDHC model also fit the observed line shape quite well. It appears that at a total pressure of 122 mbar, the effect due to speed dependence is small and hence may be neglected. This is clear from values listed in Table 1 and will be discussed in the following section.
4. Results For a given line, the collisional half-width cc was determined for at least four perturber pressures. Fig. 3 shows a typical plot of cc minus the self-broadening contribution ðcself pC 2 H2 Þ versus the N2 pressure for the R(5) line. The self-broadening coefficient were taken from Lepère et al. [10]. The collisional broadening coefficient c0 (in cm1 atm1) was determined as the slope of the best straight line obtained from the linear regression. The N2-broadening coefficients c0 are given in Table 1 along with their experimental errors. The experimental uncertainties are mainly due to the difficulties in locating accurate position of the base line, the perturbation due to the neighboring lines, the nonlinearity of sweeping in frequency of the emission of the diode and the theoretical profile used. The given errors were estimated to be the statistical error (twice the standard deviation given by the linear regression) plus 2% or 3% of the c0 value to take into account the whole experimental uncertainties. In Table 1, we present results obtained at low pressure (<100 mbar) with the Voigt, the Rautian and the Galatry models and the values obtained at higher pressure (>100 mbar) for the same models and the SDHC model. In the Fig. 4, we compare our results retrieved using different theoretical line shape models as well as for different pressure regimes. The values obtained with Rautian line shape are very close to those deduced from Galatry fits, that we do not illustrate in the Fig. 4. At low pressure (below 100 mbar), the values deduced from Voigt fits are systematically smaller than those obtained with Rautian (or Galatry) fits. At pressure above 100 mbar, the coefficients of collisional broadening are often smaller than those determined at lower pressure. When the pressure increases, the collisional broadening increases and the lorentzian profile becomes predominant. At high pressure (>100 mbar), the wings of the neighboring lines perturb the line understudy. It is the reason why the error bars corresponding to high pressure measurements are equal to twice the standard deviation plus 3% of the c0 value, instead of 2% at low pressure. The measurements made at high pressure are thus less precise. For six lines, we have made measurements at 16 different pressures up to 170 mbar. The coefficient of collisional broadening c0 (in cm1 atm1) are independent of the pressure. In the Fig. 5, we plot the collisional broadening coefficients versus the perturber pressure for the R(4) line of C2H2 diluted in N2 at room temperature. Results are presented for the considered lineshape models. At very low pressure (<30 mbar), the collisional broadening depends largely on the pressure for each model. It is due to the fact that, for such pressure, the collisional width is smaller than the Doppler width and thus the measurement of collisional width is not so precise. For pressures comprised between 30 and 100 mbar, the coefficients of collisional broadening are quite constant. In addition, we see in the Fig. 5 that the values deduced from Voigt
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L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
Table 1 N2-broadening coefficients c0 in the m4 þ m5 band of C2 H2 at room temperature. The errors given here are equal to twice the standard deviation of the linear regression plus 2% or 3% of the coefficient c0 itself. The wavenumber values are taken from Kabbadj et al. [11].
c0 ð103 cm1 atm1 at 298 K)
m0 ðcm1 Þ
Line
p < 100 mbar
p > 100 mbar
Voigt R(2) R(4) R(5) R(6) R(9) R(11) R(14) R(16) R(19) R(21) R(23) R(26)
1332.8027 1339.9523 1342.3495 1344.7530 1351.9994 1356.8555 1364.1668 1369.0519 1376.3820 1381.2619 1386.1296 1393.3956
90:7 90:7 89:9 83:9 79:6 75:3 75:3 68:6 66:9 65:3 55:9
Rautian
1:9 2:5 3:3 2:5 1:7 2:0 2:0 2:0 2:0 3:4 1:3
92:8 92:2 92:0 86:3 81:8 77:0 77:6 71:0 69:9 68:4 58:2
Galatry
2:7 2:9 3:8 3:2 2:3 2:0 2:5 2:0 2:7 3:9 1:8
92:9 92:3 92:2 86:4 81:9 77:1 77:8 71:1 69:4 68:6 58:3
2:7 3:0 3:9 3:4 2:4 2:1 2:6 2:2 2:4 4:0 1:9
Voigt
Rautian
Galatry
SDHC
100:4 3:2 92:1 2:9
101:9 3:4 93:8 3:0
101:9 3:4 93:8 3:0
98:7 3:8 91:5 3:6
82:1 2:7
82:5 2:8
82:5 2:8
82:7 3:2
75:5 2:5
76:4 2:8
76:4 2:8
76:4 2:5
67:3 2:4 64:7 2:5
68:5 2:9 66:8 3:2
68:5 2:9 66:8 3:2
68:9 2:9 64:3 2:9
7
6
100
-1
γ0 (10 cm atm )
-1
γc- γself.p C H (10 cm )
5
90
3
-3
2 2
-1
-3
4
2
80
Voigt Rautian Galatry SDHC
Voigt Rautian
1
0
70 0
10
20
30
40
50
60
70
0
20
40
60
80
100
120
140
160
180
N2-pressure (mbar)
N2-pressure (mbar) Fig. 3. Example of pressure dependence of the N2-collisional half-widths in the m4 þ m5 band of C2H2 at room temperature for the R(5) line. The slopes of the best-fit lines are the N2-broadening coefficients c0 (in 103 cm1 mbar1).
105
Fig. 5. Pressure dependence for the N2-broadening coefficient c0 for the R(4) line in the m4 þ m5 band of C2H2 at room temperature for the Voigt profile ðOÞ, the Rautian model ðÞ, the Galatry model (+) and the SDHC model () which takes into account simultaneously the Dicke narrowing and the speed dependence effect [20]. The line represents the average value of collisional broadening coefficient c0 obtained with the best adapted model. Values measured with the pressures below 30 mbar are not considered in the average procedure.
100 95
-1
γ0 (10 cm atm )
90
-1
80
-3
85
75 70 65 60 55 0
5
10
15
20
25
|m| Fig. 4. Comparison between our N2-broadening coefficients c0 in the m4 þ m5 band of C2H2 at room temperature retrieved using different theoretical line shape models as well as for different pressure regimes : r Voigt (p < 100 mbar), Rautian (p < 100 mbar), M Voigt (p < 100 mbar), Rautian p > 100 mbar and SDHC (p > 100 mbar).
fits are systematically smaller than coefficients obtained with the Rautian and Galatry models. These last models, which take into ac-
count the Dicke narrowing and represent limit cases about the mass ratio, give values very close. This is due to the ratio of the mass of the active molecule to the mass of the perturbing molecule which is nearly equal to one. In this case, the two models are similar. For pressures above 100 mbar, the coefficients continue to be constant and the SDHC model provides values very close to other determinations. On this figure it seems that no speed dependence effect appears, even at high pressure when the collision width is several times Doppler width. However, at high pressure, collisional broadening is predominant and the wings of the neighboring lines perturb the line understudy. It is then difficult to determine with high accuracy the baseline position and the measurements are less precise. Fig. 6 shows the plot of collisional narrowing coefficients versus the perturber pressure for the R(21) line in the m4 þ m5 band of C2H2 perturbed by N2. These coefficients represent a fine physical effect (Dicke narrowing) sensitive to the experimental conditions as the baseline position. A precise measurement of the collisional narrowing coefficient is thus difficult. It is the reason why this parameter is less constant than the coefficient of collisional broadening, as seen in the Fig. 6. In this figure, it seems that collisional narrowing coefficients deduced from Rautian fits are better than those ob-
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L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
1800 1600
50
jmj
-3
-1
-1
β0 (10 cm atm )
Table 2 Comparison between our N2-broadening coefficients c0 in the m4 þ m5 band of C2 H2 at room temperature and previous determinations in various bands. Devi et al. [5] and Podolske et al. [4] have also measured c0 in m4 þ m5 band. Lambot et al. [7] have studied the m5 band, while the work of Pine [8] was devoted to the m1 þ m5 band. The error bars given for our measurements are equal to twice the standard deviation of the linear regression plus 2% of the coefficient c0 itself.
Rautian Galatry SDHC
40
30
20 0
20
40
60
80
100
120
140
160
N2-pressure (mbar) Fig. 6. Pressure dependence of the N2-narrowing coefficient for the R(21) line in the m4 þ m5 band of C2H2 at room temperature for the Rautian model ðÞ, the Galatry model ðÞ and the SDHC model ðÞ which takes into account simultaneously the Dicke narrowing and the speed dependence effect [20]. The line represents the value calculated by the diffusion theory following Eq. (8).
tained with Galatry fits. For pressures below 100 mbar, the Rautian model fits the data better than other line shapes. When the pressure exceeds 100 mbar, the values deduced from the Rautian and Galatry models become very large and thus have not physical signification. For such pressures, if we consider the SDHC model, the coefficients of collisional narrowing are very close to the values obtained with the Rautian model at lower pressure. In addition these experimental values are in good agreement with the calculated b0diff , represented in the Fig. 6 by the line. Finally, we compare in the Fig. 7, our coefficients of collisional broadening with previous results obtained for various absorption bands. Our values were measured in the m4 þ m5 band by diode-laser spectroscopy and considering the Rautian fits for pressures below 100 mbar and by SDHC fits for R(2) line. Devi et al. [5] and Podolske et al. [4] have measured the N2-broadening coefficients of C2H2 by diode-laser spectroscopy and considering Voigt fits.
105 This work
100
Devi Lambot
95
Pine Calc Bouanich
85
γ
0
(10
-3
cm
-1
-1 atm )
Podolske
90
80 75 70 65 60 55 4
8
12
16
20
24
28
|m| Fig. 7. Comparison between our N2-broadening coefficients c0 in the m4 þ m5 band of C2 H2 at room temperature and previous determinations in various absorption bands. Devi et al. [5] and Podolske et al. [4] have also measured c0 in m4 þ m5 band. Lambot et al. [7] and Bouanich et al. [6] have studied the m5 band, while the work of Pine [8] was devoted to the m1 þ m5 band. The error bars given for our measurements are equal to twice the standard deviation of the linear regression plus 2% of the coefficient c0 itself.
3 5 6 7 10 12 15 17 20 22 24 27
c0 (103 cm1 atm1 at 298 K) This work
Ref. [5]
98.7 ± 2.8 92.8 ± 2.7 92.2 ± 2.9 92.0 ± 3.8 86.3 ± 3.2 81.8 ± 2.3 77.0 ± 2.0 77.6 ± 2.5 71.0 ± 2.0 69.9 ± 2.7 68.4 ± 3.9 58.2 ± 1.8
101.7 90.9 87.7 85.5
Ref. [4]
84.2
79.2 71.1 71.7
Ref. [7]
Ref. [8]
102.0
101.1 93.4 91.7 90.1
91.6 91.7 83.6
76.8 71.7 68.7 58.5
Lambot et al. [7] employed the Rautian line shape in their study of the m5 band using a diode-laser spectrometer. Because the m5 band is very intense short absorption paths were required to make the measurements. Bouanich et al. [6] have calculated the N2broadening coefficients in the m5 band using a semi-classical model. Pine [8] has measured collisional broadening in the m1 þ m5 band with a difference-frequency laser spectrometer. He has used a Rautian profile to fit the experimental lineshape. Table 2 compares our values and the previous results obtained for various absorption bands. The agreement between our measurements and previous determination is relatively good, as seen in the Fig. 7 and Table 2. 5. Conclusion In this paper, the N2-broadening coefficients of 12 lines of C2H2 have been measured in the m4 þ m5 band at room temperature using a tunable diode-laser spectrometer. The collisional widths have been individually deduced from Voigt, Rautian, Galatry and Speed Dependence Hard Collision (SDHC) model fits of each experimental lineshape. The residuals obtained with Voigt fits have always a typical signature while the other models are in excellent agreement with the experimental lineshapes. Each line have been recorded at 4 to 16 different pressures of nitrogen. Such way, we have determined precisely the collisional broadening coefficients. When 16 pressures, ranging from 4.03 to 179.5 mbar, have been considered, a study of the pressure dependence of collisional broadening and narrowing coefficients have been realized. Such way, we have shown that Voigt fits underestimate systematically the collisional broadenings. For pressures below 30 mbar, it is difficult to obtain precise measurements of collisional widths which are small. For pressures between 30 and 100 mbar, the Rautian and Galatry models give very similar results. For pressures above 100 mbar, the speed dependence hard collision model gives collisional broadenings very close to other fits, especially those of Voigt. Nevertheless, we prefer models including at least Dicke narrowing which is a fine physical effect. It would be interesting to check, for other gas mixtures, if the SDHC line shape model gives, at high pressure, values systematically closer to those determined by Voigt profile than those deduced from either Rautian or Galatry line shape model. The coefficients of collisional narrowing deduced at high pressure from the Rautian and Galatry fits are very large and have no physical significance. Considering the speed dependence effect, the coefficients of collisional narrowing deduced at high pressure are in good agreement with the determinations at lower pressure
L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
and with the calculated value using the diffusion theory. At high pressure neighboring lines can perturb the line understudy and reduce the precision of the measurements. So, for C2 H2–N2 mixture, the most accurate measurements of collisional broadening parameters can be realized for pressures ranging from 30 to 100 mbar and considering the Rautian or Galatry model. Acknowledgment M. Lepère is acknowledging support from F.R.S.-FNRS, Belgium. This work is accomplished in the framework of the European Associated Laboratory HiRes. References [1] J. Rudolph, D.H. Ehhalt, A. Khedim, J. Atmos. Chem. 2 (1984) 117. [2] P.V. Sada, G.L. Bjoraker, D.E. Jennings, G.H. McCabe, P.N. Romani, Icarus 136 (1998) 192. [3] A. Coustenis, Th. Encrenaz, B. Bezard, G. Graner, M. Dangnhu, E. Arie, Icarus 102 (1993) 240. [4] J.R. Podolske, M. Loewenstein, P. Varanasi, J. Mol. Spectrosc. 107 (1984) 241. [5] V.M. Devi, D. Ch. Benner, C.P. Rinsland, M.A.H. Smith, B.D. Sidney, J. Mol. Spectrosc. 114 (1985) 49.
15
[6] J.-P. Bouanich, D. Lambot, G. Blanquet, J. Walrand, J. Mol. Spectrosc. 140 (1990) 195. [7] D. Lambot, G. Blanquet, J.-P. Bouanich, J. Mol. Spectrosc. 136 (1989) 86. [8] A.S. Pine, J. Quant. Spectrosc. Radiat. Transfer 50 (1993) 149. [9] M. Lepère, G. Blanquet, J. Walrand, J.-P. Bouanich, J. Mol. Spectrosc. 180 (1996) 218. [10] M. Lepère, G. Blanquet, J.-P. Bouanich, J. Walrand, M. Herman, J. Vander Auwera, J. Mol. Spectrosc. 242 (2007) 25. [11] Y. Kabbadj, M. Herman, G. Di Lonardo, L. Fusina, J.W.C. Johns, J. Mol. Spectrosc. 150 (1991) 535. [12] B.H. Armstrong, J. Quant. Spectrosc. Radiat. Transfer 7 (1967) 61. [13] P.L. Varghese, R.K. Hanson, Appl. Opt. 23 (1984) 2376. [14] R.H. Dicke, Phys. Rev. 89 (1953) 472. [15] S.G. Rautian, I.I. Sobel’Man, Sov. Phys. Usp. Engl. Transl. 9 (1967) 701. [16] L. Galatry, Phys. Rev. 122 (1960) 1218. [17] J.O. Hirschfelder, Ch. F. Curtiss, R.B. Bird, Molecular Theory of Gases Liquids, J. Wiley and Sons, New York, 1967. [18] H.M. Pickett, J. Chem. Phys. 73 (1980) 6090. [19] B. Lance, G. Blanquet, J. Walrand, J.-P. Bouanich, J. Mol. Spectrosc. 185 (1997) 262. [20] Ch. Lerot, G. Blanquet, J.-P. Bouanich, J. Walrand, M. Lepère, Mol. Phys. 103 (2005) 1213. [21] G. Blanquet, J. Walrand, J.-P. Bouanich, J. Mol. Spectrosc. 159 (1993) 137. [22] A. Mouchet, G. Blanquet, P. Herbin, J. Walrand, C.P. Courtoy, J.-P. Bouanich, Can. J. Phys. 63 (1993) 527.
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Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
Diode-laser spectroscopy: Pressure dependence of N2-broadening coefficients of lines in the m4 þ m5 band of C2H2 Laurent Fissiaux, Miguël Dhyne, Muriel Lepère *,1 Laboratoire Lasers et Spectroscopies, Research center in Physics of Matter and Radiation (PMR), University of Namur (FUNDP), 61, rue de Bruxelles, B-5000 Namur, Belgium
a r t i c l e
i n f o
Article history: Received 29 October 2008 In revised form 1 December 2008 Available online 13 December 2008 Keywords: Collisional broadening Acetylene Pressure dependence Diode-laser
a b s t r a c t In this work, we have measured the N2-broadening coefficients of 12 absorption lines in the m4 þ m5 band of acetylene at room temperature, using a tunable diode-laser spectrometer. For each line under study, we have recorded spectra at 4–16 pressures of nitrogen ranging from 4.03 to 179.5 mbar. The line profiles were individually fitted, at each pressure, with different line shape models including fine effects as Dicke narrowing or/and speed dependence effect. From these fits, we have obtained the collisional half-widths at each pressure and then determined accurately the N2-broadening coefficients of 12 lines. After that, we have studied the pressure dependence of the collisional broadening and narrowing coefficients following the considered line profile model. Finally, our results are compared with the previous studies realized in various absorption bands. Ó 2008 Elsevier Inc. All rights reserved.
1. Introduction Acetylene is a minor constituent of our atmosphere [1] as well as in the atmospheres of Saturn, Jupiter [2] and Titan [3]. The measurements of self and foreign-gas broadening coefficients provide important information for the analysis of atmospheric spectra and on intermolecular potentials via theoretical calculations. To obtain such line parameters as precise as possible, it is essential to fit the experimental profile with a theoretical line shape taking into account the different physical effects affecting the broadening of line. In this work, we have measured N2-broadening coefficients of 12 C2 H2 at room temperature for 12 lines belonging to the R-branch of the m4 þ m5 band in the spectral range 1275–1394 cm1 at a high-resolution using a diode-laser spectrometer. For each line under study, we have recorded spectra at 4–16 pressures of nitrogen ranging between 4.03 and 179.5 mbar. We retrieved the collisional line widths fitting the experimental profiles by the Voigt, Rautian, Galatry lineshape models and for the high pressures (>100 mbar) by a model taking into account simultaneously the Dicke narrowing and the speed dependence effect. The large range of pressures allowed an accurate collisional broadening coefficient determination. We also studied the dependence of collisional broadening as a function of pressure to determine the best experimental conditions and the most suited theoretical line shape model. The colli-
* Corresponding author. Fax: +32 81 72 45 85. E-mail address: [email protected] (M. Lepère). 1 Research Associate with F.R.S.-FNRS, Belgium 0022-2852/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2008.12.003
sional broadening coefficients derived from our measurements are compared with values available in the literature [4–8]. Podolske et al. [4] have reported a line strength study in the m4 þ m5 band and, they have measured collisional broadenings for 3 lines of C2H2 perturbed by N2 and H2 for m4 þ m5 band. Devi et al. [5] have measured the N2- and air-broadening coefficients for 29 lines in the same band. Later, Bouanich et al. [6] and Lambot et al. [7] have realized respectively theoretical and experimental studies, for several lines in the m5 band of C2H2 perturbed by N2 and O2. The more recent study, reported by Pine [8] in 1993, was devoted to the measurement of the line mixing and the self, N2-, Ar-broadenings and line mixing were measured in the m1 þ m5 band. In this work, we have also studied the pressure dependence of the collisional narrowing coefficients following each theoretical line shape model. These experimental results have been compared with the calculated values using the theory of diffusion. 2. Experimental details The spectra of C2H2–N2 mixtures were recorded with an improved Laser Analytics (LS3 model) tunable diode-laser spectrometer previously detailed in Ref. [9]. The spectra resulted from an average of 100 scans in order to increase the signal-to-noise ratio. The relative calibration was obtained by introducing in the laser beam a confocal étalon with a free spectral range of 0.007958 cm1. Nitrogen was supplied by Air Liquide company with a purity of 99.9%, while acetylene was provided by Air Liquide company with a purity of 99.6%. The gas mixtures were contained in a White-type cell with one meter-distance between mirrors and
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L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
with KBr windows. The pressures of C2H2 in the absorption cell were always chosen to be small (ranging from 0.0067 to 0.4463 mbar). Nevertheless, the C2H2 pressure was considered for all lines, and corrections were made to take into account the small contributions due to self-broadening were determined from the measurements of Lepère et al. [10]. The pressures of pure C2H2 and C2H2 + N2 mixture were measured using three MKS Baratron gauges with full scale readings of 1.2, 120 and 1200 mbar. All data were recorded at the room temperature (i.e., 24.5 ± 1.5 °C). To obtain a good homogeneity in the mixtures, we waited 15 min before each spectrum record. An example of the spectra obtained for the R(11) line of C2H2 at 1356.8555 cm1 [11] is shown in Fig. 1. For each line under study, we have recorded the following consecutive spectra: (1) laser emission profile through the empty cell, (2) the record of the line at very low gas pressure of pure C2H2 and very small absorption, allowing the determination of the instrumental function, (3–6) the N2-broadened spectra at four different nitrogen pressures, (7) the record of the étalon fringe pattern allowing relative calibration in wavenumber, (8) the pure C2H2 saturated line which represents the 0% transmission level. 3. Data reduction The experimental absorbance aðmÞ can be deduced for each perturber pressure using the Beer–Lambert’s law as
aðmÞ ¼ ln
It ðmÞ ; I0 ðmÞ
ð1Þ
where It ðmÞ and I0 ðmÞ are respectively the transmitted through the gas sample and incident intensities at wavenumber m (cm1). The line parameters were obtained by fitting a theoretical lineshape to the measured absorbance. First, we used the Voigt profile [12] which has three adjustable parameters. This profile is simply the convolution between a Gauss function (Doppler effect) and a Lorentz function (collisional effect), assuming that both effects are independent. It can be defined as [13]
aV ðA; x; yÞ ¼ A
y
p
Z
þ1
1
expðt 2 Þ y2
þ ðx tÞ
2
dt ¼ A Re½W ðx; yÞ;
ð2Þ
with
2
1
W ðx; yÞ ¼
i
p
Z
þ1
1
expðt 2 Þ dt; x þ iy t
and
A¼
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi m m0 pffiffiffiffiffiffiffiffi c S ln 2 pffiffiffiffi ; y ¼ ln 2 c ; x ¼ ln 2 :
cD
cD p
cD
ð4Þ
Here S = S0 p1, with S0 (in cm2 atm1) the line intensity and p1 (in atm) the absorber pressure; m0 (in cm1) is the position of the line center (the eventual pressure shifts are very weak at such pressure and are not considered in this study); cD (in cm1) is the theoretical Doppler half-width that we calculate; cc (in cm1) is the collisional half-width and is equal to c0 p2 þ cself p1 where c0 (in cm1 atm1) is the collisional broadening coefficient of C2H2 diluted in N2 ; cself (in cm1 atm1) is the self-broadening coefficient, p1 and p2 (in atm) are the partial pressures of the absorbing molecule and the perturber, respectively. In reality, Doppler and collisional effects are not independent and intermolecular collisions perturb Doppler effect. The mean translation motion of the active molecules is reduced and the free streaming motion of the molecules becomes diffuse. This is well known as the Dicke effect [14]. We also fit the experimental profiles the Rautian and Sobel’man [15] and Galatry [16] models taking into account the Dicke effect and provide an additional parameter bc which represents the collisional narrowing effect due to the molecular confinement. The Rautian and Sobel’man model is also called hard collision model because it assumes that the velocity of the active molecule after the collision is independent of its velocity before the collision. This model is best suited when the perturber mass is larger than the mass of the active molecule. This profile may be described as [15]:
aR ðA; x; y; zÞ ¼ A Re
Wðx; y þ zÞ pffiffiffiffi 1 pzWðx; y þ zÞ
ð5Þ
where the parameters A, x and y are the same as defined in Eq. (4) and
z¼
pffiffiffiffiffiffiffiffi bc ln 2
ð6Þ
cD
with bc (in cm1) representing the average effect of collisions on Doppler broadening. Here, bc ¼ b0 p2 where b0 (in cm1 atm1) is the collisional narrowing coefficient. The Galatry model is also called soft collision model because it assumes that the duration of each collision is short and does not modify significantly the velocity of the active molecule. This second model is best suited when the active molecule mass is larger than the perturber one. It can be defined by [16]:
A
Z
aG ðA; x; y; zÞ ¼ pffiffiffiffi Re p
7
ð3Þ
þ1
1
zt 1 þ ezt dt exp ixt yt 2 2z ð7Þ
6 0.007958 cm
-1
5 4 3 8
N2-pressures (mbar) : 3 : 30.57 4 : 40.82 5 : 54.90 6 : 65.50
Fig. 1. Example of spectra recorded for the R(11) line at 1356.8555 cm1 in the m4 þ m5 band of C2H2 perturbed by N2. (1) The diode-laser emission profile, (2) the spectrum of the line at very low pressure of pure C2H2 and very small absorption, (3–6) the broadened line recorded at different pressures of N2, (7) the confocal étalon fringe pattern used for the relation calibration in wavenumber, (8) the saturated line giving the 0% transmission level.
with the same definition of the parameters. The collisional narrowing coefficient b0 may be compared to the dynamical friction parameter b0diff (in cm1 atm1) of the Brownian motion, expressed as [17]:
b0diff ¼
kB T ; 2pcmD
ð8Þ
where kB is the Boltzmann constant, T (in K) is the temperature, c (in m/s) is the light velocity, m (in a.m.u.) is the absorber molecular mass and D (in cm2 s1) is the mass diffusion coefficient for the C2H2 + N2 system, calculated following [17]. At low pressures (below 100 mbar), the collisional widths were several times smaller than the Doppler widths and we have considered the Voigt profile as well as the Rautian and the Galatry models.
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L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
For pressures above 100 mbar, we have used a model taking account simultaneously the Dicke narrowing and speed dependence effect. In this model, the collisional profile may no longer be represented by a simple Lorentz function, but should be described by a weighted sum of Lorentz profiles (WSL) for each velocity of the absorber [18]. In this work, we used a speed-dependent hard collision model developed by Lance et al. [19] and adapted by Lerot et al. [20]. In order to take into account the instrumental distortions, the effective Doppler half-width was fixed in the fitting procedure to the cD value given by [21]
cD ¼ ðc2DT þ c2App Þ1=2 ;
ð9Þ
where cDT and cApp are the theoretical Doppler and contribution due to instrument distortion [22]. The theoretical Doppler was calcuqffiffiffi lated as cDT ¼ 3:581 107 m0 MT with m0 (in cm1) the wavenumber of the measured transition, T (in K) the temperature, M (in a.m.u) the molecular mass. The apparatus half-width was determined by fitting to the absorbance line, recorded at very small pressure and absorption, a function expressed as
aðm m0 Þ ¼ ln
Z
þ1
fApp ðmi Þ expðkDop ðm m0 mi ÞLÞdmi ;
ð10Þ
1
with L the absorption length, fApp ðmi Þ the Gaussian instrumental profile with an adjustable half-width cApp and kDop ðm m0 Þ the theoretical Gaussian Doppler profile. Fig. 2 illustrates an example of Voigt fit obtained for the R(9) transition in the m4 þ m5 band of C2H2 (p = 0.0340 mbar) diluted in
1.6 1.4
P(N2) = 122.20 mbar
Exp Voigt
P(C2H2) = 0.0340 mbar
1.2
α(ν)
1.0 0.8 0.6 0.4 0.2 0.0 0.1
Voigt
0.0 -0.1 0.1
Rautian
(O-C)*10
0.0 -0.1 0.1
Galatry
0.0 -0.1 0.1
SDHC
0.0 -0.1 1351.99
1352.00
1352.01
1352.02
-1
ν (cm ) Fig. 2. The measured absorbance for the R(9) line in the m4 þ m5 band of C2H2 (p = 0.0340 mbar) perturbed by 122.20 mbar of N2. This experimental line shape is fitted using a Voigt profile (). The residuals, difference between observed and calculated values multiplied by 10, are represented at the bottom of the figure for the fitted Voigt, Rautian, Galatry and SDHC models.
122.20 mbar of nitrogen at room temperature. The Voigt, Rautian, Galatry and the Speed Dependence Hard Collision (SDHC) models are used to fit the experimental line shape. The residuals (observed minus calculated, 10(o–c)) are shown at the bottom of Fig. 2. The Rautian and the Galatry profiles fit the observed line shape better than the Voigt line shape because they also include the effect due to the Dicke narrowing. In the case of C2H2 broadened with N2, the mass ratio (ratio of mass of target gas that of the broadening gas) is close to 1 and hence the differences between Rautian and Galatry line shapes are not significant. The SDHC model also fit the observed line shape quite well. It appears that at a total pressure of 122 mbar, the effect due to speed dependence is small and hence may be neglected. This is clear from values listed in Table 1 and will be discussed in the following section.
4. Results For a given line, the collisional half-width cc was determined for at least four perturber pressures. Fig. 3 shows a typical plot of cc minus the self-broadening contribution ðcself pC 2 H2 Þ versus the N2 pressure for the R(5) line. The self-broadening coefficient were taken from Lepère et al. [10]. The collisional broadening coefficient c0 (in cm1 atm1) was determined as the slope of the best straight line obtained from the linear regression. The N2-broadening coefficients c0 are given in Table 1 along with their experimental errors. The experimental uncertainties are mainly due to the difficulties in locating accurate position of the base line, the perturbation due to the neighboring lines, the nonlinearity of sweeping in frequency of the emission of the diode and the theoretical profile used. The given errors were estimated to be the statistical error (twice the standard deviation given by the linear regression) plus 2% or 3% of the c0 value to take into account the whole experimental uncertainties. In Table 1, we present results obtained at low pressure (<100 mbar) with the Voigt, the Rautian and the Galatry models and the values obtained at higher pressure (>100 mbar) for the same models and the SDHC model. In the Fig. 4, we compare our results retrieved using different theoretical line shape models as well as for different pressure regimes. The values obtained with Rautian line shape are very close to those deduced from Galatry fits, that we do not illustrate in the Fig. 4. At low pressure (below 100 mbar), the values deduced from Voigt fits are systematically smaller than those obtained with Rautian (or Galatry) fits. At pressure above 100 mbar, the coefficients of collisional broadening are often smaller than those determined at lower pressure. When the pressure increases, the collisional broadening increases and the lorentzian profile becomes predominant. At high pressure (>100 mbar), the wings of the neighboring lines perturb the line understudy. It is the reason why the error bars corresponding to high pressure measurements are equal to twice the standard deviation plus 3% of the c0 value, instead of 2% at low pressure. The measurements made at high pressure are thus less precise. For six lines, we have made measurements at 16 different pressures up to 170 mbar. The coefficient of collisional broadening c0 (in cm1 atm1) are independent of the pressure. In the Fig. 5, we plot the collisional broadening coefficients versus the perturber pressure for the R(4) line of C2H2 diluted in N2 at room temperature. Results are presented for the considered lineshape models. At very low pressure (<30 mbar), the collisional broadening depends largely on the pressure for each model. It is due to the fact that, for such pressure, the collisional width is smaller than the Doppler width and thus the measurement of collisional width is not so precise. For pressures comprised between 30 and 100 mbar, the coefficients of collisional broadening are quite constant. In addition, we see in the Fig. 5 that the values deduced from Voigt
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L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
Table 1 N2-broadening coefficients c0 in the m4 þ m5 band of C2 H2 at room temperature. The errors given here are equal to twice the standard deviation of the linear regression plus 2% or 3% of the coefficient c0 itself. The wavenumber values are taken from Kabbadj et al. [11].
c0 ð103 cm1 atm1 at 298 K)
m0 ðcm1 Þ
Line
p < 100 mbar
p > 100 mbar
Voigt R(2) R(4) R(5) R(6) R(9) R(11) R(14) R(16) R(19) R(21) R(23) R(26)
1332.8027 1339.9523 1342.3495 1344.7530 1351.9994 1356.8555 1364.1668 1369.0519 1376.3820 1381.2619 1386.1296 1393.3956
90:7 90:7 89:9 83:9 79:6 75:3 75:3 68:6 66:9 65:3 55:9
Rautian
1:9 2:5 3:3 2:5 1:7 2:0 2:0 2:0 2:0 3:4 1:3
92:8 92:2 92:0 86:3 81:8 77:0 77:6 71:0 69:9 68:4 58:2
Galatry
2:7 2:9 3:8 3:2 2:3 2:0 2:5 2:0 2:7 3:9 1:8
92:9 92:3 92:2 86:4 81:9 77:1 77:8 71:1 69:4 68:6 58:3
2:7 3:0 3:9 3:4 2:4 2:1 2:6 2:2 2:4 4:0 1:9
Voigt
Rautian
Galatry
SDHC
100:4 3:2 92:1 2:9
101:9 3:4 93:8 3:0
101:9 3:4 93:8 3:0
98:7 3:8 91:5 3:6
82:1 2:7
82:5 2:8
82:5 2:8
82:7 3:2
75:5 2:5
76:4 2:8
76:4 2:8
76:4 2:5
67:3 2:4 64:7 2:5
68:5 2:9 66:8 3:2
68:5 2:9 66:8 3:2
68:9 2:9 64:3 2:9
7
6
100
-1
γ0 (10 cm atm )
-1
γc- γself.p C H (10 cm )
5
90
3
-3
2 2
-1
-3
4
2
80
Voigt Rautian Galatry SDHC
Voigt Rautian
1
0
70 0
10
20
30
40
50
60
70
0
20
40
60
80
100
120
140
160
180
N2-pressure (mbar)
N2-pressure (mbar) Fig. 3. Example of pressure dependence of the N2-collisional half-widths in the m4 þ m5 band of C2H2 at room temperature for the R(5) line. The slopes of the best-fit lines are the N2-broadening coefficients c0 (in 103 cm1 mbar1).
105
Fig. 5. Pressure dependence for the N2-broadening coefficient c0 for the R(4) line in the m4 þ m5 band of C2H2 at room temperature for the Voigt profile ðOÞ, the Rautian model ðÞ, the Galatry model (+) and the SDHC model () which takes into account simultaneously the Dicke narrowing and the speed dependence effect [20]. The line represents the average value of collisional broadening coefficient c0 obtained with the best adapted model. Values measured with the pressures below 30 mbar are not considered in the average procedure.
100 95
-1
γ0 (10 cm atm )
90
-1
80
-3
85
75 70 65 60 55 0
5
10
15
20
25
|m| Fig. 4. Comparison between our N2-broadening coefficients c0 in the m4 þ m5 band of C2H2 at room temperature retrieved using different theoretical line shape models as well as for different pressure regimes : r Voigt (p < 100 mbar), Rautian (p < 100 mbar), M Voigt (p < 100 mbar), Rautian p > 100 mbar and SDHC (p > 100 mbar).
fits are systematically smaller than coefficients obtained with the Rautian and Galatry models. These last models, which take into ac-
count the Dicke narrowing and represent limit cases about the mass ratio, give values very close. This is due to the ratio of the mass of the active molecule to the mass of the perturbing molecule which is nearly equal to one. In this case, the two models are similar. For pressures above 100 mbar, the coefficients continue to be constant and the SDHC model provides values very close to other determinations. On this figure it seems that no speed dependence effect appears, even at high pressure when the collision width is several times Doppler width. However, at high pressure, collisional broadening is predominant and the wings of the neighboring lines perturb the line understudy. It is then difficult to determine with high accuracy the baseline position and the measurements are less precise. Fig. 6 shows the plot of collisional narrowing coefficients versus the perturber pressure for the R(21) line in the m4 þ m5 band of C2H2 perturbed by N2. These coefficients represent a fine physical effect (Dicke narrowing) sensitive to the experimental conditions as the baseline position. A precise measurement of the collisional narrowing coefficient is thus difficult. It is the reason why this parameter is less constant than the coefficient of collisional broadening, as seen in the Fig. 6. In this figure, it seems that collisional narrowing coefficients deduced from Rautian fits are better than those ob-
14
L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
1800 1600
50
jmj
-3
-1
-1
β0 (10 cm atm )
Table 2 Comparison between our N2-broadening coefficients c0 in the m4 þ m5 band of C2 H2 at room temperature and previous determinations in various bands. Devi et al. [5] and Podolske et al. [4] have also measured c0 in m4 þ m5 band. Lambot et al. [7] have studied the m5 band, while the work of Pine [8] was devoted to the m1 þ m5 band. The error bars given for our measurements are equal to twice the standard deviation of the linear regression plus 2% of the coefficient c0 itself.
Rautian Galatry SDHC
40
30
20 0
20
40
60
80
100
120
140
160
N2-pressure (mbar) Fig. 6. Pressure dependence of the N2-narrowing coefficient for the R(21) line in the m4 þ m5 band of C2H2 at room temperature for the Rautian model ðÞ, the Galatry model ðÞ and the SDHC model ðÞ which takes into account simultaneously the Dicke narrowing and the speed dependence effect [20]. The line represents the value calculated by the diffusion theory following Eq. (8).
tained with Galatry fits. For pressures below 100 mbar, the Rautian model fits the data better than other line shapes. When the pressure exceeds 100 mbar, the values deduced from the Rautian and Galatry models become very large and thus have not physical signification. For such pressures, if we consider the SDHC model, the coefficients of collisional narrowing are very close to the values obtained with the Rautian model at lower pressure. In addition these experimental values are in good agreement with the calculated b0diff , represented in the Fig. 6 by the line. Finally, we compare in the Fig. 7, our coefficients of collisional broadening with previous results obtained for various absorption bands. Our values were measured in the m4 þ m5 band by diode-laser spectroscopy and considering the Rautian fits for pressures below 100 mbar and by SDHC fits for R(2) line. Devi et al. [5] and Podolske et al. [4] have measured the N2-broadening coefficients of C2H2 by diode-laser spectroscopy and considering Voigt fits.
105 This work
100
Devi Lambot
95
Pine Calc Bouanich
85
γ
0
(10
-3
cm
-1
-1 atm )
Podolske
90
80 75 70 65 60 55 4
8
12
16
20
24
28
|m| Fig. 7. Comparison between our N2-broadening coefficients c0 in the m4 þ m5 band of C2 H2 at room temperature and previous determinations in various absorption bands. Devi et al. [5] and Podolske et al. [4] have also measured c0 in m4 þ m5 band. Lambot et al. [7] and Bouanich et al. [6] have studied the m5 band, while the work of Pine [8] was devoted to the m1 þ m5 band. The error bars given for our measurements are equal to twice the standard deviation of the linear regression plus 2% of the coefficient c0 itself.
3 5 6 7 10 12 15 17 20 22 24 27
c0 (103 cm1 atm1 at 298 K) This work
Ref. [5]
98.7 ± 2.8 92.8 ± 2.7 92.2 ± 2.9 92.0 ± 3.8 86.3 ± 3.2 81.8 ± 2.3 77.0 ± 2.0 77.6 ± 2.5 71.0 ± 2.0 69.9 ± 2.7 68.4 ± 3.9 58.2 ± 1.8
101.7 90.9 87.7 85.5
Ref. [4]
84.2
79.2 71.1 71.7
Ref. [7]
Ref. [8]
102.0
101.1 93.4 91.7 90.1
91.6 91.7 83.6
76.8 71.7 68.7 58.5
Lambot et al. [7] employed the Rautian line shape in their study of the m5 band using a diode-laser spectrometer. Because the m5 band is very intense short absorption paths were required to make the measurements. Bouanich et al. [6] have calculated the N2broadening coefficients in the m5 band using a semi-classical model. Pine [8] has measured collisional broadening in the m1 þ m5 band with a difference-frequency laser spectrometer. He has used a Rautian profile to fit the experimental lineshape. Table 2 compares our values and the previous results obtained for various absorption bands. The agreement between our measurements and previous determination is relatively good, as seen in the Fig. 7 and Table 2. 5. Conclusion In this paper, the N2-broadening coefficients of 12 lines of C2H2 have been measured in the m4 þ m5 band at room temperature using a tunable diode-laser spectrometer. The collisional widths have been individually deduced from Voigt, Rautian, Galatry and Speed Dependence Hard Collision (SDHC) model fits of each experimental lineshape. The residuals obtained with Voigt fits have always a typical signature while the other models are in excellent agreement with the experimental lineshapes. Each line have been recorded at 4 to 16 different pressures of nitrogen. Such way, we have determined precisely the collisional broadening coefficients. When 16 pressures, ranging from 4.03 to 179.5 mbar, have been considered, a study of the pressure dependence of collisional broadening and narrowing coefficients have been realized. Such way, we have shown that Voigt fits underestimate systematically the collisional broadenings. For pressures below 30 mbar, it is difficult to obtain precise measurements of collisional widths which are small. For pressures between 30 and 100 mbar, the Rautian and Galatry models give very similar results. For pressures above 100 mbar, the speed dependence hard collision model gives collisional broadenings very close to other fits, especially those of Voigt. Nevertheless, we prefer models including at least Dicke narrowing which is a fine physical effect. It would be interesting to check, for other gas mixtures, if the SDHC line shape model gives, at high pressure, values systematically closer to those determined by Voigt profile than those deduced from either Rautian or Galatry line shape model. The coefficients of collisional narrowing deduced at high pressure from the Rautian and Galatry fits are very large and have no physical significance. Considering the speed dependence effect, the coefficients of collisional narrowing deduced at high pressure are in good agreement with the determinations at lower pressure
L. Fissiaux et al. / Journal of Molecular Spectroscopy 254 (2009) 10–15
and with the calculated value using the diffusion theory. At high pressure neighboring lines can perturb the line understudy and reduce the precision of the measurements. So, for C2 H2–N2 mixture, the most accurate measurements of collisional broadening parameters can be realized for pressures ranging from 30 to 100 mbar and considering the Rautian or Galatry model. Acknowledgment M. Lepère is acknowledging support from F.R.S.-FNRS, Belgium. This work is accomplished in the framework of the European Associated Laboratory HiRes. References [1] J. Rudolph, D.H. Ehhalt, A. Khedim, J. Atmos. Chem. 2 (1984) 117. [2] P.V. Sada, G.L. Bjoraker, D.E. Jennings, G.H. McCabe, P.N. Romani, Icarus 136 (1998) 192. [3] A. Coustenis, Th. Encrenaz, B. Bezard, G. Graner, M. Dangnhu, E. Arie, Icarus 102 (1993) 240. [4] J.R. Podolske, M. Loewenstein, P. Varanasi, J. Mol. Spectrosc. 107 (1984) 241. [5] V.M. Devi, D. Ch. Benner, C.P. Rinsland, M.A.H. Smith, B.D. Sidney, J. Mol. Spectrosc. 114 (1985) 49.
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