Absorption properties of infrared active gases at high pressures—I. CO2

J. Quant. Spectrosc. Radiat. Transfer Vol. 36, No. 3, pp. 265-270, 1986

0022-4073/86 $3.00 + 0.00 Pergamon Journals Ltd

Printed in Great Britain

ABSORPTION PROPERTIES OF INFRARED ACTIVE GASES AT HIGH PRESSURES--I. CO2 M. FUKABORI,T. NAKAZAWA and M. TANAKA Upper Atmosphere Research Laboratory, Tohoku University, Sendai 980, Japan (Received 4 December 1985)

Abstract--Self- and nitrogen-broadened absorptions of the 2.7 and 2.0/~m COs bands were measured at high pressures. The band intensities were found to be 76.0 + 0.6 and 1.46 + 0.01 cm-~/(atm-cm)srvfor the respective bands. The measured equivalent widths were found to be smaller under large absorber amounts than those calculated from the Lorentzian lines with half-widths linearly dependent on sample density, reflecting excess absorption in the band wings of calculated spectra. This discrepancy is examined in terms of non-Lorentzian behavior of the line profile and a non-linear density dependence of the half-width.

INTRODUCTION Experimental studies of the absorption of infrared active gases at high pressures have been made extensively. However, most studies have aimed at the determination of the band intensity with the Wilson-Wells-Penner-Weber (WWPW) technique.~'2 Recently, Bouanich's group has measured the absorption of CO and N20 over a wide pressure range and examined several theoretical and empirical models to represent the band profiles. 3-6 In this study, we measured the self- and N2-broadened absorptions of the 2.7 and 2.0/~m CO2 bands at pressures up to about 60 and 100 atm, respectively. The band intensities were determined from the N2-broadened spectra by the W W P W technique. The absorption properties for selfbroadening were examined by comparing measured equivalent widths and spectra with those obtained theoretically from line-by-line integrations, using Lorentzian and sub-Lorentzian line profiles and a non-linear dependence of the half-width on sample density, respectively.

EXPERIMENTAL

STUDIES

Measurements were made for pure CO2 and CO2-N2 mixtures using two high-pressure absorption cells with respective pathlengths of 5.02 and 1.004 cm as shown in Fig. 1. The cells were made of stainless steel, and synthetic sapphire crystals were used as window plates. The inner wall of the cell was cleaned and dried out sufficiently to avoid selective adsorption of CO2 in the mixtures. Sample gases were stored in high-pressure cylinders and were introduced into the cell through needle valves up to assigned pressures. The purity of CO2 was 99.995% and concentrations of the mixtures were 66.8, 39.8, 17.3, 9.18, 4.82, 2.01, and 1.11%. The uncertainties in concentration were estimated to be within 1% of calibrated values. The temperature of the sample gases was maintained at 303 +_ 1 K and was measured with a thermistor sensor. Pressure readings were performed by the use of two kinds of semi-conductor pressure gauges, with an accuracy of 0.1 arm over a pressure range of 1-100 arm. Absorption spectra were taken with a Hitachi-Perkin-Elmer model 125 infrared grating spectrometer. The spectral slit widths were set equal to 4 and 8 cm-1 for the 2.7 and 2.0 # m bands, respectively. The signal-to-noise ratio was better than 200:1 at 100% transmission. ANALYSIS The densities of sample gases were calculated from the PVT date given by Michels and Michels 7 for pure CO2 and from the virial equation of state, e v = l~r[1 + s ( r ) ~ ' + c ( r ) e 2 ] , 265

(1)

266

M. FUKABOR! et al.

Pressure gauge

ure gauge

Buffer v o l u m e ~

'

Gas inlet

End plate window

/ O-rinc

Cell body

Fig. l. Cross-sectional representation of the high-pressure absorption cell. for mixtures. Here, the second and third virial coefficients B(T) and C(T) were obtained from the data given by Hirschfelder et al. ~ The band intensities were estimated by using the W W P W technique: S,,[cm I/(atm-cm)s.~] = B/u = B/pL, B =~

ln(l/Tv)dv,

(2) (3)

dband where 7",. is the apparent transmittance, L the pathlength in cm, p the density of CO,, in amagat, and u the absorber amount in (atm-cm)sv P The equivalent width of an absorption band is independent of the slit function of the spectrometer, provided the band limits are chosen to include the entire band. Measured values of the equivalent width were obtained directly by integrating the spectral curves. The theoretical value of the equivalent width is

w=f~..d[l-exp(-~k,,,u)Jdv,

(4)

where K,., is the absorption coefficient of the ith line at the frequency v. The absorption coefficient for the Lorentzian line is k,

$7 n[(v - vf,)2+ .;2],

5)

(6)

(71

Absorption properties of infrared active gases at high pressures--I. CO,,

267

where v0 is the line center, 7 the half-width, S the line intensity, a r the sample density at T K, and the other terms have their usual meanings. In the calculation of equivalent widths and spectra, line parameters of CO2, except for the line intensities, were taken from the AFGL atmospheric absorption-line-parameter compilation. 9 The line intensities were calculated from the band intensities obtained in our measurements. The half-widths adopted in this compilation are N2-broadened values. The self-broadened half-widths were obtained by multiplying the compiled values by the self-broadening coefficient of 1.3 t° The value of n in equation (7) was assumed to be 0.5 according to classical pressure-broadening theory. RESULTS

AND

DISCUSSION

The relations of the quantity B / L to the density p of CO2 are shown in Figs 2(a) and (b) for the 2.7 and 2.0#m bands, respectively. The least-squares fit to these data yielded the band intensities 76.0 + 0.6 and 1.46 + 0.01 cm 1/(atm-cm)sTp for the respective bands. The band intensities obtained in this study are compared with those of other measurements 9'jM8 in Table 1. Our value is in excellent agreement especially with those of Downing et al., ~7 Tanaka and Yamanouchi, ~8and the AFGL compilation 9 for the 2.7/~m band, and is slightly lower than others for the 2.0 #m band. The equivalent widths of the self-broadened absorption calculated from the Lorentzian lines with half-widths linearly dependent on the sample density are shown in Figs 3 and 4 for the 2.7 and 2.0#m bands, respectively, together with measured values. It is evident that the calculated

120

I

I

D

400

I

i

I

I

80 300

I

E

E" i E u

U v

200

m

40 (b)

/I]

I00

I

L

~"

I

I

I

1

I

[

I

20 40 60 2 3 p ( amagat ) p (amagat) Fig. 2. Dependence of the quantity B/L on the density of CO 2 for la) the 2.7 and (b) the 2 . 0 / ~ m bands.

I

1

500-

~ 5.02 cm _~ . o

-500

-

CO 2

~ ~ ° ~

100-~"

-100

~

-

1.004 cm

v

10

I

10

I 1

]

I

10 ~

I 10

I 100

' i

I

80

5.02 c m

I 1.004¢m 100

U (atm-cm) s r p Fig. 3. Comparison of calculated and measured equivalent widths for the 2 . 7 / a m C O 2 b a n d ; ©, measured values: - - - , Lorentzian profile; . . . . , Benedict profile with a = 0.08, b = 0.8 and vm = 5; - - . - - , Benedict profile with a = 0.11, b = 0.7 a n d v~ = 5.

M . FUKABORI et al.

268

500r I

//¸

I [

~oob E,O'2 cm

lo~

,/

,-

/

,

,/

/

/

/

m,

,

/ I

~--±---

~ ...........~.... J.........J

1

lO

,

b 1

lO0

__

i

....m _ _ _

I

10 U ( o t t o - crn) 5Tp

5 0 2 cm

1~01 004 cm

Fig. 4. As in Fig. 3, but for the 2.0 l~m CO2 band; - - . - - , Benedict profile with a = 0.05, b = 0.8 and Vm ~ 5.

equivalent widths exceed measured values in the strong region of the curve of growth. This discrepancy arises from excess absorption in the band wings of the calculated spectra, as may be seen in Figs 5 and 6. To examine the cause o f such an excess absorption, we first calculated the spectra using the Lorentzian lines with half-widths given by

7"

=

CHw T.

(8)

Here, CHw is a parameter determined to provide agreement between calculated and measured equivalent widths. The differences between calculated and measured spectra were considerably improved, especially for the 2.0/~m band (Figs 5 and 6). However, the half-widths obtained in this procedure showed extremely low values of 0.5 --~ 1 c m - ' , even at pressures as high as 60 atm, and their density dependences were different for different bands and cells. These facts suggest the Table I. Band intensities of the 2.7 and 2.0,um C O 2 bands

Su

( cm-i/(atm-Cm)

sT p )

Investigators 2.7

pm

4100-3400 cm

-i

2.0

~m

5300-4700 cm

-i

Eggers (1951)

& Crawford

66

Weber, (1952)

Holm

71+14

1.70+0.34

79.7+4.8

1.61+0.11

& Penner

Burch, Gryvnak & Patty (1964,1968) Schurin (1968)

& Ellis

1.56+0.08

Downing (1973)

& Hunt

1.69

Downing, Brown H u n t (1975) Tanaka (1977) AFGL

&

& Yamanouchi

(Rothman;1981)

Present

work

76.1

75.+10.

1.75+0.25

75.1

1.61

76

1.46+0.01

0+0.6

Absorption properties of infrared active gases at high pressures--I. CO2 ].0

l.O

f

5.02 cm

0.5 / " " / •

II

'

q

1

Qtr'q

0.5

,

, :m

,1 ,'!1

i

z

U z obo m

,

269

~

1 . 0

~

© to m

1.0

&

1.004 cm 0.5

0.5

it.0 atrr 0.0

~[~4~59.8a t m

4000

3800 WAVENUMBER

(¢

! 59.8 \\ tatm

36'00 m-~)

3400

Fig. 5. Comparison of calculated and measured spectra for the 2.7 #m CO2 band; - - , measured spectra; . . . . , calculated spectra based on the Lorentzian profile and a linear dependence of the half-width on density; --.--, calculated spectra based on the Lorentzian profile and a non-linear dependence of half-width on density.

0.0

5300

5100 4900 WAVENUMBER ( c m -I)

4700

Fig. 6. As in Fig. 5, but for the 2.0pro CO2 band.

inadequacy o f the assumption used for the explanation o f excess absorption in the band wings o f calculated spectra. Winters et al. 19 have reported, in their self-broadening experiments for the 4.3 # m CO2 band, that the line profile o f CO2 is sub-Lorentzian, i.e. kv=kv, L f o r Iv - v 0 l ~ •m,

kv=k~,Lexp{-a(IV-Vol-V,,) b} for Iv-vol>>-vm

(9)

where Kv,L is the absorption coefficient o f the Lorentzian line, and a = 0.08, b = 0.8, and v,~ = 5. The equivalent widths obtained from equation (9) are also shown in Figs 3 and 4. This line profile yielded g o o d agreement between calculated and measured equivalent widths for the 2.7 # m band, but slight differences still remain at high pressures. These differences were reduced by altering the constants to a = 0.11, b = 0.7 and vm = 5. This alteration o f constants also reduced the differences between calculated and measured spectra, as is shown in Fig. 7. However, the results were somewhat different for the 2.0 # m band; the equivalent widths measured in the 5-cm cell agreed well with those calculated from equation (9) for a = 0.05, b = 0.8 and v,~ = 5, but the overall agreement between measured and calculated values of the equivalent widths and the spectrum could not be attained for both cells, even by altering the constants in equation (9), as may be seen in Figs 4 and 8. Such a p h e n o m e n o n arises from the fact that the line profile in equation (9) is not normalized. We also examined the normalized empirical line profile 2°-22

c& kv= z[( v_%)2 + 72] f o r [ v - v [ ~ < v , . , CS7

(

v,. "]~

kv = ~(v~ + ~2) \Iv - vol)

for ]v -

Vo[ >1 vm,

(10)

where C is a normalization constant given by

~/2 c = [tan_ ~ (v,~/7)] + [vm/(v~ + 72)1 [v/(~ - 1)]'

(11)

M. FUKAaORIet al.

270

1.0

'.oF t

5.02 cm

6~3 t 3tin q

0.5 z z

].o

~.l.O

S

0 uq c£ <

1.004 crn 598 a~m

0.5

05

0,0

4 000

3800 3600 WAVENUMBER(cm -1)

0.0 5300

3400

Fig. 7. Comparison of calculated and measured spectra for the 2.7#m CO 2 band. - - , measured spectra; - - - , Benedict profile with a = 0.11, b = 0.7 and v,, = 5; - - . - - , sub-Lorentzian profile given by equation (10) with vm= 8 and ~/ = 3.

5100 4900 WAVENUMBER (cm -t)

~73)

Fig. 8. Comparison of calculated and measured spectra for the 2.0/~m CO 2 band. - - , measured spectra: calculated spectra; - - - , Benedict profile with a = 0.05, b = 0.8 and v,, = 5; - - . - - , sub-Lorentzian profile given by equation (I0) with vm=6and q = 3 .

a n d Vm a n d q a r e e m p i r i c a l l y d e t e r m i n e d p a r a m e t e r s . T h e p a r a m e t e r s vm a n d q were c h o s e n to p r o v i d e the best o v e r a l l a g r e e m e n t b e t w e e n m e a s u r e d a n d c a l c u l a t e d e q u i v a l e n t w i d t h for b o t h cells. T h e v a l u e s t h u s o b t a i n e d are 3 a n d 8 f o r q a n d v,,, r e s p e c t i v e l y . T h e s p e c t r a c a l c u l a t e d f r o m e q u a t i o n (10) w i t h these v a l u e s are s h o w n in Fig. 7 f o r the 2.7 # m b a n d . T h e c a l c u l a t e d spectra w e r e also close to t h e m e a s u r e d s p e c t r a , b u t the differences b e t w e e n the t w o s p e c t r a r e m a i n e d large as c o m p a r e d w i t h t h o s e for the line profile g i v e n by e q u a t i o n (9). O n the o t h e r h a n d , a u n i q u e set o f the p a r a m e t e r s was n o t o b t a i n e d f o r t h e 2.0 # m b a n d , b e c a u s e the a b s o r p t i o n s m e a s u r e d in the l - c m cell are in the l i n e a r region. N e v e r t h e l e s s , we d e r i v e d the v a l u e v,, = 6 f r o m the results o f the 5-cm cell, a s s u m i n g t h a t the v a l u e o f q is i d e n t i c a l f o r b o t h b a n d s . T h e line profile g i v e n by e q u a t i o n (10) w i t h these v a l u e s s h o w e d fairly g o o d a g r e e m e n t b e t w e e n m e a s u r e d a n d c a l c u l a t e d spectra, as m a y be seen in Fig. 8. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

E. B. Wilson Jr and A. J. Wells, J. chem. Phys. 14, 578 (1946). S. S. Penner and D. Weber, J. chem. Phys. 19, 807 (1951). J.-P. Bouanich, Nguyen-Van-Thanh and H. Strapelias, JQSRT 26, 53 (1981). J.-P. Bouanich, JQSRT 27, 131 (1982). J.-P. Bouanich, Nguyen-Van-Thanh and I. Rossi, JQSRT 30, 9 (1983). Nguyen-Van-Thanh, J.-P. Bouanich and I. Rossi, Molec. Phys. 40, 869 (1980). A. Michels and Mrs C. Michels, Proe. R. Soc. Lond. Ser. AI60, 348 (1937). J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids. Wiley, New York (1954). L. S. Rothman, Appl. Opt. 20, 791 (1981). D. E. Burch, E. B. Singleton and D. Williams, Appl. Opt. l, 359 (1962). D. F. Eggers Jr and B. L. Crawford Jr J. chem. Phys. 20, (1951). D. Weber, R. J. Holm and S. S. Penner, J. chem. Phys. 20, 1820 (1952). D. E. Burch, D. A. Gryvnak and R. R. Patty, Absorption by CO 2 between 4500 and 5400cm ~. Aeronutronic Report U-2955, Contract NOnr 3560 (00). Philco-Ford Corporation, Newport Beach, Calif. (1964). D. E. Burch, D. A. Gryvnak and R. R. Patty, Absorption by CO 2 between 3100 and 4100cm ~. Aeronutronic Rcport U-4132, Contract NOnr 3560 (00). Philco-Ford Corporation, Newport Beach, Calif. (1968). B. Schurin and R. E. Ellis, Appl. Opt. 7, 467 (1968). H. D. Downing and R. H. Hunt, JQSRT 13, 311 (1973). H. D. Downing, L. R. Brown and R. H. Hunt, JQSRT 15, 205 (1975). M. Tanaka and T. Yamanouchi, JQSRT 17, 421 (1977). B. H. Winters, S. Silverman and W. S. Benedict, JQSRT 4, 527 (1964). M. Hirono, J. Phys. Soc. Japan 42, 954 (1977). W. R. Watkins, R. L. Spellicy, K. O. White, B. Z. Sojka and L. R. Bower, Appl. Opt. 18, 1582 (1979). M. Tanaka, T. Nakazawa and M. Fukabori, JQSRT 28, 463 (1982).