Abstract

The shapes of the extreme wings of self-broadened CO2 lines have been investigated in three spectral regions near 7000, 3800, and 2400 cm−1. Absorption measurements have been made on the high-wavenumber sides of band heads where much of the absorption by samples at a few atm is due to the extreme wings of strong lines whose centers occur below the band heads. New information has been obtained about the shapes of self-broadened CO2 lines as well as CO2 lines broadened by N2, O2, Ar, He, and H2. Beyond a few cm−1 from the line centers, all of the lines absorb less than Lorentz-shaped lines having the same half-widths. The deviation from the Lorentz shape decreases with increasing wavenumber, from one of the three spectral regions to the next. The absorption by the wings of H2- and He-broadened lines is particularly low, and the absorption decreases with increasing temperature at a rate faster than predicted by existing theories.

© 1969 Optical Society of America

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References

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  1. B. H. Winters, S. Silverman, and W. S. Benedict, J. Quant. Spectry Radiative Transfer 4, 527 (1964).
    [Crossref]
  2. D. E. Burch, D. A. Gryvnak, and R. R. Patty, J. Opt. Soc. Am. 57, 885 (1967).
    [Crossref]
  3. G. Herzberg, Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic MoleculesD. Van Nostrand Co., Inc., Princeton, N. J., 1960).
  4. L. D. Gray and J. E. Selvidge, J. Quant. Spectry Radiative Transfer 5, 291 (1965).
    [Crossref]
  5. C. P. Courtoy, Ann. Soc. Sci. Bruxelles, Serie 1, 5 (1959); also C. P. Courtoy, Can. J. Phys. 35, 608 (1957).
    [Crossref]
  6. V. R. Stull, P. J. Wyatt, and G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
    [Crossref]
  7. D. E. Burch, D. A. Gryvnak, and R. R. Patty, J. Opt. Soc. Am. 58, 335 (1968).
    [Crossref]
  8. R. P. Madden, J. Chem. Phys. 35, 2083 (1961).
    [Crossref]
  9. D. E. Burch, E. B. Singleton, and D. Williams, Appl. Opt. 1, 359 (1962).
    [Crossref]
  10. R. R. Patty, E. R. Manring, and J. A. Gardner, Appl. Opt. 7, 2241 (1968).
    [Crossref] [PubMed]
  11. T. K. McCubbin and T. R. Mooney, J. Quant. Spectry Radiative Transfer 8, 1255 (1968).
    [Crossref]
  12. W. S. Benedict and L. D. Kaplan, J. Quant. Spectry Radiative Transfer 4, 453 (1964).
    [Crossref]
  13. P. W. Anderson, Phys. Rev. 76, 647 (1949).
    [Crossref]

1968 (3)

1967 (1)

1965 (1)

L. D. Gray and J. E. Selvidge, J. Quant. Spectry Radiative Transfer 5, 291 (1965).
[Crossref]

1964 (2)

B. H. Winters, S. Silverman, and W. S. Benedict, J. Quant. Spectry Radiative Transfer 4, 527 (1964).
[Crossref]

W. S. Benedict and L. D. Kaplan, J. Quant. Spectry Radiative Transfer 4, 453 (1964).
[Crossref]

1962 (2)

V. R. Stull, P. J. Wyatt, and G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[Crossref]

D. E. Burch, E. B. Singleton, and D. Williams, Appl. Opt. 1, 359 (1962).
[Crossref]

1961 (1)

R. P. Madden, J. Chem. Phys. 35, 2083 (1961).
[Crossref]

1959 (1)

C. P. Courtoy, Ann. Soc. Sci. Bruxelles, Serie 1, 5 (1959); also C. P. Courtoy, Can. J. Phys. 35, 608 (1957).
[Crossref]

1949 (1)

P. W. Anderson, Phys. Rev. 76, 647 (1949).
[Crossref]

Anderson, P. W.

P. W. Anderson, Phys. Rev. 76, 647 (1949).
[Crossref]

Benedict, W. S.

B. H. Winters, S. Silverman, and W. S. Benedict, J. Quant. Spectry Radiative Transfer 4, 527 (1964).
[Crossref]

W. S. Benedict and L. D. Kaplan, J. Quant. Spectry Radiative Transfer 4, 453 (1964).
[Crossref]

Burch, D. E.

Courtoy, C. P.

C. P. Courtoy, Ann. Soc. Sci. Bruxelles, Serie 1, 5 (1959); also C. P. Courtoy, Can. J. Phys. 35, 608 (1957).
[Crossref]

Gardner, J. A.

Gray, L. D.

L. D. Gray and J. E. Selvidge, J. Quant. Spectry Radiative Transfer 5, 291 (1965).
[Crossref]

Gryvnak, D. A.

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic MoleculesD. Van Nostrand Co., Inc., Princeton, N. J., 1960).

Kaplan, L. D.

W. S. Benedict and L. D. Kaplan, J. Quant. Spectry Radiative Transfer 4, 453 (1964).
[Crossref]

Madden, R. P.

R. P. Madden, J. Chem. Phys. 35, 2083 (1961).
[Crossref]

Manring, E. R.

McCubbin, T. K.

T. K. McCubbin and T. R. Mooney, J. Quant. Spectry Radiative Transfer 8, 1255 (1968).
[Crossref]

Mooney, T. R.

T. K. McCubbin and T. R. Mooney, J. Quant. Spectry Radiative Transfer 8, 1255 (1968).
[Crossref]

Patty, R. R.

Plass, G. N.

V. R. Stull, P. J. Wyatt, and G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[Crossref]

Selvidge, J. E.

L. D. Gray and J. E. Selvidge, J. Quant. Spectry Radiative Transfer 5, 291 (1965).
[Crossref]

Silverman, S.

B. H. Winters, S. Silverman, and W. S. Benedict, J. Quant. Spectry Radiative Transfer 4, 527 (1964).
[Crossref]

Singleton, E. B.

Stull, V. R.

V. R. Stull, P. J. Wyatt, and G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[Crossref]

Williams, D.

Winters, B. H.

B. H. Winters, S. Silverman, and W. S. Benedict, J. Quant. Spectry Radiative Transfer 4, 527 (1964).
[Crossref]

Wyatt, P. J.

V. R. Stull, P. J. Wyatt, and G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[Crossref]

Ann. Soc. Sci. Bruxelles, Serie (1)

C. P. Courtoy, Ann. Soc. Sci. Bruxelles, Serie 1, 5 (1959); also C. P. Courtoy, Can. J. Phys. 35, 608 (1957).
[Crossref]

Appl. Opt. (2)

J. Chem. Phys. (2)

V. R. Stull, P. J. Wyatt, and G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
[Crossref]

R. P. Madden, J. Chem. Phys. 35, 2083 (1961).
[Crossref]

J. Opt. Soc. Am. (2)

J. Quant. Spectry Radiative Transfer (4)

B. H. Winters, S. Silverman, and W. S. Benedict, J. Quant. Spectry Radiative Transfer 4, 527 (1964).
[Crossref]

L. D. Gray and J. E. Selvidge, J. Quant. Spectry Radiative Transfer 5, 291 (1965).
[Crossref]

T. K. McCubbin and T. R. Mooney, J. Quant. Spectry Radiative Transfer 8, 1255 (1968).
[Crossref]

W. S. Benedict and L. D. Kaplan, J. Quant. Spectry Radiative Transfer 4, 453 (1964).
[Crossref]

Phys. Rev. (1)

P. W. Anderson, Phys. Rev. 76, 647 (1949).
[Crossref]

Other (1)

G. Herzberg, Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic MoleculesD. Van Nostrand Co., Inc., Princeton, N. J., 1960).

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Figures (19)

Fig. 1
Fig. 1

Representative spectral curves in the 7000 cm−1 region. The curves were obtained with approximately 1 cm−1 slitwidth and correspond to the following samples of pure CO2:

Fig. 2
Fig. 2

Representative spectral curves in the 3800 cm−1 region. The curves were obtained with approximately 0.6 cm−1 slitwidth and correspond to the following samples:

Fig. 3
Fig. 3

Representative spectral curves in the 2400 cm−1 region. The curves were obtained with approximately 2.5 cm−1 slitwidth and correspond to the following samples of pure CO2:

Fig. 4
Fig. 4

Normalized half-width αs0 of self-broadened CO2 lines at 1 atm plotted vs J. The curves for the two branches are based on the following empirical equation, which was derived by Winters, Silverman, and Benedict1 from data obtained by Madden.8

Fig. 5
Fig. 5

Spectral curves showing comparison of self-broadened and N2-broadened lines. All four samples represented by the curves have the same absorber thickness, and all curves were scanned with the same spectral slitwidth. Sample A is composed of pure CO2, while samples B, C, and D contain CO2 + N2. The sample parameters are:

Fig. 6
Fig. 6

κs0 for CO2 self broadening vs ν between 6900 and 7100 cm−1. The various geometrical figures on the solid curve correspond to samples having the following total pressures: × ≤ 2 atm; O ~ 8–10 atm; Δ ~ 15 atm. The Lorentz curve represents the absorption coefficient calculated by assuming that the lines have the Lorentz shape. The WSB curve represents calculated results based on the line shape found by Winters, Silverman, and Benedict1 for the 0001 band near 2400 cm−1. The position of the band head is indicated.

Fig. 7
Fig. 7

κ0 for N2, He, and self broadening between 6990 and 7010 cm−1. A portion of the curve for self broadening in Fig. 6 is repeated for comparison. The vertical dashed line indicates the position of the band head.

Fig. 8
Fig. 8

κ0 for self and N2 broadening between 3770 and 4100 cm−1. The curves represent the contribution due to the lines below 3780 cm−1; the contribution of the lines between 3780 and 4100 cm−1 has been subtracted from the observed absorption coefficient. The curves are based on data points at wavenumbers where the absorption by nearby lines is small. Because of possible errors in the corrections made, the uncertainty of the curve is large above 3900 cm−1.

Fig. 9
Fig. 9

κ0 for various gases between 3770 and 3860 cm−1. Portions of the CO2 and N2 curves in Fig. 8 have been included for comparison. Data on H2 broadening are limited to a short region where the absorption by CO2 lines is much greater than that by H2 absorption. The O2 and Ar curves are essentially coincident between 3815 and 3850 cm−1.

Fig. 10
Fig. 10

κ0 for CO2, N2, and Ar in the 2400 cm−1 region. The curves represent the contribution of lines below 2400 cm−1. Above 2570 cm−1, it is difficult to account for the contribution of the nearby bands; however, from curve B of Fig. 3, we can set upper limits on κs0 of 5 × 10−8 and 5 × 10−9 (atm cmSTP)−1 at 2710 and 2830 cm−1, respectively.

Fig. 11
Fig. 11

χ for self-broadened CO2 lines in the 7000 cm−1 region. The upper curve corresponds to measurements made at room temperature, 296K. Curves B and C correspond to 431K. B is based on the assumption that the half-widths of self-broadened lines vary inversely with absolute temperature when the pressure is maintained constant; C is applicable if the half-widths vary inversely with the square-root of temperature.

Fig. 12
Fig. 12

χ for lines broadened by CO2, N2, and He in the 7000 cm−1 region. The curve representing N2 at 431K is based on the assumption that the normalized half-widths of the lines vary inversely with the square-root of temperature. A portion of the CO2 curve in Fig. 11 has been included for comparison.

Fig. 13
Fig. 13

χ for lines broadened by CO2, N2, Ar, O2, He, and H2 in the 3800 cm−1 region. For (νν0) > 120 cm−1, the O2 and Ar curves are essentially coincident.

Fig. 14
Fig. 14

χ(νν0) for CO2, N2, and Ar in the 2400 cm−1 region.

Fig. 15
Fig. 15

Influence of assumed line width on calculated curves of χ(νν0) and κs0(ν) in the 7000 cm−1 region. The curve in the lower panel represents the experimental results for κs0. The +’s represent the values calculated on the basis of lines whose χ is given by the solid curve in the upper panel and whose half-widths are given by Fig. 4. The □’s represent values calculated on the basis of the same χ but with α0 = 0.092 cm−1 for all lines. Values of κs0 based on lines with α = 0.092 cm−1 and χ modified according to the dashed curve agree with the experimental curve to within ±2%.

Fig. 16
Fig. 16

Curves of χ and κN20 showing influence of assumed line shape on the calculated absorption coefficient in the 3800 cm−1 region. Curve A in the lower panel represents the experimental results for κN20. The circles represent the values calculated on the basis of a line shape whose χ is given by curve A in the upper panel. Variations in the line shape given by curves B, C, D, and E in the upper panel were assumed, and the corresponding calculated curves of κN20 are shown in the lower panel. The six vertical lines in the lower panel indicate the wavenumbers at which experimental measurements were made.

Fig. 17
Fig. 17

Ratio k/kmax vs (νν0) for self-broadened lines in three spectral regions. The curves correspond to a Lorentz line and to lines in the wavenumber regions indicated. The absorption coefficient at the center of a Lorentz line with α = 0.1 cm−1 is represented by kmax. The curve which represents a sample at 431K is based on a line whose strength is the same at 431K as at 296K with kmax equal to the absorption coefficient at the center of the line when the sample is at 296K.

Fig. 18
Fig. 18

Ratio k/kmax vs (νν0) for N2- and Ar-broadened lines in three spectral regions. The curves correspond to a Lorentz line and to lines in the wavenumber regions indicated. kmax is the absorption coefficient at the center of a Lorentz line with α = 0.1 cm−1.

Fig. 19
Fig. 19

k plotted vs (νν0) to show influence of χ on ∫kdν for a single line. Curves A and B represent a Lorentz line and a CO2 line in the 7000 cm−1 region, respectively, with α = 1 cm−1 and kmax = 1 (atm cmSTP)−1. Curve C was obtained by multiplying A by values of χ given in Fig. 12 for N2 lines. Curve D was obtained by multiplying C by the appropriate factor, 1.5, so that the area is the same under Curves A and D. The curves are shown for (νν0) ≤ 10 cm−1 only, but larger (νν0) were considered when calculating the areas under the curves.

Tables (3)

Tables Icon

Table I Bands containing the lines whose shapes are studied.

Tables Icon

Table II Bands containing lines in region where absorption coefficient is measured.

Tables Icon

Table III Relative half-widths of CO2 lines broadened by various gases.

Equations (13)

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u ( atm cm STP ) = p ( atm ) [ 1 + 0.005 p ] L ( cm ) 273 / θ ( K ) .
T ( ν ) = exp [ - u κ ( ν ) ] ,             or             κ ( ν ) = - ( 1 / u ) ln T ( ν ) .
k ( ν ) = S f ( α , ν - ν 0 ) ,
- f ( α , ν - ν 0 ) = 1 ,
S = - k ( ν ) d ν .
f L ( α , ν - ν 0 ) = 1 π α ( ν - ν 0 ) 2 + α 2 .             ( Lorentz )
f L ( α , ν - ν 0 ) = α / π ( ν - ν 0 ) 2 ,             [ for ( ν - ν 0 ) α ] .
f ( α , ν - ν 0 ) = f L ( α , ν - ν 0 ) χ ( ν - ν 0 ) = [ α χ ( ν - ν 0 ) ] / π [ ( ν - ν 0 ) 2 + α 2 ] .
k s = S α χ π ( ν - ν 0 ) 2 = S α s 0 p ( 1 + 0.005 p ) χ π p 0 ( ν - ν 0 ) 2 ,
κ s = i k s , i = i S i χ s , i p ( 1 + 0.005 p ) α s , i 0 π p 0 ( ν - ν 0 , i ) 2 .
κ = - 1 u ln T ( ν ) = κ s 0 p ( 1 + 0.005 p ) p 0 + κ b 0 p b p 0 = i S i π α s , i 0 p 0 ( ν - ν 0 , i ) 2 × [ χ s , i p ( 1 + 0.005 p ) + ( α b 0 α s 0 ) χ b , i p b ] .
p ( A ) = p ( C ) + p N 2 ( C ) α N 2 0 / α s 0 ,
α s 0 ( cm - 1 ) = 0.050 + 0.12 exp [ - 0.16 m ] + 0.0042 m exp [ - B m ( m - 1 ) k T ] ,