Abstract

The infrared transmittance of carbon dioxide has been calculated over a wide range of path lengths, pressures, and temperatures from 500 to 10,000 cm−1. Values of the transmittance are given at intervals of 2.5 cm−1. In addition, transmittance values are also given which have been averaged over larger intervals. All contributing spectral lines whose relative intensity is greater than 10−8 that of the strongest line in any particular band have been included in the calculation. In addition, the contributions from the eight major isotopic species have been included. The calculation of the vibrational energy levels included terms through the third power of the vibrational quantum number and also the effects of Fermi resonance. The final transmittance tables were generated using the quasi-random model of molecular band absorption.

© 1964 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. S. Ballard, L. Larmore, S. Passman, Fundamentals of Infrared for Military Application, Conf. Report, The Rand Corporation, R-297C, March31, 1956.
  2. V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).
  3. V. R. Stull, P. J. Wyatt, G. N. Plass, J. Chem. Phys. 37, 1442 (1962).
    [CrossRef]
  4. G. Herzberg, Infrared and Ramon Spectra, (Van Nostrand, Princeton, N.J., 1945).
  5. J. N. Howard, D. E. Burch, D. Williams, Sci. Rept. No. 1, AF 19(604)-516, The Ohio State University (Dec.1954);J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).
  6. D. E. Burch, D. Gryvnak, D. Williams, Appl. Opt. 1, 759 (1962).
    [CrossRef]
  7. L. I. Schiff, Quantum Mechanics, (McGraw-Hill, N.Y., 1949).
  8. W. S. Benedict, R. Herman, S. Silverman, J. Chem. Phys. 19, 1325(1951).
    [CrossRef]
  9. S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison-Wesley, Reading, Mass., 1959).
  10. R. Herman, R. F. Wallis, J. Chem. Phys. 23, 675 (1955).
    [CrossRef]
  11. V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 50, 1279 (1960).
    [CrossRef]
  12. G. Yamamoto, T. Sasamori, Sci. Rept. Tohoku Univ., Fifth Ser. 10, 37 (1958).
  13. L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
    [CrossRef]
  14. H. J. Kostkowski, “Line Half-Widths and Intensities from the Infrared Transmission of Thermally Excited CO2,” Contract No. 248(01), Johns Hopkins Univ. (1955).
  15. H. J. Kostkowski, L. D. Kaplan, J. Chem. Phys. 26, 1252 (1957).
    [CrossRef]
  16. R. P. Madden, “Study of CO2Absorption Spectra between 15 and 18 Microns,” Contract No. 248(01), Johns Hopkins Univ. (1957).
  17. C. P. Courtoy, Can. J. Phys. 35, 608 (1957).
    [CrossRef]
  18. J. H. Taylor, W. S. Benedict, J. Strong, J. Chem. Phys. 20, 1884 (1952).
    [CrossRef]
  19. W. S. Benedict (private communication).
  20. V. R. Stull, P. J. Wyatt, G. N. Plass, “The Infrared Absorption of Carbon Dioxide, Infrared Transmission Studies,” Vol. III, Rept. SSD-TDR-62-127, Space Systems Division, Air Force Systems Command, Los Angeles, Calif.
  21. P. J. Wyatt, V. R. Stull, G. N. Plass, Appl. Opt. (to be published).
  22. P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
    [CrossRef]
  23. G. N. Plass, Appl. Opt. 2, 515 (1963).
    [CrossRef]

1963 (1)

1962 (3)

1961 (1)

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

1960 (1)

1958 (1)

G. Yamamoto, T. Sasamori, Sci. Rept. Tohoku Univ., Fifth Ser. 10, 37 (1958).

1957 (2)

H. J. Kostkowski, L. D. Kaplan, J. Chem. Phys. 26, 1252 (1957).
[CrossRef]

C. P. Courtoy, Can. J. Phys. 35, 608 (1957).
[CrossRef]

1956 (1)

L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
[CrossRef]

1955 (1)

R. Herman, R. F. Wallis, J. Chem. Phys. 23, 675 (1955).
[CrossRef]

1952 (1)

J. H. Taylor, W. S. Benedict, J. Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

1951 (1)

W. S. Benedict, R. Herman, S. Silverman, J. Chem. Phys. 19, 1325(1951).
[CrossRef]

Ballard, S. S.

S. S. Ballard, L. Larmore, S. Passman, Fundamentals of Infrared for Military Application, Conf. Report, The Rand Corporation, R-297C, March31, 1956.

Benedict, W. S.

J. H. Taylor, W. S. Benedict, J. Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

W. S. Benedict, R. Herman, S. Silverman, J. Chem. Phys. 19, 1325(1951).
[CrossRef]

W. S. Benedict (private communication).

Burch, D. E.

D. E. Burch, D. Gryvnak, D. Williams, Appl. Opt. 1, 759 (1962).
[CrossRef]

J. N. Howard, D. E. Burch, D. Williams, Sci. Rept. No. 1, AF 19(604)-516, The Ohio State University (Dec.1954);J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).

Courtoy, C. P.

C. P. Courtoy, Can. J. Phys. 35, 608 (1957).
[CrossRef]

Eggers, D. F.

L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
[CrossRef]

Gryvnak, D.

Herman, R.

R. Herman, R. F. Wallis, J. Chem. Phys. 23, 675 (1955).
[CrossRef]

W. S. Benedict, R. Herman, S. Silverman, J. Chem. Phys. 19, 1325(1951).
[CrossRef]

Herzberg, G.

G. Herzberg, Infrared and Ramon Spectra, (Van Nostrand, Princeton, N.J., 1945).

Howard, J. N.

J. N. Howard, D. E. Burch, D. Williams, Sci. Rept. No. 1, AF 19(604)-516, The Ohio State University (Dec.1954);J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).

Kaplan, L. D.

H. J. Kostkowski, L. D. Kaplan, J. Chem. Phys. 26, 1252 (1957).
[CrossRef]

L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
[CrossRef]

Kostkowski, H. J.

H. J. Kostkowski, L. D. Kaplan, J. Chem. Phys. 26, 1252 (1957).
[CrossRef]

H. J. Kostkowski, “Line Half-Widths and Intensities from the Infrared Transmission of Thermally Excited CO2,” Contract No. 248(01), Johns Hopkins Univ. (1955).

Larmore, L.

S. S. Ballard, L. Larmore, S. Passman, Fundamentals of Infrared for Military Application, Conf. Report, The Rand Corporation, R-297C, March31, 1956.

Madden, R. P.

R. P. Madden, “Study of CO2Absorption Spectra between 15 and 18 Microns,” Contract No. 248(01), Johns Hopkins Univ. (1957).

Passman, S.

S. S. Ballard, L. Larmore, S. Passman, Fundamentals of Infrared for Military Application, Conf. Report, The Rand Corporation, R-297C, March31, 1956.

Penner, S. S.

S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison-Wesley, Reading, Mass., 1959).

Plass, G. N.

G. N. Plass, Appl. Opt. 2, 515 (1963).
[CrossRef]

P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
[CrossRef]

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

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 50, 1279 (1960).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, “The Infrared Absorption of Carbon Dioxide, Infrared Transmission Studies,” Vol. III, Rept. SSD-TDR-62-127, Space Systems Division, Air Force Systems Command, Los Angeles, Calif.

P. J. Wyatt, V. R. Stull, G. N. Plass, Appl. Opt. (to be published).

Sasamori, T.

G. Yamamoto, T. Sasamori, Sci. Rept. Tohoku Univ., Fifth Ser. 10, 37 (1958).

Schiff, L. I.

L. I. Schiff, Quantum Mechanics, (McGraw-Hill, N.Y., 1949).

Silverman, S.

W. S. Benedict, R. Herman, S. Silverman, J. Chem. Phys. 19, 1325(1951).
[CrossRef]

Strong, J.

J. H. Taylor, W. S. Benedict, J. Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

Stull, V. R.

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

P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 50, 1279 (1960).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, “The Infrared Absorption of Carbon Dioxide, Infrared Transmission Studies,” Vol. III, Rept. SSD-TDR-62-127, Space Systems Division, Air Force Systems Command, Los Angeles, Calif.

P. J. Wyatt, V. R. Stull, G. N. Plass, Appl. Opt. (to be published).

Taylor, J. H.

J. H. Taylor, W. S. Benedict, J. Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

Wallis, R. F.

R. Herman, R. F. Wallis, J. Chem. Phys. 23, 675 (1955).
[CrossRef]

Williams, D.

D. E. Burch, D. Gryvnak, D. Williams, Appl. Opt. 1, 759 (1962).
[CrossRef]

J. N. Howard, D. E. Burch, D. Williams, Sci. Rept. No. 1, AF 19(604)-516, The Ohio State University (Dec.1954);J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).

Wyatt, P. J.

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

P. J. Wyatt, V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 52, 1209 (1962).
[CrossRef]

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

V. R. Stull, P. J. Wyatt, G. N. Plass, “The Infrared Absorption of Carbon Dioxide, Infrared Transmission Studies,” Vol. III, Rept. SSD-TDR-62-127, Space Systems Division, Air Force Systems Command, Los Angeles, Calif.

P. J. Wyatt, V. R. Stull, G. N. Plass, Appl. Opt. (to be published).

Yamamoto, G.

G. Yamamoto, T. Sasamori, Sci. Rept. Tohoku Univ., Fifth Ser. 10, 37 (1958).

Appl. Opt. (2)

Bull. Am. Phys. Soc. (1)

V. R. Stull, P. J. Wyatt, G. N. Plass, Bull. Am. Phys. Soc. 6, 336 (1961).

Can. J. Phys. (1)

C. P. Courtoy, Can. J. Phys. 35, 608 (1957).
[CrossRef]

J. Chem. Phys. (6)

J. H. Taylor, W. S. Benedict, J. Strong, J. Chem. Phys. 20, 1884 (1952).
[CrossRef]

L. D. Kaplan, D. F. Eggers, J. Chem. Phys. 25, 876 (1956).
[CrossRef]

H. J. Kostkowski, L. D. Kaplan, J. Chem. Phys. 26, 1252 (1957).
[CrossRef]

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

W. S. Benedict, R. Herman, S. Silverman, J. Chem. Phys. 19, 1325(1951).
[CrossRef]

R. Herman, R. F. Wallis, J. Chem. Phys. 23, 675 (1955).
[CrossRef]

J. Opt. Soc. Am. (2)

Sci. Rept. Tohoku Univ., Fifth Ser. (1)

G. Yamamoto, T. Sasamori, Sci. Rept. Tohoku Univ., Fifth Ser. 10, 37 (1958).

Other (10)

S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison-Wesley, Reading, Mass., 1959).

G. Herzberg, Infrared and Ramon Spectra, (Van Nostrand, Princeton, N.J., 1945).

J. N. Howard, D. E. Burch, D. Williams, Sci. Rept. No. 1, AF 19(604)-516, The Ohio State University (Dec.1954);J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).

L. I. Schiff, Quantum Mechanics, (McGraw-Hill, N.Y., 1949).

R. P. Madden, “Study of CO2Absorption Spectra between 15 and 18 Microns,” Contract No. 248(01), Johns Hopkins Univ. (1957).

H. J. Kostkowski, “Line Half-Widths and Intensities from the Infrared Transmission of Thermally Excited CO2,” Contract No. 248(01), Johns Hopkins Univ. (1955).

W. S. Benedict (private communication).

V. R. Stull, P. J. Wyatt, G. N. Plass, “The Infrared Absorption of Carbon Dioxide, Infrared Transmission Studies,” Vol. III, Rept. SSD-TDR-62-127, Space Systems Division, Air Force Systems Command, Los Angeles, Calif.

P. J. Wyatt, V. R. Stull, G. N. Plass, Appl. Opt. (to be published).

S. S. Ballard, L. Larmore, S. Passman, Fundamentals of Infrared for Military Application, Conf. Report, The Rand Corporation, R-297C, March31, 1956.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

A comparison of the theoretical calculations of the transmittance with the experimental measurements of Burch et al.6 for a pressure of 15.6 mm Hg and 46.4 atm-cm of CO2.

Fig. 2
Fig. 2

A comparison of the theoretical calculations of the transmittance with the experimental measurements of Burch et al.6 for a pressure of 137 mm Hg and 0.195 atm-cm of CO2.

Fig. 3
Fig. 3

A comparison of the theoretical calculations of the transmittance with the experimental measurements of Burch et al.6 for a pressure of 542 mm Hg and 0.759 atm-cm of CO2.

Tables (5)

Tables Icon

Table I Groups of Infrared-Active CO2 Transitions

Tables Icon

Table II Rotational Constants for C12O216

Tables Icon

Table III Relative Intensities 15-μ CO2 Bands

Tables Icon

Table IV Normalization Constants

Tables Icon

Table V Transmittance at 1-Atm Pressure Averaged over 50 cm−1 Intervals

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

( 1 ) Δ l = 0 , Δ υ 2 - even , Δ υ 3 - odd ( 2 ) Δ l = ± 1 , Δ υ 2 - odd , Δ υ 3 - even
( 1 ) Δ l = 0 ( 2 ) Δ l = ± 1
F υ ( j ) = B υ j ( j + 1 ) ,
B υ = B e i = 1 3 α i ( υ i + 1 2 d i ) ,
B e ( i ) = B e ( ρ 1 ρ 2 ρ 3 ) 2 / 3 ,
α j ( i ) = α j ρ j 3
ρ 1 = [ m ( O ) / m ( O ) ( i ) ] 1 / 2 , ρ 2 = ρ 3 = ρ 1 { 1 + [ m ( O ) ( i ) / m ( C ) ( i ) ] 1 + [ m ( O ) / m ( C ) ] } 1 / 2 ,
S υ , l , j υ , l , j = 8 π 3 3 h c ω υ , l , j υ , l , j N Q p exp { h c [ G ( υ , l ) + F υ ( j ) ] k T } × | M υ l j υ , l , j | 2 s ( j , l ) [ 1 exp ( h c ω υ j l υ , j , l k T ) ] ,
s ( j , l ) = { [ ( j + 1 ) 2 l 2 ] / ( j + 1 ) , Δ j = + 1 , Δ l = 0 , [ ( 2 j + 1 ) l 2 ] / [ j ( j + 1 ) ] , Δ j = 0 , Δ l = 0 , ( j 2 l 2 ) / j , Δ j = 1 , Δ l = 0 ,
s ( j , l ) = { [ ( j + 2 ± l ) ( j + 1 ± l ) ] / [ 2 ( j + 1 ) ] , Δ j = ± 1 , Δ l = ± l , [ ( j + 1 ± l ) ( j l ) ( 2 j + 1 ) ] / [ 2 j ( j + 1 ) ] , Δ j = 0 , Δ l = ± 1 , [ ( j 1 l ) ( j l ) ] / 2 j , Δ j = 1 , Δ l = ± 1.
α υ , l υ , l = j j S υ , j , l υ , j , l = ( 8 π 3 / 3 h c ) ω ¯ υ , l υ , l ( N / Q p ) exp [ h c G ( υ , l ) / k T ] · | R υ , l υ , l | 2 j j s ( j , l ) exp [ h c F υ [ ( j ) / k T ] ,
ω ¯ υ , l υ , l j j s ( j , l ) exp [ h c F υ ( j ) / k T ] = j j ω υ , l , j υ , l , j × exp [ h c F υ ( j ) / k T ] · f υ , l , j υ , l , j s ( j , l ) × [ 1 exp ( h c ω υ , l , j υ , l , j / k T ) ] .
[ 1 exp ( h c ω υ , l , j υ , l , j / k T ) ] [ 1 exp ( h c ω υ , l υ , l / k T ) ] 1 ,
S υ , l , j υ , l , j = C υ , l υ , l ( ω υ , l , j υ , l , j / ω υ , l υ , l ) s ( j , l ) × exp [ h c F υ ( j ) / k T ] ,
C υ , l υ , l = α υ , l υ , l { j j s ( j , l ) exp [ h c F υ ( j ) / k T ] } 1 .
C υ , l υ , l ( T ) = I R C υ * , l * υ * , l *′ ( T 0 ) [ N ( T ) Q ( T 0 ) / N ( T 0 ) Q ( T ) ] · exp { h c G ( υ * , l * ) k T 0 h c G ( υ , l ) k T } ,
Q ( T ) = j = 1 3 [ 1 exp ( h c ω i 0 k T ) ] d i [ k T h c B e + 1 3 + 1 15 h c B e k T + 4 315 ( h c B e k T ) 2 + 1 315 ( h c B e k T ) 3 + ] exp [ h c G ( 0,0 ) k T ] ,
b ( ν , ν i ) = { ( α / π ) [ ( ν ν i ) 2 + α 2 ] 1 , | ν ν i | d , ( A α / π ) [ ( ν ν i ) 2 + α 2 ] 1 exp [ a | ν ν i | b ] , | ν ν i | d ,
α = α 0 ( p / p 0 ) ( T 0 / T ) 1 / 2 ,
ξ 0 k = p 0 S k / π α 0 ,
T = T j i j T i .
T j = k = 1 5 { 0 1 exp [ ρ 2 ξ 0 k , j u p ( ρ 2 + y 2 ) ] d y } n k j ,
T i = 1 2 k = 1 5 { D i exp [ A ρ 2 ξ 0 k , i u exp [ a ( 1 2 D ) b y b ] p y 2 ] d y } n k i ,

Metrics