Abstract

The optical properties of black polyethylene have been measured from 3 to 4000 cm−1. The scatter of data from different sources is caused by differences of carbon particle sizes, concentrations of the carbon in the polyethylene, and form of the carbon. An empirical fit of the absorption coefficient appears to demonstrate Rayleigh absorption. A physical model for absorption, with the electron mean free path about equal to the carbon-particle diameter, is proposed. Surface- and bulk-plasma effects may be inferred.

© 1970 Optical Society of America

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References

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  1. D. E. McCarthy, J. Opt. Soc. Am. 57, 699 (1967).
    [Crossref]
  2. R. J. Bell and G. M. Goldman, J. Opt. Soc. Am. 57, 1552 (1967).
    [Crossref]
  3. J. A. Bastin, A. E. Gear, G. O. Jones, H. J. T. Smith, and P. J. Wright, Proc. Roy. Soc. (London) 278A, 543 (1964).
  4. J. N. Gaitskell, R. A. Newstead, and J. A. Bastin, Phil. Trans. (GB) 264A, 195 (1969).
  5. D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
    [Crossref]
  6. Dow Chemical Company, Midland, Mich.
  7. Beckman Instrument Company, Fullerton, Calif.
  8. Monsanto Chemical Company, Kenilworth, N. J.
  9. U. S. Industrial Chemicals, St. Louis, Mo.
  10. J. Strong, Concepts of Classical Optics (W. H. Freeman and Company, San Franciso, 1958), p. 232.
  11. T. S. Moss, Optical Properties of Semi-Conductors (Butterworth and Company, London, 1961), p. 14.
  12. M. Kerker, The Scattering of Light (Academic Press Inc., New York, 1969).
  13. R. G. Newton, Scattering Theory of Waves and Particles (McGraw–Hill Book Co., New York, 1966), p. 54.
  14. J. M. Stone, Radiation and Optics (McGraw–Hill Book Co., New York, 1963), p. 387, prob. 15–13.
  15. S. J. Williamson, dissertation, Massachusetts Institute of Technology (May1965).
  16. T. J. McMahon and R. J. Bell, Phys. Rev. 182, 526 (1969).
    [Crossref]
  17. C. Kittel, Introduction to Solid State Physics, 3rd ed. (John Wiley & Sons, Inc., New York, 1966), p. 249, prob. 6.
  18. D. C. Tsui, Phys. Rev. Letters 22, 293 (1969).
    [Crossref]
  19. K. L. Ngai, E. N. Economou, and M. H. Cohen, Phys. Rev. Letters 22, 1375 (1969).
    [Crossref]
  20. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, Phys. Rev. Letters 21, 1530 (1969).
    [Crossref]

1969 (5)

J. N. Gaitskell, R. A. Newstead, and J. A. Bastin, Phil. Trans. (GB) 264A, 195 (1969).

T. J. McMahon and R. J. Bell, Phys. Rev. 182, 526 (1969).
[Crossref]

D. C. Tsui, Phys. Rev. Letters 22, 293 (1969).
[Crossref]

K. L. Ngai, E. N. Economou, and M. H. Cohen, Phys. Rev. Letters 22, 1375 (1969).
[Crossref]

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, Phys. Rev. Letters 21, 1530 (1969).
[Crossref]

1967 (2)

1964 (1)

J. A. Bastin, A. E. Gear, G. O. Jones, H. J. T. Smith, and P. J. Wright, Proc. Roy. Soc. (London) 278A, 543 (1964).

1961 (1)

D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
[Crossref]

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, Phys. Rev. Letters 21, 1530 (1969).
[Crossref]

Bastin, J. A.

J. N. Gaitskell, R. A. Newstead, and J. A. Bastin, Phil. Trans. (GB) 264A, 195 (1969).

J. A. Bastin, A. E. Gear, G. O. Jones, H. J. T. Smith, and P. J. Wright, Proc. Roy. Soc. (London) 278A, 543 (1964).

Bell, R. J.

T. J. McMahon and R. J. Bell, Phys. Rev. 182, 526 (1969).
[Crossref]

R. J. Bell and G. M. Goldman, J. Opt. Soc. Am. 57, 1552 (1967).
[Crossref]

Bloor, D.

D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
[Crossref]

Cohen, M. H.

K. L. Ngai, E. N. Economou, and M. H. Cohen, Phys. Rev. Letters 22, 1375 (1969).
[Crossref]

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, Phys. Rev. Letters 21, 1530 (1969).
[Crossref]

Dean, T. J.

D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
[Crossref]

Economou, E. N.

K. L. Ngai, E. N. Economou, and M. H. Cohen, Phys. Rev. Letters 22, 1375 (1969).
[Crossref]

Gaitskell, J. N.

J. N. Gaitskell, R. A. Newstead, and J. A. Bastin, Phil. Trans. (GB) 264A, 195 (1969).

Gear, A. E.

J. A. Bastin, A. E. Gear, G. O. Jones, H. J. T. Smith, and P. J. Wright, Proc. Roy. Soc. (London) 278A, 543 (1964).

Goldman, G. M.

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, Phys. Rev. Letters 21, 1530 (1969).
[Crossref]

Jones, G. O.

J. A. Bastin, A. E. Gear, G. O. Jones, H. J. T. Smith, and P. J. Wright, Proc. Roy. Soc. (London) 278A, 543 (1964).

D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
[Crossref]

Kerker, M.

M. Kerker, The Scattering of Light (Academic Press Inc., New York, 1969).

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 3rd ed. (John Wiley & Sons, Inc., New York, 1966), p. 249, prob. 6.

Martin, D. H.

D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
[Crossref]

Mawer, P. A.

D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
[Crossref]

McCarthy, D. E.

McMahon, T. J.

T. J. McMahon and R. J. Bell, Phys. Rev. 182, 526 (1969).
[Crossref]

Moss, T. S.

T. S. Moss, Optical Properties of Semi-Conductors (Butterworth and Company, London, 1961), p. 14.

Newstead, R. A.

J. N. Gaitskell, R. A. Newstead, and J. A. Bastin, Phil. Trans. (GB) 264A, 195 (1969).

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles (McGraw–Hill Book Co., New York, 1966), p. 54.

Ngai, K. L.

K. L. Ngai, E. N. Economou, and M. H. Cohen, Phys. Rev. Letters 22, 1375 (1969).
[Crossref]

Perry, C. H.

D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
[Crossref]

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, Phys. Rev. Letters 21, 1530 (1969).
[Crossref]

Smith, H. J. T.

J. A. Bastin, A. E. Gear, G. O. Jones, H. J. T. Smith, and P. J. Wright, Proc. Roy. Soc. (London) 278A, 543 (1964).

Stone, J. M.

J. M. Stone, Radiation and Optics (McGraw–Hill Book Co., New York, 1963), p. 387, prob. 15–13.

Strong, J.

J. Strong, Concepts of Classical Optics (W. H. Freeman and Company, San Franciso, 1958), p. 232.

Tsui, D. C.

D. C. Tsui, Phys. Rev. Letters 22, 293 (1969).
[Crossref]

Williamson, S. J.

S. J. Williamson, dissertation, Massachusetts Institute of Technology (May1965).

Wright, P. J.

J. A. Bastin, A. E. Gear, G. O. Jones, H. J. T. Smith, and P. J. Wright, Proc. Roy. Soc. (London) 278A, 543 (1964).

J. Opt. Soc. Am. (2)

Phil. Trans. (GB) (1)

J. N. Gaitskell, R. A. Newstead, and J. A. Bastin, Phil. Trans. (GB) 264A, 195 (1969).

Phys. Rev. (1)

T. J. McMahon and R. J. Bell, Phys. Rev. 182, 526 (1969).
[Crossref]

Phys. Rev. Letters (3)

D. C. Tsui, Phys. Rev. Letters 22, 293 (1969).
[Crossref]

K. L. Ngai, E. N. Economou, and M. H. Cohen, Phys. Rev. Letters 22, 1375 (1969).
[Crossref]

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, Phys. Rev. Letters 21, 1530 (1969).
[Crossref]

Proc. Roy. Soc. (London) (2)

J. A. Bastin, A. E. Gear, G. O. Jones, H. J. T. Smith, and P. J. Wright, Proc. Roy. Soc. (London) 278A, 543 (1964).

D. Bloor, T. J. Dean, G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. (London) 260, 510 (1961).
[Crossref]

Other (11)

Dow Chemical Company, Midland, Mich.

Beckman Instrument Company, Fullerton, Calif.

Monsanto Chemical Company, Kenilworth, N. J.

U. S. Industrial Chemicals, St. Louis, Mo.

J. Strong, Concepts of Classical Optics (W. H. Freeman and Company, San Franciso, 1958), p. 232.

T. S. Moss, Optical Properties of Semi-Conductors (Butterworth and Company, London, 1961), p. 14.

M. Kerker, The Scattering of Light (Academic Press Inc., New York, 1969).

R. G. Newton, Scattering Theory of Waves and Particles (McGraw–Hill Book Co., New York, 1966), p. 54.

J. M. Stone, Radiation and Optics (McGraw–Hill Book Co., New York, 1963), p. 387, prob. 15–13.

S. J. Williamson, dissertation, Massachusetts Institute of Technology (May1965).

C. Kittel, Introduction to Solid State Physics, 3rd ed. (John Wiley & Sons, Inc., New York, 1966), p. 249, prob. 6.

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Figures (2)

Fig. 1
Fig. 1

Transmittance vs wavenumber, of black polyethylene. − − − U. S. Industrial Chemicals Company (0.150±0.007 mm), + + + Dow Chemical Company (0.157±0.005 mm), -●-●-●- Monsanto Chemical Company (0.165±0.007 mm), -×-×-×- Dow Chemical Company (3.40 mm).

Fig. 2
Fig. 2

Absorption coefficient vs wavenumber, of black polyethylene. Circles, Dow Chemical Company, Ref. 2; squares, Dow Chemical Company, this work: Circles with a horizontal slash are from a sample from Monsanto Chemical Company and open triangles are from a sample from U. S. Industrial Chemicals Company. Queen Mary College data: filled triangle, cyanogen-laser data; double crosses, solar transit using gauze filters; diamonds, solar transit using a cooled detector; dots, grating spectrometer; and cross, 2.7-mm superhetrodyne system. Curve A is the long wavelength asymptote with ( ν ¯ ) 3 2 dependence. Curve B is a plot of the results of Eq. (6).

Tables (1)

Tables Icon

Table I Data on black polyethylene from different manufactures.

Equations (14)

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m = 2 n ν ¯ t cos ϕ ,
T = ( 1 - R ) 2 e - α t / 1 - R 2 e - 2 α t ,
R [ ( n - 1 ) / n + 1 ] 2
n [ 1 + ( 1 - T 0 ) 1 2 ] / [ 1 - ( 1 - T 0 ) 1 2 ] ,
α = ( t 2 - t 1 ) - 1 ln ( T 1 / T 2 ) ,
α = [ 2.27 × 10 - 2 ( ν ¯ ) 3 2 1 + 2.12 × 10 - 3 ( ν ¯ ) ] cm - 1 ,
α = ( N a ν ¯ ) Im { [ ( n c n m ) 2 - 1 ] / [ ( n c n m ) 2 + 2 ] } ,
n c = n + i k .
A = 8 π 2 R 3 n m ,
α = ( N A ν ¯ ) 3 ( 2 n k n m 2 ) - 1 1 + ( n 2 - k 2 n m 2 + 2 ) 2 ( 2 n k n m 2 ) - 2 .
2.12 × 10 - 3 ( ν ¯ ) = ( n 2 - k 2 n m 2 + 2 ) 2 ( 2 n k n m 2 ) - 2
2.27 × 10 - 2 ( ν ¯ ) 1 2 = 3 N A ( 2 n k n m 2 ) - 1 .
ρ = N [ ( 4 π / 3 ) R 3 ] ρ c ρ m × 100 ,
n k 7.0 ( ν ¯ ) - 1 4