Abstract

An apparatus designed to measure the optical constants of a powder suspended in a liquid is described. A laser source (3.391 μm) and attenuated total reflection approach are used. The accuracy of the apparatus is evaluated by comparing measured results for a liquid hydrocarbon with published results obtained using a different technique. An error analysis is presented. Data obtained for a carbon black powder are discussed and compared with previously published results from specular reflection measurements. The applicability of the Maxwell-Garnett effective medium theory is considered.

© 1983 Optical Society of America

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References

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  1. J. Fahrenfort, Spectrochim. Acta 17, 698 (1961).
    [CrossRef]
  2. V. P. Tomaselli, R. Rivera, D. C. Edewaard, K. D. Möller, Appl. Opt. 20, 3961 (1981).
    [CrossRef] [PubMed]
  3. B. Crawford, T. G. Goplen, D. Swanson, “The Measurement of Optical Constants in the Infrared by Attenuated Total Reflection,” in Advances in Infrared and Raman Spectroscopy, Vol. 4, R. J. H. Clark, R. E. Hester, Eds. (Heyden, London, 1978), Chap. 2.
  4. T. Hirschfeld, Appl. Spectrosc. 32, 160 (1978).
    [CrossRef]
  5. T. Hirschfeld, Appl. Spectrosc. 24, 277 (1970).
    [CrossRef]
  6. T. G. Goplen, D. G. Cameron, R. N. Jones, Appl. Spectrosc. 34, 657 (1980).
    [CrossRef]
  7. J. C. Maxwell Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904);Philos. Trans. R. Soc. London Ser. A 205, 237 (1906).
    [CrossRef]
  8. Cabot Corp., Technical Report S-36, Boston, Mass. 02110.
  9. E. M. Dannenberg, “Carbon Black,” in Kirk-Othmer: Encyclopedia of Chemical Technology, Vol. 4 (Wiley, New York, 1978), pp. 631–666.
  10. G. A. Niklasson, H. G. Craighead, Appl. Opt. 22, 1237 (1983).
    [CrossRef] [PubMed]
  11. S. G. Jennings, J. Opt. Soc. Am. 71, 923 (1981).
    [CrossRef]

1983 (1)

1981 (2)

1980 (1)

1978 (1)

1970 (1)

1961 (1)

J. Fahrenfort, Spectrochim. Acta 17, 698 (1961).
[CrossRef]

1904 (1)

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904);Philos. Trans. R. Soc. London Ser. A 205, 237 (1906).
[CrossRef]

Cameron, D. G.

Craighead, H. G.

Crawford, B.

B. Crawford, T. G. Goplen, D. Swanson, “The Measurement of Optical Constants in the Infrared by Attenuated Total Reflection,” in Advances in Infrared and Raman Spectroscopy, Vol. 4, R. J. H. Clark, R. E. Hester, Eds. (Heyden, London, 1978), Chap. 2.

Dannenberg, E. M.

E. M. Dannenberg, “Carbon Black,” in Kirk-Othmer: Encyclopedia of Chemical Technology, Vol. 4 (Wiley, New York, 1978), pp. 631–666.

Edewaard, D. C.

Fahrenfort, J.

J. Fahrenfort, Spectrochim. Acta 17, 698 (1961).
[CrossRef]

Goplen, T. G.

T. G. Goplen, D. G. Cameron, R. N. Jones, Appl. Spectrosc. 34, 657 (1980).
[CrossRef]

B. Crawford, T. G. Goplen, D. Swanson, “The Measurement of Optical Constants in the Infrared by Attenuated Total Reflection,” in Advances in Infrared and Raman Spectroscopy, Vol. 4, R. J. H. Clark, R. E. Hester, Eds. (Heyden, London, 1978), Chap. 2.

Hirschfeld, T.

Jennings, S. G.

Jones, R. N.

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904);Philos. Trans. R. Soc. London Ser. A 205, 237 (1906).
[CrossRef]

Möller, K. D.

Niklasson, G. A.

Rivera, R.

Swanson, D.

B. Crawford, T. G. Goplen, D. Swanson, “The Measurement of Optical Constants in the Infrared by Attenuated Total Reflection,” in Advances in Infrared and Raman Spectroscopy, Vol. 4, R. J. H. Clark, R. E. Hester, Eds. (Heyden, London, 1978), Chap. 2.

Tomaselli, V. P.

Appl. Opt. (2)

Appl. Spectrosc. (3)

J. Opt. Soc. Am. (1)

Philos. Trans. R. Soc. London Ser. A (1)

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904);Philos. Trans. R. Soc. London Ser. A 205, 237 (1906).
[CrossRef]

Spectrochim. Acta (1)

J. Fahrenfort, Spectrochim. Acta 17, 698 (1961).
[CrossRef]

Other (3)

B. Crawford, T. G. Goplen, D. Swanson, “The Measurement of Optical Constants in the Infrared by Attenuated Total Reflection,” in Advances in Infrared and Raman Spectroscopy, Vol. 4, R. J. H. Clark, R. E. Hester, Eds. (Heyden, London, 1978), Chap. 2.

Cabot Corp., Technical Report S-36, Boston, Mass. 02110.

E. M. Dannenberg, “Carbon Black,” in Kirk-Othmer: Encyclopedia of Chemical Technology, Vol. 4 (Wiley, New York, 1978), pp. 631–666.

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Figures (9)

Fig. 1
Fig. 1

Perpendicular reflectance vs angle of incidence curves for various values of extinction coefficients. Critical angle is 21.83°.

Fig. 2
Fig. 2

Parallel reflectance vs angle of incidence curves for various values of extinction coefficient. Critical angle is 21.83°.

Fig. 3
Fig. 3

Schematic diagram of apparatus used to make ATR measurements. (a) Top view of components. The solid line is the path of laser radiation, the broken line is the path of electrical signal. Components are: L1, infrared laser (3.391-μm output); L2, visible laser (used for positioning of prism when mirror M2 is inserted in path); C, chopper; M1, plane mirror; P, prism; I, irises; D, detector; A, amplifier; and R, recorder. (b) Side view of prism showing sample S and path of laser beam.

Fig. 4
Fig. 4

Reflectance curves for toluene. Solid curves are data calculated from results reported in Ref. 6. Open circles are measured data obtained with apparatus described in text.

Fig. 5
Fig. 5

Calculated error in index of refraction. Curves for various absorption coefficients were generated using algorithm given in text and assuming an error of ±0.01 in reflectance values and ±0.2° in angle of incidence. Curves are specific for apparatus used in this study.

Fig. 6
Fig. 6

Calculated error in absorption coefficient. See caption of Fig. 5 for details.

Fig. 7
Fig. 7

Index of refraction of Mogul-L carbon black suspension as a function of weight fraction of powder in host material. Error bars represent deviations from the average value of several measurements.

Fig. 8
Fig. 8

Absorption coefficient of Mogul-L carbon black suspension as a function of weight fraction of powder in host material. Error bars represent deviations from the average value of several measurements.

Fig. 9
Fig. 9

Permittivity of Mogul-L carbon black suspension as a function of volume fraction of powder in host material. Open circles are the results calculated from the optical constant data. Dotted line is the linear regression fit of data points. Solid curve is the behavior of equivalent two-component systetims as predicted by Maxwell Garnett theory (MGT).

Tables (1)

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Table I Optical Constants of Mogul L Carbon Black Powder at 3.391 μm

Equations (15)

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R s = 1 4 a cos θ [ a 2 + G + ( a + cos θ ) 2 ] ,
a = { [ ( G 2 + 4 k 2 N 4 ) 1 / 4 G ] / 2 } 1 / 2 ,
G = sin 2 θ N 2 ( 1 k 2 ) ,
N = n 2 / n 1 .
R p = R s [ 1 4 a sin θ tan θ a 2 + G + ( a + sin θ tan θ ) 2 ] .
n 2 = n 1 { [ ( X 2 + 4 Y 2 ) 1 / 2 + X ] / 2 } 1 / 2 ,
k = { [ ( X 2 + 4 Y 2 ) 1 / 2 X ] / 2 Y } ,
X = 2 a 2 ( F s + F p ) / 2 + ( 1 + tan 2 θ ) / 2 ,
Y = a [ ( a F s a 2 cos 2 θ ) ( a F p a 2 sin 2 θ tan 2 θ ) ] 1 / 4 ,
a = ( 1 tan 2 θ ) / ( F s F p ) ,
F s = 2 cos θ ( 1 + R s ) / ( 1 R s ) ,
F p = 2 sin θ tan θ ( 1 R p / R s ) ( 1 + R p / R s ) .
ɛ = n 2 k 2 ,
ɛ = 2 nk .
ɛ 12 = ɛ 2 [ 1 + 3 f υ ( ɛ 1 ɛ 2 ) ( 1 f υ ) ɛ 1 + ( 2 + f υ ) ɛ 2 ] ,

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