Abstract

The mean scattering cross section of a polydispersion upon which electromagnetic radiation is incident is found to depend primarily upon the ratio of the third to second moment of the size distribution function, i.e., the volume—surface mean diameter, and is only weakly dependent on the shape of the size distribution function. This result is applicable to mean diameters ranging from very large to very small compared with the wavelength of incident light. Mean scattering coefficients are presented for polydispersions with refractive indices varying from <i>m</i>-1«1 to <i>m</i>=1.85. The results of this investigation can be used to measure mean particle size, as represented by the ratio of third to second moment of size distribution function, to an accuracy comparable to experimental accuracy even though the size distribution function is not known.

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  1. D. Sinclair, J. Opt. Soc. Am. 37, 475 (1947).
  2. R. M. Tabibian, W. Heller, and J. M. Epel, J. Colloid. Sci. 11, 195 (1956).
  3. W. Heller, Interdisciplinary Conference on Electromagnetic Scattering (Pergamon Press, New York, N. Y., 1963), p. 101.
  4. H. C. van de Hulst, Light Scattering By Small Particles (John Wiley & Sons, New York, N. Y., 1956), p. 114.
  5. M. L. Wallach and W. Heller, J. Phys. Chem. 68, 924 (1964).
  6. R. A. Dobbins, AIAA J. 1, 1940 (1963).
  7. Ref. 4, p. 176.
  8. R. A. Mugele and H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).
  9. J. H. Roberts and M. J. Webb AIAA J. 2, 3583 (1964).
  10. Ref. 4, p. 177.
  11. R. B. Penndorf, J. Opt. Soc. Am. 47, 1010 (1957).
  12. See Ref. 4, p. 70.
  13. Our attention has been directed by a reviewer to the extensive tabulation of scattering coefficients due to Kerker et al.14 deposited with the American Documentation Institute. We have checked our calculations with the results of a calculation using the tabulation of Kerker et al. and find that we obtain for ρ32 = 6.0, m = 1.76, = 3.104. From Table II for the same ρ32 and m = 1.75 we find = 3.233.
  14. M. Kerker et al., J. Phys. Chem. 65, 1713 (1961).
  15. E. J. Meehan and Z. Z. Hugus, J. Opt. Soc. Am. 51, 260 (1961).
  16. R. B. Penndorf, J. Phys. Chem. 62, 1537 (1958).

Dobbins, R. A.

R. A. Dobbins, AIAA J. 1, 1940 (1963).

Epel, J. M.

R. M. Tabibian, W. Heller, and J. M. Epel, J. Colloid. Sci. 11, 195 (1956).

Evans, H. D.

R. A. Mugele and H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).

Heller, W.

W. Heller, Interdisciplinary Conference on Electromagnetic Scattering (Pergamon Press, New York, N. Y., 1963), p. 101.

R. M. Tabibian, W. Heller, and J. M. Epel, J. Colloid. Sci. 11, 195 (1956).

M. L. Wallach and W. Heller, J. Phys. Chem. 68, 924 (1964).

Hugus, Z. Z.

E. J. Meehan and Z. Z. Hugus, J. Opt. Soc. Am. 51, 260 (1961).

Kerker, M.

M. Kerker et al., J. Phys. Chem. 65, 1713 (1961).

Meehan, E. J.

E. J. Meehan and Z. Z. Hugus, J. Opt. Soc. Am. 51, 260 (1961).

Mugele, R. A.

R. A. Mugele and H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).

Penndorf, R. B.

R. B. Penndorf, J. Phys. Chem. 62, 1537 (1958).

R. B. Penndorf, J. Opt. Soc. Am. 47, 1010 (1957).

Roberts, J. H.

J. H. Roberts and M. J. Webb AIAA J. 2, 3583 (1964).

Sinclair, D.

D. Sinclair, J. Opt. Soc. Am. 37, 475 (1947).

Tabibian, R. M.

R. M. Tabibian, W. Heller, and J. M. Epel, J. Colloid. Sci. 11, 195 (1956).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering By Small Particles (John Wiley & Sons, New York, N. Y., 1956), p. 114.

Wallach, M. L.

M. L. Wallach and W. Heller, J. Phys. Chem. 68, 924 (1964).

Webb, M. J.

J. H. Roberts and M. J. Webb AIAA J. 2, 3583 (1964).

Other (16)

D. Sinclair, J. Opt. Soc. Am. 37, 475 (1947).

R. M. Tabibian, W. Heller, and J. M. Epel, J. Colloid. Sci. 11, 195 (1956).

W. Heller, Interdisciplinary Conference on Electromagnetic Scattering (Pergamon Press, New York, N. Y., 1963), p. 101.

H. C. van de Hulst, Light Scattering By Small Particles (John Wiley & Sons, New York, N. Y., 1956), p. 114.

M. L. Wallach and W. Heller, J. Phys. Chem. 68, 924 (1964).

R. A. Dobbins, AIAA J. 1, 1940 (1963).

Ref. 4, p. 176.

R. A. Mugele and H. D. Evans, Ind. Eng. Chem. 43, 1317 (1951).

J. H. Roberts and M. J. Webb AIAA J. 2, 3583 (1964).

Ref. 4, p. 177.

R. B. Penndorf, J. Opt. Soc. Am. 47, 1010 (1957).

See Ref. 4, p. 70.

Our attention has been directed by a reviewer to the extensive tabulation of scattering coefficients due to Kerker et al.14 deposited with the American Documentation Institute. We have checked our calculations with the results of a calculation using the tabulation of Kerker et al. and find that we obtain for ρ32 = 6.0, m = 1.76, = 3.104. From Table II for the same ρ32 and m = 1.75 we find = 3.233.

M. Kerker et al., J. Phys. Chem. 65, 1713 (1961).

E. J. Meehan and Z. Z. Hugus, J. Opt. Soc. Am. 51, 260 (1961).

R. B. Penndorf, J. Phys. Chem. 62, 1537 (1958).

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