Abstract

Light-scattering functions and particle-scattering factors from Rayleigh–Gans theory have been computed for ellipsoids of revolution having the axial ratios: 0, 14,1/22,12,1/2, 1, 2, 2, 22, 4, ∞.

© 1969 Optical Society of America

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References

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  1. An instructive discussion of particle-scattering factors and a useful collection of formulae for their calculation is given by E. P. Geiduschek and A. Holtzer, in Advances in Biological and Medical Physics, Vol. VI, C. A. Tobias and J. H. Lawrence, Eds. (Academic Press Inc., New York, 1958).
  2. N. Saito and Y. Ikeda, J. Phys. Soc. Japan 6, 305 (1957).
  3. L. C. Roess and C. G. Shull, J. Appl. Phys. 18, 308 (1947).
    [Crossref]
  4. A. L. Koch, Biochem. Biophys. Acta 51, 429 (1961).
    [Crossref]
  5. A. L. Koch, J. Theoret. Biol. 18, 133 (1968).
    [Crossref]
  6. P. Doty and J. T. Edsall, in Advances in Protein Chemistry, Vol. VI, M. L. Anson, J. T. Edsall, and K. Bailey, Eds. (Academic Press Inc., New York, 1951), p. 76.
  7. W. H. Beattie and H. C. Jung, J. Colloid Interface Sci. 27, 581 (1968).
    [Crossref]
  8. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 87.
  9. P. Doty and R. F. Steiner, J. Chem. Phys. 18, 1211 (1950).
    [Crossref]
  10. W. H. Beattie and C. Booth, J. Phys. Chem.64, 696 (1960); and computations (private communication).
    [Crossref]
  11. P. Becher, J. Phys. Chem. 63, 1213 (1959).
    [Crossref]

1968 (2)

A. L. Koch, J. Theoret. Biol. 18, 133 (1968).
[Crossref]

W. H. Beattie and H. C. Jung, J. Colloid Interface Sci. 27, 581 (1968).
[Crossref]

1961 (1)

A. L. Koch, Biochem. Biophys. Acta 51, 429 (1961).
[Crossref]

1959 (1)

P. Becher, J. Phys. Chem. 63, 1213 (1959).
[Crossref]

1957 (1)

N. Saito and Y. Ikeda, J. Phys. Soc. Japan 6, 305 (1957).

1950 (1)

P. Doty and R. F. Steiner, J. Chem. Phys. 18, 1211 (1950).
[Crossref]

1947 (1)

L. C. Roess and C. G. Shull, J. Appl. Phys. 18, 308 (1947).
[Crossref]

Beattie, W. H.

W. H. Beattie and H. C. Jung, J. Colloid Interface Sci. 27, 581 (1968).
[Crossref]

W. H. Beattie and C. Booth, J. Phys. Chem.64, 696 (1960); and computations (private communication).
[Crossref]

Becher, P.

P. Becher, J. Phys. Chem. 63, 1213 (1959).
[Crossref]

Booth, C.

W. H. Beattie and C. Booth, J. Phys. Chem.64, 696 (1960); and computations (private communication).
[Crossref]

Doty, P.

P. Doty and R. F. Steiner, J. Chem. Phys. 18, 1211 (1950).
[Crossref]

P. Doty and J. T. Edsall, in Advances in Protein Chemistry, Vol. VI, M. L. Anson, J. T. Edsall, and K. Bailey, Eds. (Academic Press Inc., New York, 1951), p. 76.

Edsall, J. T.

P. Doty and J. T. Edsall, in Advances in Protein Chemistry, Vol. VI, M. L. Anson, J. T. Edsall, and K. Bailey, Eds. (Academic Press Inc., New York, 1951), p. 76.

Geiduschek, E. P.

An instructive discussion of particle-scattering factors and a useful collection of formulae for their calculation is given by E. P. Geiduschek and A. Holtzer, in Advances in Biological and Medical Physics, Vol. VI, C. A. Tobias and J. H. Lawrence, Eds. (Academic Press Inc., New York, 1958).

Holtzer, A.

An instructive discussion of particle-scattering factors and a useful collection of formulae for their calculation is given by E. P. Geiduschek and A. Holtzer, in Advances in Biological and Medical Physics, Vol. VI, C. A. Tobias and J. H. Lawrence, Eds. (Academic Press Inc., New York, 1958).

Ikeda, Y.

N. Saito and Y. Ikeda, J. Phys. Soc. Japan 6, 305 (1957).

Jung, H. C.

W. H. Beattie and H. C. Jung, J. Colloid Interface Sci. 27, 581 (1968).
[Crossref]

Koch, A. L.

A. L. Koch, J. Theoret. Biol. 18, 133 (1968).
[Crossref]

A. L. Koch, Biochem. Biophys. Acta 51, 429 (1961).
[Crossref]

Roess, L. C.

L. C. Roess and C. G. Shull, J. Appl. Phys. 18, 308 (1947).
[Crossref]

Saito, N.

N. Saito and Y. Ikeda, J. Phys. Soc. Japan 6, 305 (1957).

Shull, C. G.

L. C. Roess and C. G. Shull, J. Appl. Phys. 18, 308 (1947).
[Crossref]

Steiner, R. F.

P. Doty and R. F. Steiner, J. Chem. Phys. 18, 1211 (1950).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 87.

Biochem. Biophys. Acta (1)

A. L. Koch, Biochem. Biophys. Acta 51, 429 (1961).
[Crossref]

J. Appl. Phys. (1)

L. C. Roess and C. G. Shull, J. Appl. Phys. 18, 308 (1947).
[Crossref]

J. Chem. Phys. (1)

P. Doty and R. F. Steiner, J. Chem. Phys. 18, 1211 (1950).
[Crossref]

J. Colloid Interface Sci. (1)

W. H. Beattie and H. C. Jung, J. Colloid Interface Sci. 27, 581 (1968).
[Crossref]

J. Phys. Chem. (1)

P. Becher, J. Phys. Chem. 63, 1213 (1959).
[Crossref]

J. Phys. Soc. Japan (1)

N. Saito and Y. Ikeda, J. Phys. Soc. Japan 6, 305 (1957).

J. Theoret. Biol. (1)

A. L. Koch, J. Theoret. Biol. 18, 133 (1968).
[Crossref]

Other (4)

P. Doty and J. T. Edsall, in Advances in Protein Chemistry, Vol. VI, M. L. Anson, J. T. Edsall, and K. Bailey, Eds. (Academic Press Inc., New York, 1951), p. 76.

An instructive discussion of particle-scattering factors and a useful collection of formulae for their calculation is given by E. P. Geiduschek and A. Holtzer, in Advances in Biological and Medical Physics, Vol. VI, C. A. Tobias and J. H. Lawrence, Eds. (Academic Press Inc., New York, 1958).

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 87.

W. H. Beattie and C. Booth, J. Phys. Chem.64, 696 (1960); and computations (private communication).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Variation of particle-scattering factor, P(θ), with parameter y for prolate ellipsoids of revolution having semi-axes a, a, and b. Parameter is b/a, and y = (2πb/λ′) sin(θ/2). Ellipsoids are rodlike for b/a→∞ and spherical for b/a = 1.

Fig. 2
Fig. 2

Variation of particle-scattering factor, P(θ), with parameter x for oblate ellipsoids of revolution having semi-axes a, a, and b. Parameter is b/a, and x = (2πa/λ′) sin(θ/2). Particles are disk-like for b/a → 0.

Fig. 3
Fig. 3

Variation of P(θ) with parameter y for infinitely long rods — – — – — and rod-like ellipsoids of revolution —— and with x for infinitesimally thin disks — — — — and disk-like ellipsoids of revolution – – – –.

Fig. 4
Fig. 4

Variation of P(θ) with geometric-mean size parameter, ( x 2 y ) 1 3 for prolate ellipsoids of revolution. Parameter is ratio of semi-axes, b/a.

Fig. 5
Fig. 5

Variation of P(θ) with geometric-mean size parameter, ( x 2 y ) 1 3 for oblate ellipsoids of revolution. Parameter is ratio of semi-axes, b/a.

Fig. 6
Fig. 6

Variation of scattering function, U(x,y), with geometric-mean size parameter, ( x 2 y ) 1 3 for prolate ellipsoids of revolution. Parameter is ratio of semi-axes, b/a.

Fig. 7
Fig. 7

Variation of scattering function, U(x,y), with geometric-mean size parameter, ( x 2 y ) 1 3 for oblate ellipsoids of revolution. Parameter is ratio of semi-axes, b/a.

Tables (1)

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Table I Particle-shape parameters.

Equations (6)

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R θ = n k 4 V 2 ( m - 1 2 π ) 2 1 + cos 2 θ 2 P ( θ ) ,
R θ / c = k ( m - 1 ) 2 x 2 y P ( θ ) ( 1 + cos 2 θ ) / 6 π ρ s 3 .
U ( x , y ) = x 2 y P ( θ ) / 4.
R θ / c = 2 k ( m - 1 ) 2 U ( x , y ) ( 1 + cos 2 θ ) / 3 π ρ s 3 .
P ( θ ) = n = 0 ( - 1 ) n 3 ( 4 ! ) ( 2 n + 2 ) ( 2 n + 5 ) ( 2 n + 6 ) ! ( 2 x ) 2 n × r = 0 n n ! r ! ( n - r ) ! p r ( 2 r + 1 ) = 1 - x 2 5 ( 1 + p 3 ) + 3 x 4 175 ( 1 + 2 p 3 + p 2 5 ) - 4 x 6 4725 ( 1 + 3 p 3 + 3 p 2 5 + p 3 7 ) + ,
P ( θ ) = 9 10 y 6 - 3 2 y 4 + 3 5 cos 2 y y 2 ( 1 - 1 2 y 2 + 3 2 y 4 ) + 3 5 sin 2 y y 3 ( 1 2 + 3 y 2 ) + 6 5 y 0 2 y sin Z Z d Z .