Abstract

Information theory and the Rayleigh-Gans-Debye and anomalous diffraction approximations are used to obtain criteria for choosing an aggregate model. They suggest a simple one with appropriate gross features. The hollow sphere of equal mass and total volume is chosen, actually a slightly heterogeneous population of hollow spheres. The average sphere volume is that of the aggregate; the volume and refractive index of the coat are those of the particles; the volume and refractive index of the sphere core are those of the spaces between the particles. The effects of aggregation on transmitted and scattered light were measured with two transmittance photometers and a 90° scattering photometer. Observed effects of aggregation are qualitatively accounted for with this method of predicting aggregate scattering. The method is also used to survey predicted effects of aggregation of blood platelets on suspension transmittance.

© 1982 Optical Society of America

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References

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  1. G. V. R. Born, Nature London 194, 927 (1962).
    [CrossRef]
  2. F. Michal, G. V. R. Born, Nature London New Biol. 231, 220 (1971).
  3. R. A. Haworth, D. R. Hunter, Arch. Biochem. Biophys. 195, 460 (1979).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. P. Latimer, J. Coll. Interface Sci. 53, 102 (1975).
    [CrossRef]
  9. P. Latimer, Ann. Rev. Biophys. Bioeng. 11, 129 (1982).
    [CrossRef]
  10. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
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    [CrossRef]
  13. A. Brunsting, “Light Scattering by Mammalian Cells,” Dissertation, U. New Mexico, Albuquerque (1972).
  14. P. Latimer, P. Barber, J. Coll. Interface Sci. 63, 310 (1978).
    [CrossRef]
  15. P. Latimer, Appl. Opt. 19, 3039 (1980).
    [CrossRef] [PubMed]
  16. R. A. Meyer, A. Brunsting, Biophys. J. 15, 191 (1975).
    [CrossRef] [PubMed]
  17. P. Latimer, Appl. Opt. 17, 2162 (1978).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. G. V. R. Born, M. Hume, Nature London 215, 1027 (1967).
    [CrossRef] [PubMed]
  26. F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 139, 97 (1969).
    [CrossRef]
  27. M. B. Zucker, Sci. Am.86 (June1980).
    [CrossRef] [PubMed]
  28. N. J. Cusack, S. M. O. Hourani, Br. J. Pharmacol. 73, 405 (1981).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1982 (1)

P. Latimer, Ann. Rev. Biophys. Bioeng. 11, 129 (1982).
[CrossRef]

1981 (1)

N. J. Cusack, S. M. O. Hourani, Br. J. Pharmacol. 73, 405 (1981).
[CrossRef] [PubMed]

1980 (2)

1979 (2)

P. Latimer, Biophys. J. 27, 117 (1979).
[CrossRef] [PubMed]

R. A. Haworth, D. R. Hunter, Arch. Biochem. Biophys. 195, 460 (1979).
[CrossRef] [PubMed]

1978 (2)

P. Latimer, P. Barber, J. Coll. Interface Sci. 63, 310 (1978).
[CrossRef]

P. Latimer, Appl. Opt. 17, 2162 (1978).
[CrossRef] [PubMed]

1977 (1)

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophys. 180, 151 (1977).
[CrossRef] [PubMed]

1975 (3)

R. A. Meyer, A. Brunsting, Biophys. J. 15, 191 (1975).
[CrossRef] [PubMed]

P. Latimer, Appl. Opt. 14, 2324 (1975).
[CrossRef] [PubMed]

P. Latimer, J. Coll. Interface Sci. 53, 102 (1975).
[CrossRef]

1972 (3)

P. Latimer, J. Coll. Interface Sci. 39, 497 (1972).
[CrossRef]

P. Latimer, J. Opt. Soc. Am. 62, 497 (1972).
[CrossRef]

D. A. Cross, P. Latimer, Appl. Opt. 11, 1225 (1972).
[CrossRef] [PubMed]

1971 (1)

F. Michal, G. V. R. Born, Nature London New Biol. 231, 220 (1971).

1970 (2)

S. Cronberg, Coagulation 3, 139 (1970).

S. K. Friedlander, Aerosol Sci. 1, 295 (1970).
[CrossRef]

1969 (1)

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 139, 97 (1969).
[CrossRef]

1967 (1)

G. V. R. Born, M. Hume, Nature London 215, 1027 (1967).
[CrossRef] [PubMed]

1962 (1)

G. V. R. Born, Nature London 194, 927 (1962).
[CrossRef]

1952 (1)

G. Oster, D. P. Riley, Acta Crystallogr. 5, 272 (1952).
[CrossRef]

1951 (1)

A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
[CrossRef]

Ackerman, E.

E. Ackerman, Biophysical Science (Prentice-Hall, Englewood Cliffs, N.J., 1962).

Aden, A. L.

A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
[CrossRef]

Barber, P.

P. Latimer, P. Barber, J. Coll. Interface Sci. 63, 310 (1978).
[CrossRef]

Beniot, H.

C. Wippler, J. A. DeVries, H. Beniot, at IUPAC Symposium on Macromolecules, Wiesbaden, Germany (1959).

Born, G. V. R.

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophys. 180, 151 (1977).
[CrossRef] [PubMed]

F. Michal, G. V. R. Born, Nature London New Biol. 231, 220 (1971).

G. V. R. Born, M. Hume, Nature London 215, 1027 (1967).
[CrossRef] [PubMed]

G. V. R. Born, Nature London 194, 927 (1962).
[CrossRef]

Brunsting, A.

R. A. Meyer, A. Brunsting, Biophys. J. 15, 191 (1975).
[CrossRef] [PubMed]

A. Brunsting, “Light Scattering by Mammalian Cells,” Dissertation, U. New Mexico, Albuquerque (1972).

Bryant, F. D.

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 139, 97 (1969).
[CrossRef]

Cronberg, S.

S. Cronberg, Coagulation 3, 139 (1970).

Cross, D. A.

Cusack, N. J.

N. J. Cusack, S. M. O. Hourani, Br. J. Pharmacol. 73, 405 (1981).
[CrossRef] [PubMed]

DeVries, J. A.

C. Wippler, J. A. DeVries, H. Beniot, at IUPAC Symposium on Macromolecules, Wiesbaden, Germany (1959).

Friedlander, S. K.

S. K. Friedlander, Aerosol Sci. 1, 295 (1970).
[CrossRef]

Haworth, R. A.

R. A. Haworth, D. R. Hunter, Arch. Biochem. Biophys. 195, 460 (1979).
[CrossRef] [PubMed]

Hourani, S. M. O.

N. J. Cusack, S. M. O. Hourani, Br. J. Pharmacol. 73, 405 (1981).
[CrossRef] [PubMed]

Hume, M.

G. V. R. Born, M. Hume, Nature London 215, 1027 (1967).
[CrossRef] [PubMed]

Hunter, D. R.

R. A. Haworth, D. R. Hunter, Arch. Biochem. Biophys. 195, 460 (1979).
[CrossRef] [PubMed]

Kerker, M.

A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
[CrossRef]

Latimer, P.

P. Latimer, Ann. Rev. Biophys. Bioeng. 11, 129 (1982).
[CrossRef]

P. Latimer, Appl. Opt. 19, 3039 (1980).
[CrossRef] [PubMed]

P. Latimer, Biophys. J. 27, 117 (1979).
[CrossRef] [PubMed]

P. Latimer, Appl. Opt. 17, 2162 (1978).
[CrossRef] [PubMed]

P. Latimer, P. Barber, J. Coll. Interface Sci. 63, 310 (1978).
[CrossRef]

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophys. 180, 151 (1977).
[CrossRef] [PubMed]

P. Latimer, Appl. Opt. 14, 2324 (1975).
[CrossRef] [PubMed]

P. Latimer, J. Coll. Interface Sci. 53, 102 (1975).
[CrossRef]

P. Latimer, J. Coll. Interface Sci. 39, 497 (1972).
[CrossRef]

P. Latimer, J. Opt. Soc. Am. 62, 497 (1972).
[CrossRef]

D. A. Cross, P. Latimer, Appl. Opt. 11, 1225 (1972).
[CrossRef] [PubMed]

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 139, 97 (1969).
[CrossRef]

Meyer, R. A.

R. A. Meyer, A. Brunsting, Biophys. J. 15, 191 (1975).
[CrossRef] [PubMed]

Michal, F.

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophys. 180, 151 (1977).
[CrossRef] [PubMed]

F. Michal, G. V. R. Born, Nature London New Biol. 231, 220 (1971).

Moore, D.

D. Moore, M.S. Thesis, Auburn U., Auburn, Ala. (1968).

Oster, G.

G. Oster, D. P. Riley, Acta Crystallogr. 5, 272 (1952).
[CrossRef]

Pollard, E. C.

R. B. Setlow, E. C. Pollard, Molecular Biophysics (Addison-Wesley, Reading, Mass., 1979), p. 69.

Riley, D. P.

G. Oster, D. P. Riley, Acta Crystallogr. 5, 272 (1952).
[CrossRef]

Seiber, B. A.

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 139, 97 (1969).
[CrossRef]

Setlow, R. B.

R. B. Setlow, E. C. Pollard, Molecular Biophysics (Addison-Wesley, Reading, Mass., 1979), p. 69.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wippler, C.

C. Wippler, J. A. DeVries, H. Beniot, at IUPAC Symposium on Macromolecules, Wiesbaden, Germany (1959).

Zucker, M. B.

M. B. Zucker, Sci. Am.86 (June1980).
[CrossRef] [PubMed]

Acta Crystallogr. (1)

G. Oster, D. P. Riley, Acta Crystallogr. 5, 272 (1952).
[CrossRef]

Aerosol Sci. (1)

S. K. Friedlander, Aerosol Sci. 1, 295 (1970).
[CrossRef]

Ann. Rev. Biophys. Bioeng. (1)

P. Latimer, Ann. Rev. Biophys. Bioeng. 11, 129 (1982).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. (1)

A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
[CrossRef]

Arch. Biochem. Biophys. (3)

R. A. Haworth, D. R. Hunter, Arch. Biochem. Biophys. 195, 460 (1979).
[CrossRef] [PubMed]

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 139, 97 (1969).
[CrossRef]

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophys. 180, 151 (1977).
[CrossRef] [PubMed]

Biophys. J. (2)

R. A. Meyer, A. Brunsting, Biophys. J. 15, 191 (1975).
[CrossRef] [PubMed]

P. Latimer, Biophys. J. 27, 117 (1979).
[CrossRef] [PubMed]

Br. J. Pharmacol. (1)

N. J. Cusack, S. M. O. Hourani, Br. J. Pharmacol. 73, 405 (1981).
[CrossRef] [PubMed]

Coagulation (1)

S. Cronberg, Coagulation 3, 139 (1970).

J. Coll. Interface Sci. (3)

P. Latimer, J. Coll. Interface Sci. 53, 102 (1975).
[CrossRef]

P. Latimer, J. Coll. Interface Sci. 39, 497 (1972).
[CrossRef]

P. Latimer, P. Barber, J. Coll. Interface Sci. 63, 310 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

P. Latimer, J. Opt. Soc. Am. 62, 497 (1972).
[CrossRef]

Nature London (2)

G. V. R. Born, Nature London 194, 927 (1962).
[CrossRef]

G. V. R. Born, M. Hume, Nature London 215, 1027 (1967).
[CrossRef] [PubMed]

Nature London New Biol. (1)

F. Michal, G. V. R. Born, Nature London New Biol. 231, 220 (1971).

Sci. Am. (1)

M. B. Zucker, Sci. Am.86 (June1980).
[CrossRef] [PubMed]

Other (7)

C. Wippler, J. A. DeVries, H. Beniot, at IUPAC Symposium on Macromolecules, Wiesbaden, Germany (1959).

H. Quastler, Ed., Information Theory in Biology (U. Illinois Press, Urbana, 1953).

E. Ackerman, Biophysical Science (Prentice-Hall, Englewood Cliffs, N.J., 1962).

R. B. Setlow, E. C. Pollard, Molecular Biophysics (Addison-Wesley, Reading, Mass., 1979), p. 69.

A. Brunsting, “Light Scattering by Mammalian Cells,” Dissertation, U. New Mexico, Albuquerque (1972).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

D. Moore, M.S. Thesis, Auburn U., Auburn, Ala. (1968).

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Figures (12)

Fig. 1
Fig. 1

Photometer optical system: a well-collimated light beam enters the scattering suspension. The axial transmittance photocell receives the undeviated light plus that scattered at angles up to γ.

Fig. 2
Fig. 2

Extinctions of suspensions of homogeneous and hollow spheres as functions of particle volume when 0.1% concentration by volume and L = 1 cm and λ = 413 nm. Curves are shown for the indicated values of γ: solid, E(0); dashed E(5°). The relative refractive index of the homogeneous spheres and that of the coats of the hollow spheres is m = 1.05; that of the hollow sphere cores is 1.0. The volume of the coat is half of the sphere volume. For plotting, the volume of a hollow sphere is taken as the volume of its coat only.

Fig. 3
Fig. 3

Extinctions of suspensions of randomly oriented homogeneous spheroids: prolate (υ = 3) and oblate (υ = 0.33) as functions of particle volume for three γ values (L = 1.0 cm): solid, E(0); long dashes, E(2°); and short dashes, E(5°). Suspension concentration is 0.1% by volume, m = 1.05, and λ = 413 nm.

Fig. 4
Fig. 4

Extinctions of 0.1% suspensions of homogeneous and hollow spheres of m = 1.19 as functions of the volume of a single particle thereof (see Fig. 2).

Fig. 5
Fig. 5

Extinctions of 0.1% suspensions of randomly oriented homogeneous spheroids m = 1.19, prolate (υ = 3.0), and oblate (υ = 0.33) as functions of the volume of a single particle thereof (see Fig. 3).

Fig. 6
Fig. 6

Angular dependence of scattering by a 50-μm3 sphere (4.58-μm diam) of refractive index 1.05, λ = 413 nm. The polar plot (right) is of log (intensity) + constant. The parameters are those of the particles in Fig. 2 near the maximum E(0).

Fig. 7
Fig. 7

E(5°)/E(0) as a function of particle size for the spheres and spheroids of Figs. 2 and 3, m = 1.05.

Fig. 8
Fig. 8

E(5°)/E(0) as a function of particle size for the spheres and spheroids of Figs. 4 and 5, m = 1.19.

Fig. 9
Fig. 9

Experimental extinctions of suspensions of polystyrene latex spheres in water as functions of salt concentration (molarity): (left) sphere diameter, 0.264 μm; (right) diameter, 1.099 μm; λ = 413 nm in water.

Fig. 10
Fig. 10

Predicted extinctions of water suspensions of aggregates of latex spheres (m = 1.19) as functions of number of spheres per aggregate; (left) spheres of 0.264-μm diam in water and (right) spheres of 1.099-μm diam.

Fig. 11
Fig. 11

Angular dependence of the net scattering by 100 single latex spheres and by an aggregate of these 100 spheres (F = 0.5)—theoretical predictions. Single sphere diameter is 1.099 μm, n = 1.19, and n = 413 nm: (left) conventional semilog plot; (right) polar semilog plot with the beam and photocell acceptance angle indicated.

Fig. 12
Fig. 12

Predicted extinction E(γ) of suspensions of blood platelets (prp) as functions of aggregate size, which was assumed to be uniform. The extinction cross sections R(γ) for the single platelets for γ = 0, 2, 5, and 30° are, respectively, 2.85, 2.66, 1.84, and 0.024 μm2 for λ = 444 nm.

Equations (3)

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E ( γ ) = 0.434 NLR ( γ ) ,
S ( θ ) = k 2 / 2 π [ 1 exp ( i ϕ ) exp ( ik ξ θ ) ] d ξ d η ,
F = F 0 + ( 1 F 0 ) / J 1 / 2 ,

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